A countermovement jump with an arm swing is defined by four functional degrees of freedom and an enhanced proximal-to-distal delay.

A countermovement jump with an arm swing is defined by four functional degrees of freedom and an enhanced proximal-to-distal delay. | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article A countermovement jump with an arm swing is defined by four functional degrees of freedom and an enhanced proximal-to-distal delay. Christina M. Cefai, Joseph W. Shaw, Emily J. Cushion, Daniel J. Cleather This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4142464/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 02 Sep, 2024 Read the published version in Scientific Reports → Version 1 posted 11 You are reading this latest preprint version Abstract An abundance of degrees of freedom (DOF) exist when executing a countermovement jump (CMJ). This research aims to simplify the understanding of this complex system by comparing jump performance and independent functional DOF (fDOF) present in CMJs without (CMJ NoArms ) and with (CMJ Arms ) an arm swing. Principal component analysis was used on 39 muscle forces and 15 3-dimensional joint contact forces obtained from kinematic and kinetic data, analyzed in FreeBody (a segment-based musculoskeletal model). Jump performance was greater in CMJ Arms with the increased ground contact time resulting in higher external ( p = .012), hip ( p < .001) and ankle ( p = .009) vertical impulses, and slower hip extension enhancing the proximal-to-distal joint extension strategy. This allowed the hip muscles to generate higher forces and greater time-normalized hip vertical impulse ( p = .006). Three fDOF were found for the muscle forces and 3-dimensional joint contact forces during CMJ NoArms , while four fDOF were present for CMJ Arms . This suggests that the underlying anatomy provides mechanical constraints during a CMJ, reducing the demand on the control system. The additional fDOF present in CMJ Arms suggests that the arms are not mechanically coupled with the lower extremity, resulting in additional variation within individual motor strategies. Health sciences/Anatomy/Musculoskeletal system Physical sciences/Engineering/Biomedical engineering principal component analysis motor control strategy mechanical coupling degrees of freedom proximal-to-distal arm swing Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction In human movement, the movement of multiple segments, each with six degrees of freedom (DOF), is coordinated through motor control strategies [ 1 ] . The movement (or resistance to movement) of these segments is created by the muscles acting upon each segment, where many more muscle activation strategies exist than segmental kinematic DOFs. This results in many possible strategies to achieve the same outcome, and therefore an abundance of possible motor control strategies, allowing an individual to adapt to additional or unexpected tasks and demands [ 2 ] . This creates an indeterminant problem with more DOFs present than constraints [ 1 ] . Researchers have shown that the number of DOFs utilized by individuals can be reduced, for example, through conscious freezing of DOF during motor skill learning [ 3 , 4 , 5 , 6 ] . Neuromechanical synergies [ 7 ] , mechanical coupling, [ 8 , 9 ] and the anatomy of the musculoskeletal system itself [ 10 ] effectively create additional constraints on the system which can reduce the number of independent DOF and the demand on the central control system [ 8 ] . One of the methods used to simplify the understanding of this complex motor control system is by identifying what have been termed “functional degrees of freedom” (fDOF), representing the main characteristics of the movement system [ 1 ] . These are found through the dimensional reduction technique of principal component analysis (PCA), transforming the original data into a new orthogonal coordinate system, and reducing the correlation that may be present between DOF [ 11 ] . Therefore, the fDOF are defined by the minimum number of independent principal components (PCs) required to define a high percentage of variance in the original data [ 1 ] . During the countermovement vertical jump (CMJ), a common movement pattern observed is the proximal-to-distal strategy, where proximal segments begin to rotate before their distal segment [ 12 ] . This improves the mechanical efficiency of the movement and increases jump height, compared to the simultaneous acceleration of all segments [ 13 ] . Adding an arm swing to a CMJ improves jump performance through a combination of factors. Firstly, the ground reaction force (GRF) profile is altered [ 14 ] and the time of the countermovement is prolonged, increasing the net impulse and, therefore, take-off velocity [ 15 , 16 , 17 , 18 ] . Secondly, a delay in the proximal-to-distal strategy is observed to allow the arms to accelerate upwards before extending the lower limbs [ 16 , 19 ] , resulting in increased net joint moments (NJM) at the hip and ankle [ 15 , 16 , 17 , 19 , 20 ] . Thirdly, the arm swing itself creates a ‘pull mechanism’ in which the shoulder flexor muscles increase the vertical work done and energy generated [ 14 , 17 , 21 ] and increases the height of the center of mass at take-off [ 15 , 17 ] . While research has looked into the effects of an arm swing on jump performance, its effect on independent DOF present in muscular activation and 3-dimensional (3D) joint contact forces (JCF) is currently unknown. It is hypothesized that adding an arm swing will increase the variation observed in muscle forces and 3D JCFs at an individual participant and group level, increasing the number of fDOF present for the CMJ. Therefore, the purpose of this study is two-fold. Firstly, external and lower-limb joint impulses will be compared in a CMJ with (CMJ Arms ) and without an arm swing (CMJ NoArms ) to assess the impact of arm swing on jump performance for the participants within this study. The second aim is to compare the fDOF exhibited in CMJ NoArms and CMJ Arms for the 3D JCF and muscle forces. Methods Study Design and Participants A cross-sectional study design was utilized to investigate the effect of an arm swing on a CMJ. The data used in this study were collected previously by Cushion et al. [ 12 ] . Twenty-one healthy participants (10 women: height = 167.4 ± 6.9 cm, weight = 62.9 ± 7.3 kg; 11 men: height = 178.0 ± 7.6 cm, weight = 82.4 ± 7.2 kg) who were free from musculoskeletal injuries, gave informed consent after understanding the details of the study. Ethical approval was provided by the ethics sub-committee of St Mary’s University, Twickenham. Procedure Participants attended a single data collection session during which 18 reflective markers were placed on the participants’ pelvis and right lower limb, according to Cleather and Bull [ 22 ] . A standardized warmup ending with vertical jumps was performed by all participants. A Vicon 14-camera motion capture system (Vicon MX System, Nexux2.2 software, Vicon Motion System Ltd, Oxford, UK) was used to record kinematic data at 200Hz, synchronously with kinetic data recorded at 1000Hz using two force plates (Kistler Type 9287BA, BioWare 3.24 software, Kistler Instruments Ltd, Hampshire, UK). Following the warmup, all participants were asked to perform five separate maximum effort CMJs with their hands placed on their hips for the entire trial (CMJ NoArms ) and another five separate maximum effort CMJs with the use of an arm swing (CMJ Arms ). For all jumps, participants were instructed to take-off and land with one foot on each force-plate. A self-selected duration of break was taken between individual jumps, and a two-minute break was given between the different jumps to mitigate fatigue. The order of jumps was counterbalanced to avoid any order effect. Full data collection details can be found in Cushion et al. (2019) [ 12 ] . Data Analysis The kinematic and kinetic data were preprocessed using a 5th order Woltring filter with a cutoff frequency of 10Hz [ 12 ] . The start of the movement was defined as the frame when the right anterior superior iliac spine marker began to descend below stationary height and ended when the GRFs were 0 N on take-off [ 12 ] . FreeBody [ 22 ] —an open-source segment-based musculoskeletal model of the lower limb—was used to create the participants’ scaled musculoskeletal models composed of five rigid segments with six kinematic DOF each (the foot, shank, thigh, pelvis, and patella), 163 muscle elements defining 39 muscles, and 14 ligament elements. The muscle, ligament, and 3D JCFs at the ankle, medial and lateral tibiofemoral joints, patellofemoral joint, and the hip were calculated at each time frame based on an optimization approach to inverse dynamics [ 23 ] using FreeBody [ 22 ] . This was done using MATLAB’s constrained nonlinear programming solver (‘fmincon’), specifically the sequential quadratic programming (‘sqp’) algorithm (The MathWorks, Inc., MA, version R2023b) to solve the 193 unknowns with only 22 equations of motion. Where the optimization failed to solve within the muscle and ligament force constraints set according to the participant’s body mass, the upper bound limits were increased incrementally until the maximum force limit of the muscles and ligaments was increased by five times, where the smaller stabilizing muscles around the foot and ankle were the main limiting factor for a few frames. When a solution was still not found, the solver’s constraint tolerance was relaxed from 1 × 10 − 6 to 1 × 10 − 3 . Trials were included in the data analysis only if a solution was found for the trial. This resulted in 18 participants being kept in the analysis (8 women: height = 168.1 ± 6.9 cm, weight = 62.8 ± 6.9 kg; 10 men: height = 178.0 ± 8.0 cm, weight = 82.4 ± 7.5 kg), where a solution was found for both CMJ NoArms and CMJ Arms . The force vectors of the 163 muscle elements were summed to define the 39 muscles and normalized to the participant’s bodyweight. The vertical external and joint impulses were calculated from the area underneath the vertical GRF and JCF-time curves respectively. The impulses were averaged across trials for each participant (participant-level impulse) before averaging across participants (group-level impulse). The modified Akima piecewise cubic Hermite interpolation (‘makima’), that is MATLAB’s specific modification of Akima’s interpolation method which reduces excessive local undulations [ 24 , 25 ] , was then used to time normalize all trials to 501 points in MATLAB (The MathWorks, Inc., MA, version R2023b) before recalculating the impulses from their respective force-time normalized curves, resulting in time-normalized external and joint vertical impulses. Statistical Analysis A Wilcoxon matched-pairs test (α = 0.05) and a two-way repeated measure ANOVA (two-way interaction and main effect α = 0.05) were used to compare the participants’ external vertical impulses (not normally distributed data) and five vertical joint impulses respectively for CMJ NoArms and CMJ Arms . Using the Bonferroni adjustments for the 95% confidence interval and significance level (α = 0.01), a simple effects analysis was also performed to compare each joint individually between jumps. These statistical tests were repeated for the time-normalized impulses, however a repeated measures t-test was used for the time-normalized external vertical impulses (normally distributed data). All data were assessed for outliers beyond 1.5 times the interquartile range of the upper of lower extremity, as visualized on a box plot. It was also assessed by Shapiro-Wilk’s test of normality (α = 0.05), and by Mauchly’s test of sphericity (α = 0.05) for the five joints. The statistical analyses were conducted in IBM SPSS Statistics (The International Business Machines Corporation, NY, version 29.0.1.1). The participant-level composite muscle and 3D JCF curves were calculated by averaging across each trial’s output vectors at every time point for both jumps. Group-level composite curves were also calculated by averaging the participant-level curves for each muscle. Principal component analyses were performed in MATLAB (The MathWorks, Inc., MA, version R2023b) on the participant-level muscle force and 3D JCF composite curves for CMJ NoArms and CMJ Arms at a participant and group level (Table 1 ). After assessing for the three assumptions (outliers, normality and sphericity) as defined previously, a three-way repeated measure ANOVA (three and two-way interactions and main effects, α = 0.05) was performed in IBM SPSS Statistics to compare the cumulative explained variation of the muscle and 3D JCFs by PCs 1 to 3 at participant level, with and without the use of an arm swing. Simple effects were considered statistically significant at α = 0.017 (Bonferroni adjustment for 3 PC levels). The fDOF were defined as number of PCs required to explain 95% variation of the muscle forces and 3D JCFs for CMJ NoArms and CMJ Arms per participant [ 1 ] . Table 1 The number of PCAs performed for muscle forces and JCFs at participant and group level. Their input time series data and matrix dimensions are also defined. The analyses were performed for both jumps (CMJ NoArms and CMJ Arms ). Variable Time series data used Analysis level Input matrix dimensions Number of separate analyses Muscle forces Participant composite muscle forces (39 muscles per participant) Participant Level 501 data points x 39 force vectors 36 PCAs (2 jumps x 18 participants) Group Level 501 data points x 702 force vectors (39 muscles x 18 participants) 2 PCAs (2 jumps) Joint contact forces Participant composite 3-dimensional JCFs (5 joints x 3 dimensions per participant) Participant Level 501 data points x 15 force vectors 36 PCAs (2 jumps x 18 participants) Group Level 501 data points x 270 force vectors (15 JCF x 18 participants) 2 PCAs (2 jumps) The 39 group-level muscle composite curves were categorized into seven muscle groups according to peak force timing and force curve profile. After listing all muscles in order of peak timings, groups 1 and 2 were separated after visual inspection of their force-time curves as group 2 had slightly later force peaks with a different profile in CMJ Arms . Groups 2 and 3 exhibited a large gap between muscle peak force timings in CMJ Arms , creating a clear distinction between groups, while muscles in group 4 had a qualitatively slower rate of force production to muscles in group 3 upon visual inspection of their force-time curves. Groups 5 to 7 were categorized based on their force profiles as they all exhibited a peak at or close to 100% of the countermovement time. Group 5 showed earlier activation than group 6 while group 7 muscles exhibited a unique curve profile with both a ‘bell-shape’ force curve and a peak at the end of the countermovement. A linear combination of PC1 to PC5 was defined for each muscle group based on the coefficients resulting from the group-level PCAs. The muscles’ average coefficients for PC1 to PC5 were calculated from the 18 instances of the muscle within the coefficient matrix. The sum of the average coefficients for all muscles included in each group were calculated for PC1 to PC5 to define the muscle group’s PC combination. The group’s PC combination was simplified after normalizing to the highest coefficient by only retaining PC1 and PC2 with a normalized coefficient larger than 0.2 and PC3, PC4 and PC5 with a normalized coefficient larger than 0.35. When PC5 was the main contributor to the PC combination, the cutoff coefficients for PC1 to PC4 was 0.1. Different cut-off coefficients were defined due to lower PC score magnitudes found in PC3, PC4 and PC5, thus having little impact on the PC combination at lower normalized coefficients. The muscle group PC combinations (without normalized coefficients) were plotted against real time by multiplying the normalized time with the average lengths of the CMJ NoArms and CMJ Arms jumps. The “principal impulse” was calculated from the area under these curves by taking the minimum PC score as the base, rather than 0. The total muscle impulse for each group was calculated through the summation of the group-level average muscle impulses. A Pearson’s correlation was run in IBM SPSS Statistics to determine the relationship between “principal impulse” and muscle impulse, irrespective of jump (CMJ Arms and CMJ NoArms ). Results Jump Performance Significant differences in external impulse were found between CMJ NoArms and CMJ Arms ( p = .012; medians: CMJ NoArms = 0.515 BW∙s, CMJ Arms = 0.571 BW∙s) and joint impulse ( p = .009; mean difference of 0.178 BW∙s, 95% CI, 0.051 to 0.305 BW∙s) (Fig. 1 a). However, only the ankle ( p = .009, mean difference = 0.307 BW∙s) and hip joints ( p < .001, mean difference = 0.315 BW∙s) had significantly different impulses in CMJ Arms compared to CMJ NoArms (Fig. 1 a). When normalising for time, the external vertical impulse was similar for both the CMJ NoArms (0.669 BW∙s∙s − 1 ) and CMJ Arms (0.667 BW∙s∙s − 1 ), and the main effect of an arm swing on joint impulse ( p = .158) and ankle joint impulse ( p = .324) was no longer statistically significant (Fig. 1 b). Only the time-normalised vertical hip joint impulse remained significantly different with the use of arm swing ( p = .006, mean difference = 0.185 BW∙s∙s − 1 ). Participant-Level PCA Participants exhibited between one and three fDOFs during the CMJ NoArms and CMJ Arms (Table 2 ). The cumulative explained variation of the muscle forces and 3D JCFs by PC1 to PC3 was significantly greater in CMJ NoArms compared to CMJ Arms ( p = .034, mean difference = 0.975%) (Table 2 ). This resulted in a higher number of fDOF present during the CMJ Arms compared to CMJ NoArms . There was also a weak trend in which participants who exhibited 2 fDOF had a higher external vertical impulse than those with only 1 fDOF, and a similar or higher impulse than those requiring 3 fDOF (Table 2 ). Table 2 a) Number of PCs required to explain 95% of the 39 composite muscle forces (original DOF in input matrix: 501 data points x 39 participant composite muscles) and 15 joint contact forces (original DOF in input matrix: 501 data points x 15 forces (5 joins x 3 dimensions)) per participant (n = 18) and the average external vertical impulse (mean ± standard deviation) grouped by number of PCs required for CMJ NoArms and CMJ Arms . b) Mean ± standard deviation of the cumulative explained percentage of the muscle forces and joint contact forces by PC1, PC2 and PC3 for CMJ NoArms and CMJ Arms . Muscle Forces Joint Contact Forces a) Original DOF Mean fDOF No. of fDOF Freq. Mean External Vertical Impulse (BW∙s) Original DOF Mean fDOF No. of fDOF Freq. Mean External Vertical Impulse (BW∙s) CMJ NoArms 39 1.78 1 4 0.52 ± 0.04 15 2 1 2 0.55 ± 0.03 2 14 0.61 ± 0.17 2 14 0.61 ± 0.18 3 0 n/a 3 2 0.52 ± 0.08 CMJ Arms 39 2 1 1 0.51 15 2.28 1 0 n/a 2 16 0.51 ± 0.07 2 13 0.53 ± 0.06 3 1 0.81 3 5 0.53 ± 0.16 b) PC1 (%) PC2 (%) PC3 (%) PC1 (%) PC2 (%) PC3 (%) CMJ NoArms a 83.4 ± 7.9 98.1 ± 0.9 99.1 ± 0.5 89.8 ± 4.5 97.0 ± 1.5 98.8 ± 0.6 CMJ Arms a 85.5 ± 8.3 97.2 ± 1.3 98.9 ± 0.5 87.6 ± 4.9 96.0 ± 2.0 98.2 ± 0.9 Significance 0.606 0.007 b 0.014 b 0.007 b 0.015 b 0.002 b a There was a significant main effect for the use of an arm swing in the percentage of cumulative explained variation, mean difference = 0.975%, p = .034. b There was a significant difference ( p < .017 - Bonferroni adjustment for 3 PC levels) for the cumulative explained variation between CMJ NoArms and CMJ Arms . Group-Level PCA Figure 2 shows the first five normalised PC curves describing the group’s muscle and 3D JCFs for the CMJ NoArms and CMJ Arms . An increase in frequency can be seen from PC1 to PC5, with the maxima and minima, particularly in PC3, being delayed for CMJ Arms (peak 1 = 50%, peak 2 = 75.2%, peak 3 = 91.6%) compared to CMJ NoArms (peak 1 = 48.8%, peak 2 = 71.7%, peak 3 = 89.8%). A higher percentage of cumulative variation is explained for both variables for the CMJ NoArms (e.g. PC1–3: muscles = 97.3%; 3D JCFs: 96.6%) than with the same number of PCs for the CMJ Arms (e.g. PC1–3: muscles = 95.1%; 3D JCFs: 93.3%). The 270 DOF present for the group’s 3D JCF were described by 3 fDOF for CMJ NoArms and 4 fDOF for CMJ Arms . Muscle groupings and their linear PC combination Figure 3 depicts all 39 group-composite muscle force curves for CMJ NoArms and CMJ Arms with their representative PC combination. Muscle groups 1 to 4 contain the prime movers, including the biceps femoris (group 1), gluteus maximus (group 2), vastus lateralis (group 3) and soleus (group 4), with sequential peak force timings. The original 702 DOFs can be described by three and four fDOF for the prime movers during the CMJ NoArms and CMJ Arms respectively. The subtraction of PC2 from PC1 moves the peak earlier in the countermovement (groups 1 and 2). The addition of PC3 in CMJ Arms group 1 resulted in a superimposed curve at 80–90% of the countermovement. While CMJ NoArms group 3 is solely defined by PC1, CMJ Arms required the subtraction of PC4 to increase the rate of force development till 44% of the countermovement, which was reduced by PC2, while both PCs delay the peak defined by PC1. In group 4, the peak was delayed by the subtraction or addition of PC3 for CMJ NoArms and CMJ Arms respectively due to their opposing profiles. While the stabilising muscles in groups 5 to 7 are well defined for the CMJ NoArms , only group 5’s PC combination vaguely followed the muscle profiles for CMJ Arms . Real time comparison of CMJ NoArms and CMJ Arms The real time differences between the CMJ Arms (0.904 s) and CMJ NoArms (0.803 s) curves can be seen in Fig. 4 . The delay between the peak force of group 1’s hip extensor and group 3’s knee extensor is prolonged in CMJ Arms (0.196 s) compared to CMJ NoArms (0.062 s). However, the peaks of muscle group 1 (CMJ NoArms = 0.530 s, CMJ Arms = 0.533 s) and group 2 (CMJ NoArms = 0.557 s, CMJ Arms = 0.595 s) occur at similar times for both jumps. The time delay between the peak of the knee extensors to plantar flexors (CMJ NoArms = 0.077 s, CMJ Arms = 0.058 s) and plantar flexors to take-off (CMJ NoArms = 0.133 s, CMJ Arms = 0.117 s) is also similar between jumps. The principal impulse is larger in all groups for CMJ Arms than CMJ NoArms (Fig. 4 ). There was a statistically significant, strong positive correlation between principal impulse and muscle impulse (r(8) = .994, p < .001). Discussion The purpose of this study was to understand the effect of an arm swing during a CMJ on performance and fDOF. The results confirmed the hypothesis of improved performance with the use of an arm swing during a CMJ through increased external and joint impulses, particularly at the hip and ankle joints, and an increased joint extension proximal-to-distal delay. This study showed that the key characteristics of the movement which had 270 kinetic DOFs and 702 muscle force DOFs at a group level, could be described by a reduced number of fDOF. The CMJ Arms exhibited four fDOF to define muscle forces and 3D JCFs at a group level, while the CMJ NoArms resulted in only three fDOF for both variables. This confirms the second hypothesis that more fDOF are utilized in CMJ Arms compared to CMJ NoArms . The prolonged countermovement due to the use of an arm swing resulted in increased vertical external impulse, in agreement with previous literature [ 15 , 16 , 17 , 18 ] , and increased hip and ankle joint impulses, which is in agreement with Chiu et al. [ 19 ] and Hara et al. [ 20 ] who found a similar pattern in the NJM. However, it was only the hip that exhibited an improved vertical JCF-time profile with an added arm swing, as it was the only joint impulse that remained significantly greater after removing the effect of increased time (by time normalization). This can be explained by the increase in delay in the proximal-to-distal strategy which occurred between peak hip and knee extensor forces, but not between the knee extensors, plantar flexors and take-off. The time between hip and knee extensor peaks increased to allow the forward arm swing to begin the upward acceleration and propulsive phase before the leg begins to extend [ 16 ] , maximising energy transfer from the elbows and shoulders to the trunk and pelvis creating the ‘pull mechanism’ [ 17 ] . This resulted in slower hip extension and muscle contraction within an improved region of the force-velocity curve at which the muscles are able to generate more force [ 26 ] . Therefore, the inclusion of an arm swing likely improves the hip JCF-time profile by enhancing the proximal-to-distal strategy of the countermovement. Unlike the increase in time-normalised impulse at the hip, the vertical external and ankle impulses only increased when calculated in real time, indicating that a longer ground contact time was the main factor contributing to increased impulse. However, previous studies have shown an increase in ankle NJM with the use of an arm swing in a CMJ [ 15 , 16 , 17 , 19 , 20 ] . Even though the average vertical JCF did not increase significantly, the ankle NJM may have increased due to the larger moment arm created about the ankle joint due to the anterior projection of the centre of mass with an arm swing [ 19 ] . The vertical impulses at the tibiofemoral and patellofemoral joints did not increase with an added arm swing, even when time was not normalised. As previously discussed, the delay in the proximal-to-distal strategy with the added arm swing occurs just after the breaking phase of the countermovement and prior to leg extension, increasing the forces produced by the biarticulate hamstrings and the gastrocnemius. These muscles generate a flexion moment on the tibia and femur respectively, requiring the knee extensors to be used maximally during the closed chain extension present in jumping [ 10 ] . The patellofemoral JCF has been modelled based on the quadriceps tendon and patellar tendon forces while the tibiofemoral JCF was modelled as a result of the opposing posterior cruciate ligament and patellar tendon forces [ 27 ] . The maximally used quadriceps during the CMJ NoArms and CMJ Arms , together with their diminished ability to transfer tension to the patellar tendon while in knee flexion [ 9 ] (the posture which is prolonged during CMJ Arms ), may explain the similar tibiofemoral and patellofemoral vertical impulses during both jumps. The results of the participant-level PCA where only one to three fDOF were required to describe the main characteristics of both the CMJ NoArms and CMJ Arms , suggests that a large number of constraints exist in individual CMJ motor control strategies. On average, only one additional fDOF was needed to define the 3D JCF and muscle forces separately for all 18 participants in the CMJ NoArms (three total fDOF) and two additional fDOF were needed for CMJ Arms (four total fDOF). This shows that there was a high degree of similarity between participants in their proximal-to-distal movement pattern, suggesting that underlying mechanical constraints exist within our musculoskeletal system, enforcing this movement pattern [ 12 ] . At the maximum depth of the countermovement before the propulsion phase, the quadriceps are able to generate more force about the femur through the quadriceps tendon than about the tibia through the patellar tendon due to the knee flexion and geometry of patella [ 9 ] . This enhances the proximal-to-distal strategy in which the femur extends prior to the tibia in vertical jumping [ 27 ] . The biarticulate muscles, apart from creating a rotational effect not only on their proximal and distal segments, but also on their intermediate segment [ 28 ] , are able to transfer energy from their proximal-to-distal segment [ 10 ] . Therefore, the biarticulate muscles and the geometry of the patella define additional constraints on the system through mechanical coupling during vertical jumps, reinforcing the proximal-to-distal delay and reducing the load on the central control system [ 8 ] . While the lower limb segments exhibit mechanical coupling, the anatomy of the upper limb is not mechanically linked and constrained to that of the lower limb. Thus, the inclusion of an arm swing exhibited greater variability both within (participant-level fDOF) and between (group-level fDOF) participants' movement strategies. The higher variation for CMJ Arms can also be seen in the stabilization muscles with varying activation and peak timings in CMJ Arms (Fig. 3 , muscle groups 5–7). Theoretically, simply prolonging the proximal-to-distal strategy in CMJ Arms could have been defined by only three fDOF at a group level, particularly as the peaks in PC2 and PC3 are already delayed in CMJ Arms compared to CMJ NoArms . However, CMJ Arms required the inclusion of PC4 to describe the force-time curve of the vastus lateralis as some participants exhibited double curves or multiple peaks in the knee extensor force-time curve, while others exhibited a smoother single curve. Similar patterns have been found in knee extensor NJM, where a smoother curve resulted in improved jump performance, compared to knee NJMs consisting of multiple peaks [ 19 ] . The CMJ Arms also required an additional use of PC3 in muscle group 1 (including the biceps femoris), which describes a slight increase in muscle force late in the CMJ propulsion phase. This may have been caused by the delayed peak of the knee extensor requiring additional antagonistic co-contraction of the biarticulate biceps femoris for stability at the knee joint to avoid hyperextension on take-off [ 8 , 9 ] . The effect of increased variability and number of fDOF on jump performance can be seen more clearly on a participant level. Participants exhibiting two fDOF had a higher vertical external impulse compared to those who only had one fDOF (Table 2 ) as it would represent the majority of muscles working simultaneously. At a participant level, two fDOF are sufficient to define a proximal-to-distal strategy as the PC score curves are able to follow the individual’s strategy more closely than at a group level and reduces the need for more generic PC curves. The addition of the third fDOF at participant level may indicate excessive variation and reduced coordination within the individual’s motor strategy, resulting in decreased performance. However, the sample size of participants exhibiting one and three fDOFs is too small to make conclusive comparisons between the groups. Vertical jumping is present in many sports with different demands and constraints. It may not be possible for the potential benefits of a prolonged ground contact time in CMJ Arms to be fully utilized, such as when fast reaction is required, or when speed is determined by music’s tempo in dance. However, the lack of direct mechanical coupling between the arms and the lower extremity, as described by the additional fDOF, emphasises the importance of training CMJ Arms to improve the individual’s jump performance. Possible sources of variation in CMJ Arms which may effect and improve jump height include arm swing timing and technique [ 16 , 18 ] . Individual’s dynamic core flexion strength has been shown to affect the musculoskeletal ability to transfer the energy generated from the arms to the distal segments [ 29 ] . Due to the contribution of shoulder musculature to the vertical energy generated by the arm swing, it has been suggested that shoulder flexor strength may also alter performance in CMJ Arms [ 21 ] , although further research is needed. Therefore, training a specific optimal technique, and increasing shoulder and dynamic core flexion strength may be crucial to reduce variation within the individual’s movement strategy and improve jump performance. As noted by Cleather and Cushion [ 30 ] , even though the motor strategies used in both CMJs can be described by three or four fDOF, it does not imply that every participant’s motor strategy is the same. In fact, the PC combination for each participant and each muscle can be easily identified from the PCA’s coefficient matrix, resulting in different curve profiles, peak timings and motor strategies from the same PCs. The small number of fDOF present simply indicate that the muscle forces and JCFs are tightly constrained during CMJs and that individual strategies can be defined by a linear combination of the same PCs [ 30 ] , as can be seen from the multiple curves resulting from different combinations of the CMJ’s PCs (Fig. 3 ). Future research may explore whether additional constraints are present between the lower extremity, trunk and upper limb segments through a full-body musculoskeletal model and PCA. Jump performance can also be investigated to identify the movement characteristics describing the most effective arm swing technique to improve jump height. A strength of this study is the inclusion of time normalisation in the vertical impulse analysis. This allowed for a distinction between solely the difference in time or a combined difference of time and vertical force as the main contribution for change in impulse between CMJ NoArms and CMJ Arms . Another strength is the comparison of the muscle group principal component combinations between jumps in real time, clearly indicating the similarities and differences in the timings of the proximal-to-distal strategy. This detail is lost when comparing muscle activity in normalised time [ 16 ] . Although Kovács et al. [ 16 ] found the same sequence of muscle peak timings using electromyography, no differences were found in muscle peak timings between the jumps. This can be misleading as true differences in peak timing may still exist due to the prolonged CMJ Arms , while the difference found in the vastus lateralis activation between 38–56% of CMJ Arms and CMJ NoArms may not be significant in real time. The principal impulse for each muscle group also closely represented the sum of the group’s muscle impulses, with a strong positive correlation. This demonstrates further the usefulness of PCA as a data reduction method to simplify the understanding of complex motor control strategies. However, it is important to keep in mind that this technique is based solely on linear relationships between the DOF. Therefore, the number of fDOF may be overestimated as non-linear relationships may still exist in the identified fDOF and thus may not be entirely independent [ 1 ] . It should also be noted that the muscle groups categorization and cut-off coefficients for the group’s PC combination were based on the interpretation of the group’s composite muscle force curves. Even though a rigorous method was followed for these steps, muscle group categorization and cut-off coefficients were determined using mainly a qualitative visual inspection of the curves. In addition, individual strategies may have varied and slightly different muscle group categorizations and PC linear combinations may have emerged between participants. There were several possible ways to interpret the results of this study, however the method followed was chosen due to the similarity in movement strategies found previously between participants for CMJ Arms and CMJ NoArms [ 12 ] , suggesting that an in-depth group analysis was suitable to compare muscle forces between jumps. In conclusion, jump performance improved with an added arm swing as it increased the ground contact time, resulting in higher vertical impulses. The increased ground contact time to perform the arm swing was mainly used by the lower extremity to decrease the hip extension velocity, allowing the hip muscles to generate higher forces, and to delay knee extension, enhancing the proximal-to-distal strategy. The PCA has shown that muscle activation and joint kinetics in the lower limb exhibit very similar patterns within and between individuals. This suggests that the underlying anatomy, such as biarticulate muscles and the patella, provide mechanical constraints and coupling during a CMJ, reducing the load on the central control system [ 8 ] . The inclusion of an arm swing required an additional fDOF (four in total) to describe the main characteristics of the movement, suggesting that the arms are not directly mechanically coupled with the lower extremity, resulting in additional variation within individual motor strategies. Declarations Data Availability The datasets collected by Cushion et al. [ 12 ] which were analysed during this study are available from the corresponding author on reasonable request. Acknowledgments The research work disclosed in this publication is partially funded by the ENDEAVOUR II Scholarships Scheme (Malta). Project may be co-funded by the ESF+ 2021-2027. Author Contributions C.C. wrote the manuscript, completed the data analysis and prepared all figures. J.S. and D.C. supervised and contributed to the writing of the manuscript, data analysis and preparation of all figures. E.C. performed the data collection. All authors were involved in conceptualization of the study, and reviewed the manuscript. Additional Information Competing Interests Statement The authors declare no competing interests. References Li, Z.-M. Functional degrees of freedom. Motor Control 10 , 301–310 (2006). Latash, M.L. The bliss (not the problem) of motor abundance (not redundancy). Exp. Brain. Res. 217 , 1–5 (2012). Gray, R. Changes in movement coordination associated with skill acquisition in baseball batting: freezing/freeing degrees of freedom and functional variability. Front. Psychol. 11 , 1295; 10.3389/fpsyg.2020.01295 (2020). Guimarães, A.N., Ugrinowitsch, H., Dascal, J.B., Porto, A.B. & Okazaki, V.H.A. ‘Freezing degrees of freedom during motor learning: A systematic review. Motor Control 24 , 457–471 (2020). Konczak, J., Vander Velden, H. & Jaeger, L. Learning to play the violin: Motor control by freezing, not freeing degrees of freedom. J. Mot. Behav. 41 , 243–252 (2009). van Ginneken, W.F.,et al. Conscious control is associated with freezing of mechanical degrees of freedom during motor learning. J. Mot. Behav. 50 , 436–456 (2018). Nordin, A.D. & Dufek, J.S. Neuromechanical synergies in single-leg landing reveal changes in movement control. Hum. Mov. Sci. 49 , 66–78 (2016). Blickhan, R., et al. Intelligence by mechanics. Philos. Trans. A Math. Phys. Eng. Sci. 365 , 199-220 (2006). Cleather, D.J., Southgate, D.F. & Bull, A.M. On the role of the patella, ACL and joint contact forces in the extension of the knee. PLoS ONE 9 ,12; 10.1371/journal.pone.0115670 (2014). Cleather, D.J., Southgate, D.F.L. & Bull, A.M.J. The role of the biarticular hamstrings and gastrocnemius muscles in closed chain lower limb extension. J. Theor. Biol. 365 , 217–225 (2015). Daffertshofer, A., Lamoth, C.J., Meijer, O.G. & Beek, P.J. PCA in studying coordination and variability: A tutorial. Clin. Biomech. 19 , 415–428 (2004). Cushion, E.J., Warmenhoven, J., North, J.S. & Cleather, D.J. Principal component analysis reveals the proximal to distal pattern in vertical jumping is governed by two functional degrees of freedom. Front. Bioeng. Biotechnol. 7, 193; 10.3389/fbioe.2019.00193 (2019). Bobbert, M.F. & van Soest, A.J. ‘Knoek’ Why do people jump the way they do?. Exerc. Sport Sci. Rev. 29 , 95–102 (2001). Mosier, E.M., Fry, A.C. & Lane, M.T. Kinetic contributions of the upper limbs during counter-movement vertical jumps with and without arm swing. J. Strength. Cond. Res. 33 , 2066–2073 (2019). Feltner, M.E., Bishop, E.J. & Perez, C.M. Segmental and kinetic contributions in vertical jumps performed with and without an arm swing. Res. Q. Exerc. Sport 75 , 216–230 (2004). Kovács, B., et al. Arm swing during vertical jumps does not increase EMG activity of the lower limb muscles. Physical Activity Health 7 , 132–142. (2023). Lees, A., Vanrenterghem, J. and De Clercq, D. Understanding how an arm swing enhances performance in the vertical jump. J. Biomech. 37 , 1929–1940 (2004). Vaverka, F., et al. Effect of an arm swing on countermovement vertical jump performance in elite volleyball players. J. Hum. Kinet. 53 , 41–50 (2016). Chiu, L.Z.F., Bryanton, M.A. & Moolyk, A.N. Proximal-to-distal sequencing in vertical jumping with and without arm swing. J. Strength. Cond. Res. 28 , 1195–1202 (2014). Hara, M., Shibayama, A., Takeshita, D., Hay, D.C. & Fukashiro S. A comparison of the mechanical effect of arm swing and countermovement on the lower extremities in vertical jumping. Hum. Mov. Sci. 27 , 636–648 (2008). Domire, Z.J. & Challis, J.H. An induced energy analysis to determine the mechanism for performance enhancement as a result of arm swing during jumping. Sports Biomech. 9 , 38–46 (2010). Cleather, D.J. & Bull, A.M. The development of a segment-based musculoskeletal model of the lower limb: Introducing FreeBody. R. Soc. Open Sci. , 2 , 140449; 10.1098/rsos.140449 (2015). Winter, D.A. Biomechanics And Motor Control Of Human Movement . (Wiley, 2005). Akima, H. A new method of interpolation and smooth curve fitting based on local procedures. J. ACM. 17 , 589-602 (1970). Akima, H. A method of bivariate interpolation and smooth surface fitting based on local procedures. Commun. ACM. 17 , 18-20 (1974). Hill, A.V. The heat of shortening and the dynamic constants of muscle. Proc. R. Soc. B: Biol. Sci. 126 , 136-195 (1938). Cleather, D.J. The patella: A mechanical determinant of coordination during vertical jumping. J. Theor. Biol. 446 , 205–211 (2018). Zatsiorsky, V. & Latash, M. What is a joint torque for joints spanned by multiarticular muscles? J. Appl. Biomech. 9 , 333–336 (1993). Guo, L., Wu, Y. & Li, L. Dynamic core flexion strength is important for using arm-swing to improve countermovement jump height. Appl. Sci . 10 , 7676; 10.3390/app10217676 (2020). Cleather, D. & Cushion, E. Muscular coordination during vertical jumping. J. Human Perf. Health 2019 , a1-10; 10.29359/JOHPAH.1.4.01 (2019). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 02 Sep, 2024 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 11 Jul, 2024 Reviewers agreed at journal 17 Jun, 2024 Reviews received at journal 15 Jun, 2024 Reviews received at journal 13 Jun, 2024 Reviewers agreed at journal 05 Jun, 2024 Reviewers agreed at journal 04 Jun, 2024 Reviewers invited by journal 04 Jun, 2024 Editor assigned by journal 27 May, 2024 Editor invited by journal 29 Mar, 2024 Submission checks completed at journal 29 Mar, 2024 First submitted to journal 21 Mar, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4142464","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":286666558,"identity":"25891951-826b-432f-a726-ac58b40fc815","order_by":0,"name":"Christina M. Cefai","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAklEQVRIiWNgGAWjYDACCQaGA2ASCD4wGNgAKcbGA4S1JIC1MM5gMEgD0Q0EtTAwJDBAtTAcBrPwauGf3fvw4M8fFnn87YcPNvwoOG+3tv0w0JYam2icltw5bnCYJ0GiWOJMWmJjj8Ht5G1nEoFajqXlNuDQYiCRBnRMgkRiww0e8wc8QC1mB4BaGBsO49Vy8AdQy/wb/B8b/xicSzY7/5CwlgNAhyVuuMHD2MxjcMDO7AYBWyRuAB3GkyaRuPFMmmGzjEFygtkNoC0JePzCPyON+eMPm7rEeccPP2x888fO3ux8+sMHH2pscGrBAIlglQnEKgcBe1IUj4JRMApGwcgAANMSZsKLXqnLAAAAAElFTkSuQmCC","orcid":"","institution":"St Mary's University Twickenham London","correspondingAuthor":true,"prefix":"","firstName":"Christina","middleName":"M.","lastName":"Cefai","suffix":""},{"id":286666559,"identity":"9ab8d5c1-10b9-49db-b720-562e0aaa736c","order_by":1,"name":"Joseph W. Shaw","email":"","orcid":"","institution":"St Mary's University Twickenham London","correspondingAuthor":false,"prefix":"","firstName":"Joseph","middleName":"W.","lastName":"Shaw","suffix":""},{"id":286666560,"identity":"cb350147-d42e-4599-bb33-7e034c05204a","order_by":2,"name":"Emily J. Cushion","email":"","orcid":"","institution":"University of Essex","correspondingAuthor":false,"prefix":"","firstName":"Emily","middleName":"J.","lastName":"Cushion","suffix":""},{"id":286666561,"identity":"cdb25542-a965-4179-ae0c-fb3226428772","order_by":3,"name":"Daniel J. Cleather","email":"","orcid":"","institution":"St Mary's University Twickenham London","correspondingAuthor":false,"prefix":"","firstName":"Daniel","middleName":"J.","lastName":"Cleather","suffix":""}],"badges":[],"createdAt":"2024-03-21 09:48:52","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4142464/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4142464/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-024-70194-z","type":"published","date":"2024-09-02T16:08:22+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":54106271,"identity":"018efeae-737a-4b12-be40-a5b4f38d715c","added_by":"auto","created_at":"2024-04-04 17:21:01","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":168474,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ea)\u003c/strong\u003e Mean external vertical impulses and joint impulses for the countermovement jump without (open black markers) and with (solid grey markers) the use of an arm swing. \u003cstrong\u003eb)\u003c/strong\u003e Time-normalised mean external vertical impulses and joint impulses for the countermovement jump without (open black markers) and with (solid grey markers) the use of an arm swing.\u003c/p\u003e\n\u003cp\u003eThe capped lines show the upper and lower bounds of the Bonferroni adjusted 95% confidence interval (CI) of the mean impulses for CMJ\u003csub\u003eNoArms\u003c/sub\u003e (black line) and CMJ\u003csub\u003eArms\u003c/sub\u003e (grey line).\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4142464/v1/e434653f0df4bf29a748d970.jpeg"},{"id":54106272,"identity":"551fe220-eb0c-4b8d-9e0f-3ab061b72412","added_by":"auto","created_at":"2024-04-04 17:21:01","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":320170,"visible":true,"origin":"","legend":"\u003cp\u003eNormalised principal component score curves and their respective explained variation percentage (E%) and cumulative explained variation (CE%) describing the muscle forces (solid lines; input matrix: 501 data points x 702 muscles (39 participant composite muscles x 18 participants)) and 3-dimensional joint contact forces (dashed lines; input matrix: 501 data points x 270 forces (5 joins x 3 dimensions x 18 participants)) for a countermovement jump without (CMJ\u003csub\u003eNoArms\u003c/sub\u003e, black lines) and with (CMJ\u003csub\u003eArms\u003c/sub\u003e, grey lines) the use of an arm swing. The numbers in the legend represent the peak PC score, with the negative numbers in muscle force’s PC3 CMJ\u003csub\u003eArms\u003c/sub\u003e and joint contact force’s PC1 indicating that the curve is inverted for comparison.\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4142464/v1/8382dd87991cde440a722f56.jpeg"},{"id":54106273,"identity":"79051b79-ab6a-43d2-ad49-beb5070ac0a7","added_by":"auto","created_at":"2024-04-04 17:21:01","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":969660,"visible":true,"origin":"","legend":"\u003cp\u003eGroup-level composite muscle force curves (grey lines) grouped by peak relative time and force profile together with the linear composition of principal components (PC - black line) defining the muscle group. The peak of the principal component composition (vertical black line) occurs within the range of peak relative timings of the group of muscles (shaded grey area) for the CMJ\u003csub\u003eNoArms \u003c/sub\u003e(left) and CMJ\u003csub\u003eArms \u003c/sub\u003e(right).\u003c/p\u003e\n\u003cp\u003e* Peak forces increased from CMJ\u003csub\u003eNoArms \u003c/sub\u003e(left) to CMJ\u003csub\u003eArms \u003c/sub\u003e(right).\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4142464/v1/be668253b98f9044292d64a1.jpeg"},{"id":54106274,"identity":"8c4c4949-61a0-4a8f-b8c8-bc7ef0212499","added_by":"auto","created_at":"2024-04-04 17:21:01","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":361540,"visible":true,"origin":"","legend":"\u003cp\u003eLinear combinations of PC score curves defining five muscle groups plotted against the average length of the CMJ\u003csub\u003eNoArms\u003c/sub\u003e (0.803s, black line) and CMJ\u003csub\u003eArms\u003c/sub\u003e (0.904s, grey line) in order of peak timings (vertical lines). The muscles for each group are listed in descending order of peak force magnitude. The PC composition defines the sum of the average coefficients for the principal components of each muscle represented in the group for the CMJ\u003csub\u003eNoArms\u003c/sub\u003e (black) and CMJ\u003csub\u003eArms\u003c/sub\u003e (grey).\u003c/p\u003e\n\u003cp\u003ePCi is the “principal impulse” (area under the group’s PC curve with the curve’s minimum taken as the base) generated in CMJ\u003csub\u003eNoArms\u003c/sub\u003e (black) and CMJ\u003csub\u003eArms\u003c/sub\u003e (grey). Mi is the actual sum of the muscle mean impulses (BW∙s) in the CMJ\u003csub\u003eNoArms\u003c/sub\u003e (black) and CMJ\u003csub\u003eArms\u003c/sub\u003e (grey). These variables exhibit a significant strong positive correlation (r(8)=.994, p \u0026lt; 0.001).\u003c/p\u003e\n\u003cp\u003e* Muscle with a peak force greater than 1 body weight.\u003c/p\u003e\n\u003cp\u003e\u003csup\u003ea\u003c/sup\u003e The adductor magnus had the second highest peak force in muscle group 3 during the CMJ\u003csub\u003eArms.\u003c/sub\u003e\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4142464/v1/c739c53136252725b5868161.jpeg"},{"id":64186285,"identity":"4f5b8760-c725-4321-b7ff-073729eac626","added_by":"auto","created_at":"2024-09-09 16:26:26","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2430108,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4142464/v1/eed2df5c-58f8-4770-9447-fcac21ed907c.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A countermovement jump with an arm swing is defined by four functional degrees of freedom and an enhanced proximal-to-distal delay.","fulltext":[{"header":"Introduction","content":"\u003cp\u003eIn human movement, the movement of multiple segments, each with six degrees of freedom (DOF), is coordinated through motor control strategies\u003csup\u003e[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/sup\u003e. The movement (or resistance to movement) of these segments is created by the muscles acting upon each segment, where many more muscle activation strategies exist than segmental kinematic DOFs. This results in many possible strategies to achieve the same outcome, and therefore an abundance of possible motor control strategies, allowing an individual to adapt to additional or unexpected tasks and demands\u003csup\u003e[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]\u003c/sup\u003e. This creates an indeterminant problem with more DOFs present than constraints\u003csup\u003e[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eResearchers have shown that the number of DOFs utilized by individuals can be reduced, for example, through conscious freezing of DOF during motor skill learning\u003csup\u003e[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]\u003c/sup\u003e. Neuromechanical synergies\u003csup\u003e[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]\u003c/sup\u003e, mechanical coupling,\u003csup\u003e[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]\u003c/sup\u003e and the anatomy of the musculoskeletal system itself\u003csup\u003e[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]\u003c/sup\u003e effectively create additional constraints on the system which can reduce the number of independent DOF and the demand on the central control system\u003csup\u003e[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/sup\u003e. One of the methods used to simplify the understanding of this complex motor control system is by identifying what have been termed \u0026ldquo;functional degrees of freedom\u0026rdquo; (fDOF), representing the main characteristics of the movement system\u003csup\u003e[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/sup\u003e. These are found through the dimensional reduction technique of principal component analysis (PCA), transforming the original data into a new orthogonal coordinate system, and reducing the correlation that may be present between DOF\u003csup\u003e[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]\u003c/sup\u003e. Therefore, the fDOF are defined by the minimum number of independent principal components (PCs) required to define a high percentage of variance in the original data\u003csup\u003e[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eDuring the countermovement vertical jump (CMJ), a common movement pattern observed is the proximal-to-distal strategy, where proximal segments begin to rotate before their distal segment\u003csup\u003e[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/sup\u003e. This improves the mechanical efficiency of the movement and increases jump height, compared to the simultaneous acceleration of all segments\u003csup\u003e[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]\u003c/sup\u003e. Adding an arm swing to a CMJ improves jump performance through a combination of factors. Firstly, the ground reaction force (GRF) profile is altered\u003csup\u003e[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]\u003c/sup\u003e and the time of the countermovement is prolonged, increasing the net impulse and, therefore, take-off velocity\u003csup\u003e[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]\u003c/sup\u003e. Secondly, a delay in the proximal-to-distal strategy is observed to allow the arms to accelerate upwards before extending the lower limbs\u003csup\u003e[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e, resulting in increased net joint moments (NJM) at the hip and ankle\u003csup\u003e[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/sup\u003e. Thirdly, the arm swing itself creates a \u0026lsquo;pull mechanism\u0026rsquo; in which the shoulder flexor muscles increase the vertical work done and energy generated\u003csup\u003e[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]\u003c/sup\u003e and increases the height of the center of mass at take-off\u003csup\u003e[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eWhile research has looked into the effects of an arm swing on jump performance, its effect on independent DOF present in muscular activation and 3-dimensional (3D) joint contact forces (JCF) is currently unknown. It is hypothesized that adding an arm swing will increase the variation observed in muscle forces and 3D JCFs at an individual participant and group level, increasing the number of fDOF present for the CMJ. Therefore, the purpose of this study is two-fold. Firstly, external and lower-limb joint impulses will be compared in a CMJ with (CMJ\u003csub\u003eArms\u003c/sub\u003e) and without an arm swing (CMJ\u003csub\u003eNoArms\u003c/sub\u003e) to assess the impact of arm swing on jump performance for the participants within this study. The second aim is to compare the fDOF exhibited in CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e for the 3D JCF and muscle forces.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eStudy Design and Participants\u003c/p\u003e \u003cp\u003eA cross-sectional study design was utilized to investigate the effect of an arm swing on a CMJ. The data used in this study were collected previously by Cushion et al.\u003csup\u003e[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/sup\u003e. Twenty-one healthy participants (10 women: height\u0026thinsp;=\u0026thinsp;167.4\u0026thinsp;\u0026plusmn;\u0026thinsp;6.9 cm, weight\u0026thinsp;=\u0026thinsp;62.9\u0026thinsp;\u0026plusmn;\u0026thinsp;7.3 kg; 11 men: height\u0026thinsp;=\u0026thinsp;178.0\u0026thinsp;\u0026plusmn;\u0026thinsp;7.6 cm, weight\u0026thinsp;=\u0026thinsp;82.4\u0026thinsp;\u0026plusmn;\u0026thinsp;7.2 kg) who were free from musculoskeletal injuries, gave informed consent after understanding the details of the study. Ethical approval was provided by the ethics sub-committee of St Mary\u0026rsquo;s University, Twickenham.\u003c/p\u003e \u003cp\u003eProcedure\u003c/p\u003e \u003cp\u003eParticipants attended a single data collection session during which 18 reflective markers were placed on the participants\u0026rsquo; pelvis and right lower limb, according to Cleather and Bull\u003csup\u003e[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003c/sup\u003e. A standardized warmup ending with vertical jumps was performed by all participants. A Vicon 14-camera motion capture system (Vicon MX System, Nexux2.2 software, Vicon Motion System Ltd, Oxford, UK) was used to record kinematic data at 200Hz, synchronously with kinetic data recorded at 1000Hz using two force plates (Kistler Type 9287BA, BioWare 3.24 software, Kistler Instruments Ltd, Hampshire, UK).\u003c/p\u003e \u003cp\u003eFollowing the warmup, all participants were asked to perform five separate maximum effort CMJs with their hands placed on their hips for the entire trial (CMJ\u003csub\u003eNoArms\u003c/sub\u003e) and another five separate maximum effort CMJs with the use of an arm swing (CMJ\u003csub\u003eArms\u003c/sub\u003e). For all jumps, participants were instructed to take-off and land with one foot on each force-plate. A self-selected duration of break was taken between individual jumps, and a two-minute break was given between the different jumps to mitigate fatigue. The order of jumps was counterbalanced to avoid any order effect. Full data collection details can be found in Cushion et al. (2019) \u003csup\u003e[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eData Analysis\u003c/h2\u003e \u003cp\u003eThe kinematic and kinetic data were preprocessed using a 5th order Woltring filter with a cutoff frequency of 10Hz\u003csup\u003e[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/sup\u003e. The start of the movement was defined as the frame when the right anterior superior iliac spine marker began to descend below stationary height and ended when the GRFs were 0 N on take-off\u003csup\u003e[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/sup\u003e. FreeBody\u003csup\u003e[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003c/sup\u003e\u0026mdash;an open-source segment-based musculoskeletal model of the lower limb\u0026mdash;was used to create the participants\u0026rsquo; scaled musculoskeletal models composed of five rigid segments with six kinematic DOF each (the foot, shank, thigh, pelvis, and patella), 163 muscle elements defining 39 muscles, and 14 ligament elements. The muscle, ligament, and 3D JCFs at the ankle, medial and lateral tibiofemoral joints, patellofemoral joint, and the hip were calculated at each time frame based on an optimization approach to inverse dynamics\u003csup\u003e[\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]\u003c/sup\u003e using FreeBody\u003csup\u003e[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003c/sup\u003e. This was done using MATLAB\u0026rsquo;s constrained nonlinear programming solver (\u0026lsquo;fmincon\u0026rsquo;), specifically the sequential quadratic programming (\u0026lsquo;sqp\u0026rsquo;) algorithm (The MathWorks, Inc., MA, version R2023b) to solve the 193 unknowns with only 22 equations of motion. Where the optimization failed to solve within the muscle and ligament force constraints set according to the participant\u0026rsquo;s body mass, the upper bound limits were increased incrementally until the maximum force limit of the muscles and ligaments was increased by five times, where the smaller stabilizing muscles around the foot and ankle were the main limiting factor for a few frames. When a solution was still not found, the solver\u0026rsquo;s constraint tolerance was relaxed from 1 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e to 1 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e. Trials were included in the data analysis only if a solution was found for the trial. This resulted in 18 participants being kept in the analysis (8 women: height\u0026thinsp;=\u0026thinsp;168.1\u0026thinsp;\u0026plusmn;\u0026thinsp;6.9 cm, weight\u0026thinsp;=\u0026thinsp;62.8\u0026thinsp;\u0026plusmn;\u0026thinsp;6.9 kg; 10 men: height\u0026thinsp;=\u0026thinsp;178.0\u0026thinsp;\u0026plusmn;\u0026thinsp;8.0 cm, weight\u0026thinsp;=\u0026thinsp;82.4\u0026thinsp;\u0026plusmn;\u0026thinsp;7.5 kg), where a solution was found for both CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003eThe force vectors of the 163 muscle elements were summed to define the 39 muscles and normalized to the participant\u0026rsquo;s bodyweight. The vertical external and joint impulses were calculated from the area underneath the vertical GRF and JCF-time curves respectively. The impulses were averaged across trials for each participant (participant-level impulse) before averaging across participants (group-level impulse). The modified Akima piecewise cubic Hermite interpolation (\u0026lsquo;makima\u0026rsquo;), that is MATLAB\u0026rsquo;s specific modification of Akima\u0026rsquo;s interpolation method which reduces excessive local undulations\u003csup\u003e[\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]\u003c/sup\u003e, was then used to time normalize all trials to 501 points in MATLAB (The MathWorks, Inc., MA, version R2023b) before recalculating the impulses from their respective force-time normalized curves, resulting in time-normalized external and joint vertical impulses.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eStatistical Analysis\u003c/h2\u003e \u003cp\u003eA Wilcoxon matched-pairs test (α\u0026thinsp;=\u0026thinsp;0.05) and a two-way repeated measure ANOVA (two-way interaction and main effect α\u0026thinsp;=\u0026thinsp;0.05) were used to compare the participants\u0026rsquo; external vertical impulses (not normally distributed data) and five vertical joint impulses respectively for CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e. Using the Bonferroni adjustments for the 95% confidence interval and significance level (α\u0026thinsp;=\u0026thinsp;0.01), a simple effects analysis was also performed to compare each joint individually between jumps. These statistical tests were repeated for the time-normalized impulses, however a repeated measures t-test was used for the time-normalized external vertical impulses (normally distributed data). All data were assessed for outliers beyond 1.5 times the interquartile range of the upper of lower extremity, as visualized on a box plot. It was also assessed by Shapiro-Wilk\u0026rsquo;s test of normality (α\u0026thinsp;=\u0026thinsp;0.05), and by Mauchly\u0026rsquo;s test of sphericity (α\u0026thinsp;=\u0026thinsp;0.05) for the five joints. The statistical analyses were conducted in IBM SPSS Statistics (The International Business Machines Corporation, NY, version 29.0.1.1).\u003c/p\u003e \u003cp\u003eThe participant-level composite muscle and 3D JCF curves were calculated by averaging across each trial\u0026rsquo;s output vectors at every time point for both jumps. Group-level composite curves were also calculated by averaging the participant-level curves for each muscle. Principal component analyses were performed in MATLAB (The MathWorks, Inc., MA, version R2023b) on the participant-level muscle force and 3D JCF composite curves for CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e at a participant and group level (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). After assessing for the three assumptions (outliers, normality and sphericity) as defined previously, a three-way repeated measure ANOVA (three and two-way interactions and main effects, α\u0026thinsp;=\u0026thinsp;0.05) was performed in IBM SPSS Statistics to compare the cumulative explained variation of the muscle and 3D JCFs by PCs 1 to 3 at participant level, with and without the use of an arm swing. Simple effects were considered statistically significant at α\u0026thinsp;=\u0026thinsp;0.017 (Bonferroni adjustment for 3 PC levels). The fDOF were defined as number of PCs required to explain 95% variation of the muscle forces and 3D JCFs for CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e per participant\u003csup\u003e[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe number of PCAs performed for muscle forces and JCFs at participant and group level. Their input time series data and matrix dimensions are also defined. The analyses were performed for both jumps (CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVariable\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTime series data used\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAnalysis level\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eInput matrix dimensions\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNumber of separate analyses\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cb\u003eMuscle forces\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eParticipant composite muscle forces\u003c/p\u003e \u003cp\u003e(39 muscles per participant)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eParticipant Level\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e501 data points x 39 force vectors\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e36 PCAs\u003c/p\u003e \u003cp\u003e(2 jumps x\u003c/p\u003e \u003cp\u003e18 participants)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup Level\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e501 data points x 702 force vectors\u003c/p\u003e \u003cp\u003e(39 muscles x 18 participants)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2 PCAs\u003c/p\u003e \u003cp\u003e(2 jumps)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cb\u003eJoint contact forces\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eParticipant composite 3-dimensional JCFs\u003c/p\u003e \u003cp\u003e(5 joints x 3 dimensions per participant)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eParticipant Level\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e501 data points x 15 force vectors\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e36 PCAs\u003c/p\u003e \u003cp\u003e(2 jumps x\u003c/p\u003e \u003cp\u003e18 participants)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGroup Level\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e501 data points x 270 force vectors\u003c/p\u003e \u003cp\u003e(15 JCF x 18 participants)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2 PCAs\u003c/p\u003e \u003cp\u003e(2 jumps)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe 39 group-level muscle composite curves were categorized into seven muscle groups according to peak force timing and force curve profile. After listing all muscles in order of peak timings, groups 1 and 2 were separated after visual inspection of their force-time curves as group 2 had slightly later force peaks with a different profile in CMJ\u003csub\u003eArms\u003c/sub\u003e. Groups 2 and 3 exhibited a large gap between muscle peak force timings in CMJ\u003csub\u003eArms\u003c/sub\u003e, creating a clear distinction between groups, while muscles in group 4 had a qualitatively slower rate of force production to muscles in group 3 upon visual inspection of their force-time curves. Groups 5 to 7 were categorized based on their force profiles as they all exhibited a peak at or close to 100% of the countermovement time. Group 5 showed earlier activation than group 6 while group 7 muscles exhibited a unique curve profile with both a \u0026lsquo;bell-shape\u0026rsquo; force curve and a peak at the end of the countermovement. A linear combination of PC1 to PC5 was defined for each muscle group based on the coefficients resulting from the group-level PCAs. The muscles\u0026rsquo; average coefficients for PC1 to PC5 were calculated from the 18 instances of the muscle within the coefficient matrix. The sum of the average coefficients for all muscles included in each group were calculated for PC1 to PC5 to define the muscle group\u0026rsquo;s PC combination. The group\u0026rsquo;s PC combination was simplified after normalizing to the highest coefficient by only retaining PC1 and PC2 with a normalized coefficient larger than 0.2 and PC3, PC4 and PC5 with a normalized coefficient larger than 0.35. When PC5 was the main contributor to the PC combination, the cutoff coefficients for PC1 to PC4 was 0.1. Different cut-off coefficients were defined due to lower PC score magnitudes found in PC3, PC4 and PC5, thus having little impact on the PC combination at lower normalized coefficients.\u003c/p\u003e \u003cp\u003eThe muscle group PC combinations (without normalized coefficients) were plotted against real time by multiplying the normalized time with the average lengths of the CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e jumps. The \u0026ldquo;principal impulse\u0026rdquo; was calculated from the area under these curves by taking the minimum PC score as the base, rather than 0. The total muscle impulse for each group was calculated through the summation of the group-level average muscle impulses. A Pearson\u0026rsquo;s correlation was run in IBM SPSS Statistics to determine the relationship between \u0026ldquo;principal impulse\u0026rdquo; and muscle impulse, irrespective of jump (CMJ\u003csub\u003eArms\u003c/sub\u003e and CMJ\u003csub\u003eNoArms\u003c/sub\u003e).\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cp\u003eJump Performance\u003c/p\u003e\n\u003cp\u003eSignificant differences in external impulse were found between CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.012; medians: CMJ\u003csub\u003eNoArms\u003c/sub\u003e = 0.515 BW∙s, CMJ\u003csub\u003eArms\u003c/sub\u003e = 0.571 BW∙s) and joint impulse (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.009; mean difference of 0.178 BW∙s, 95% CI, 0.051 to 0.305 BW∙s) (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea). However, only the ankle (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.009, mean difference\u0026thinsp;=\u0026thinsp;0.307 BW∙s) and hip joints (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, mean difference\u0026thinsp;=\u0026thinsp;0.315 BW∙s) had significantly different impulses in CMJ\u003csub\u003eArms\u003c/sub\u003e compared to CMJ\u003csub\u003eNoArms\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea). When normalising for time, the external vertical impulse was similar for both the CMJ\u003csub\u003eNoArms\u003c/sub\u003e (0.669 BW∙s∙s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) and CMJ\u003csub\u003eArms\u003c/sub\u003e (0.667 BW∙s∙s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e), and the main effect of an arm swing on joint impulse (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.158) and ankle joint impulse (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.324) was no longer statistically significant (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb). Only the time-normalised vertical hip joint impulse remained significantly different with the use of arm swing (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.006, mean difference\u0026thinsp;=\u0026thinsp;0.185 BW∙s∙s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e).\u003c/p\u003e\n\u003cp\u003eParticipant-Level PCA\u003c/p\u003e\n\u003cp\u003eParticipants exhibited between one and three fDOFs during the CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). The cumulative explained variation of the muscle forces and 3D JCFs by PC1 to PC3 was significantly greater in CMJ\u003csub\u003eNoArms\u003c/sub\u003e compared to CMJ\u003csub\u003eArms\u003c/sub\u003e (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.034, mean difference\u0026thinsp;=\u0026thinsp;0.975%) (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e). This resulted in a higher number of fDOF present during the CMJ\u003csub\u003eArms\u003c/sub\u003e compared to CMJ\u003csub\u003eNoArms\u003c/sub\u003e. There was also a weak trend in which participants who exhibited 2 fDOF had a higher external vertical impulse than those with only 1 fDOF, and a similar or higher impulse than those requiring 3 fDOF (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003ctable id=\"Tab2\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003e\u003cstrong\u003ea)\u003c/strong\u003e Number of PCs required to explain 95% of the 39 composite muscle forces (original DOF in input matrix: 501 data points x 39 participant composite muscles) and 15 joint contact forces (original DOF in input matrix: 501 data points x 15 forces (5 joins x 3 dimensions)) per participant (n\u0026thinsp;=\u0026thinsp;18) and the average external vertical impulse (mean\u0026thinsp;\u0026plusmn;\u0026thinsp;standard deviation) grouped by number of PCs required for CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e. \u003cstrong\u003eb)\u003c/strong\u003e Mean\u0026thinsp;\u0026plusmn;\u0026thinsp;standard deviation of the cumulative explained percentage of the muscle forces and joint contact forces by PC1, PC2 and PC3 for CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n\u003cth colspan=\"8\" align=\"left\"\u003e\n\u003cp\u003eMuscle Forces\u003c/p\u003e\n\u003c/th\u003e\n\u003cth colspan=\"9\" align=\"left\"\u003e\n\u003cp\u003eJoint Contact Forces\u003c/p\u003e\n\u003c/th\u003e\n\u003cth colspan=\"1\" align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003ea)\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eOriginal DOF\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eMean fDOF\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eNo. of fDOF\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eFreq.\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eMean External Vertical Impulse (BW∙s)\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eOriginal DOF\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eMean fDOF\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eNo. of fDOF\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eFreq.\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eMean External Vertical Impulse (BW∙s)\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eCMJ\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eNoArms\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e39\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e1.78\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.52\u0026thinsp;\u0026plusmn;\u0026thinsp;0.04\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e15\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e0.55\u0026thinsp;\u0026plusmn;\u0026thinsp;0.03\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e14\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.61\u0026thinsp;\u0026plusmn;\u0026thinsp;0.17\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e14\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e0.61\u0026thinsp;\u0026plusmn;\u0026thinsp;0.18\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003en/a\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e0.52\u0026thinsp;\u0026plusmn;\u0026thinsp;0.08\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eCMJ\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eArms\u003c/strong\u003e\u003c/sub\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e39\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.51\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e15\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" rowspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e2.28\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003en/a\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e16\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.51\u0026thinsp;\u0026plusmn;\u0026thinsp;0.07\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e13\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e0.53\u0026thinsp;\u0026plusmn;\u0026thinsp;0.06\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e0.81\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e0.53\u0026thinsp;\u0026plusmn;\u0026thinsp;0.16\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eb)\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003ePC1\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e(%)\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003ePC2\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e(%)\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003ePC3\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e(%)\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003ePC1\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e(%)\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003ePC2\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e(%)\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003ePC3\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e(%)\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eCMJ\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eNoArms\u003c/strong\u003e\u003c/sub\u003e\u003csup\u003e\u003cstrong\u003ea\u003c/strong\u003e\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e83.4\u0026thinsp;\u0026plusmn;\u0026thinsp;7.9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e98.1\u0026thinsp;\u0026plusmn;\u0026thinsp;0.9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e99.1\u0026thinsp;\u0026plusmn;\u0026thinsp;0.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e89.8\u0026thinsp;\u0026plusmn;\u0026thinsp;4.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e97.0\u0026thinsp;\u0026plusmn;\u0026thinsp;1.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e98.8\u0026thinsp;\u0026plusmn;\u0026thinsp;0.6\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eCMJ\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003eArms\u003c/strong\u003e\u003c/sub\u003e\u003csup\u003e\u003cstrong\u003ea\u003c/strong\u003e\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e85.5\u0026thinsp;\u0026plusmn;\u0026thinsp;8.3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e97.2\u0026thinsp;\u0026plusmn;\u0026thinsp;1.3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e98.9\u0026thinsp;\u0026plusmn;\u0026thinsp;0.5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e87.6\u0026thinsp;\u0026plusmn;\u0026thinsp;4.9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e96.0\u0026thinsp;\u0026plusmn;\u0026thinsp;2.0\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e98.2 \u0026plusmn;\u0026thinsp;0.9\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e\u003cstrong\u003eSignificance\u003c/strong\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e0.606\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e0.007\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e0.014\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e0.007\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"3\" align=\"left\"\u003e\n\u003cp\u003e0.015\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\n\u003cp\u003e0.002\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"17\" align=\"left\"\u003e\n\u003cp\u003e\u003csup\u003ea\u003c/sup\u003e There was a significant main effect for the use of an arm swing in the percentage of cumulative explained variation, mean difference\u0026thinsp;=\u0026thinsp;0.975%, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.034.\u003c/p\u003e\n\u003cp\u003e\u003csup\u003eb\u003c/sup\u003e There was a significant difference (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.017 - Bonferroni adjustment for 3 PC levels) for the cumulative explained variation between CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e.\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd colspan=\"2\" align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eGroup-Level PCA\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e shows the first five normalised PC curves describing the group\u0026rsquo;s muscle and 3D JCFs for the CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e. An increase in frequency can be seen from PC1 to PC5, with the maxima and minima, particularly in PC3, being delayed for CMJ\u003csub\u003eArms\u003c/sub\u003e (peak 1\u0026thinsp;=\u0026thinsp;50%, peak 2\u0026thinsp;=\u0026thinsp;75.2%, peak 3\u0026thinsp;=\u0026thinsp;91.6%) compared to CMJ\u003csub\u003eNoArms\u003c/sub\u003e (peak 1\u0026thinsp;=\u0026thinsp;48.8%, peak 2\u0026thinsp;=\u0026thinsp;71.7%, peak 3\u0026thinsp;=\u0026thinsp;89.8%). A higher percentage of cumulative variation is explained for both variables for the CMJ\u003csub\u003eNoArms\u003c/sub\u003e (e.g. PC1\u0026ndash;3: muscles\u0026thinsp;=\u0026thinsp;97.3%; 3D JCFs: 96.6%) than with the same number of PCs for the CMJ\u003csub\u003eArms\u003c/sub\u003e (e.g. PC1\u0026ndash;3: muscles\u0026thinsp;=\u0026thinsp;95.1%; 3D JCFs: 93.3%). The 270 DOF present for the group\u0026rsquo;s 3D JCF were described by 3 fDOF for CMJ\u003csub\u003eNoArms\u003c/sub\u003e and 4 fDOF for CMJ\u003csub\u003eArms\u003c/sub\u003e.\u003c/p\u003e\n\u003cp\u003eMuscle groupings and their linear PC combination\u003c/p\u003e\n\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e depicts all 39 group-composite muscle force curves for CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e with their representative PC combination. Muscle groups 1 to 4 contain the prime movers, including the biceps femoris (group 1), gluteus maximus (group 2), vastus lateralis (group 3) and soleus (group 4), with sequential peak force timings. The original 702 DOFs can be described by three and four fDOF for the prime movers during the CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e respectively. The subtraction of PC2 from PC1 moves the peak earlier in the countermovement (groups 1 and 2). The addition of PC3 in CMJ\u003csub\u003eArms\u003c/sub\u003e group 1 resulted in a superimposed curve at 80\u0026ndash;90% of the countermovement. While CMJ\u003csub\u003eNoArms\u003c/sub\u003e group 3 is solely defined by PC1, CMJ\u003csub\u003eArms\u003c/sub\u003e required the subtraction of PC4 to increase the rate of force development till 44% of the countermovement, which was reduced by PC2, while both PCs delay the peak defined by PC1. In group 4, the peak was delayed by the subtraction or addition of PC3 for CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e respectively due to their opposing profiles. While the stabilising muscles in groups 5 to 7 are well defined for the CMJ\u003csub\u003eNoArms\u003c/sub\u003e, only group 5\u0026rsquo;s PC combination vaguely followed the muscle profiles for CMJ\u003csub\u003eArms\u003c/sub\u003e.\u003c/p\u003e\n\u003cp\u003eReal time comparison of CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e\u003c/p\u003e\n\u003cp\u003eThe real time differences between the CMJ\u003csub\u003eArms\u003c/sub\u003e (0.904 s) and CMJ\u003csub\u003eNoArms\u003c/sub\u003e (0.803 s) curves can be seen in Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e. The delay between the peak force of group 1\u0026rsquo;s hip extensor and group 3\u0026rsquo;s knee extensor is prolonged in CMJ\u003csub\u003eArms\u003c/sub\u003e (0.196 s) compared to CMJ\u003csub\u003eNoArms\u003c/sub\u003e (0.062 s). However, the peaks of muscle group 1 (CMJ\u003csub\u003eNoArms\u003c/sub\u003e = 0.530 s, CMJ\u003csub\u003eArms\u003c/sub\u003e = 0.533 s) and group 2 (CMJ\u003csub\u003eNoArms\u003c/sub\u003e = 0.557 s, CMJ\u003csub\u003eArms\u003c/sub\u003e = 0.595 s) occur at similar times for both jumps. The time delay between the peak of the knee extensors to plantar flexors (CMJ\u003csub\u003eNoArms\u003c/sub\u003e = 0.077 s, CMJ\u003csub\u003eArms\u003c/sub\u003e = 0.058 s) and plantar flexors to take-off (CMJ\u003csub\u003eNoArms\u003c/sub\u003e = 0.133 s, CMJ\u003csub\u003eArms\u003c/sub\u003e = 0.117 s) is also similar between jumps. The principal impulse is larger in all groups for CMJ\u003csub\u003eArms\u003c/sub\u003e than CMJ\u003csub\u003eNoArms\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e). There was a statistically significant, strong positive correlation between principal impulse and muscle impulse (r(8)\u0026thinsp;=\u0026thinsp;.994, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001).\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe purpose of this study was to understand the effect of an arm swing during a CMJ on performance and fDOF. The results confirmed the hypothesis of improved performance with the use of an arm swing during a CMJ through increased external and joint impulses, particularly at the hip and ankle joints, and an increased joint extension proximal-to-distal delay. This study showed that the key characteristics of the movement which had 270 kinetic DOFs and 702 muscle force DOFs at a group level, could be described by a reduced number of fDOF. The CMJ\u003csub\u003eArms\u003c/sub\u003e exhibited four fDOF to define muscle forces and 3D JCFs at a group level, while the CMJ\u003csub\u003eNoArms\u003c/sub\u003e resulted in only three fDOF for both variables. This confirms the second hypothesis that more fDOF are utilized in CMJ\u003csub\u003eArms\u003c/sub\u003e compared to CMJ\u003csub\u003eNoArms\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003eThe prolonged countermovement due to the use of an arm swing resulted in increased vertical external impulse, in agreement with previous literature \u003csup\u003e[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]\u003c/sup\u003e, and increased hip and ankle joint impulses, which is in agreement with Chiu et al.\u003csup\u003e[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e and Hara et al.\u003csup\u003e[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/sup\u003e who found a similar pattern in the NJM. However, it was only the hip that exhibited an improved vertical JCF-time profile with an added arm swing, as it was the only joint impulse that remained significantly greater after removing the effect of increased time (by time normalization). This can be explained by the increase in delay in the proximal-to-distal strategy which occurred between peak hip and knee extensor forces, but not between the knee extensors, plantar flexors and take-off. The time between hip and knee extensor peaks increased to allow the forward arm swing to begin the upward acceleration and propulsive phase before the leg begins to extend\u003csup\u003e[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]\u003c/sup\u003e, maximising energy transfer from the elbows and shoulders to the trunk and pelvis creating the \u0026lsquo;pull mechanism\u0026rsquo;\u003csup\u003e[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]\u003c/sup\u003e. This resulted in slower hip extension and muscle contraction within an improved region of the force-velocity curve at which the muscles are able to generate more force\u003csup\u003e[\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]\u003c/sup\u003e. Therefore, the inclusion of an arm swing likely improves the hip JCF-time profile by enhancing the proximal-to-distal strategy of the countermovement.\u003c/p\u003e \u003cp\u003eUnlike the increase in time-normalised impulse at the hip, the vertical external and ankle impulses only increased when calculated in real time, indicating that a longer ground contact time was the main factor contributing to increased impulse. However, previous studies have shown an increase in ankle NJM with the use of an arm swing in a CMJ\u003csup\u003e[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/sup\u003e. Even though the average vertical JCF did not increase significantly, the ankle NJM may have increased due to the larger moment arm created about the ankle joint due to the anterior projection of the centre of mass with an arm swing\u003csup\u003e[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe vertical impulses at the tibiofemoral and patellofemoral joints did not increase with an added arm swing, even when time was not normalised. As previously discussed, the delay in the proximal-to-distal strategy with the added arm swing occurs just after the breaking phase of the countermovement and prior to leg extension, increasing the forces produced by the biarticulate hamstrings and the gastrocnemius. These muscles generate a flexion moment on the tibia and femur respectively, requiring the knee extensors to be used maximally during the closed chain extension present in jumping\u003csup\u003e[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]\u003c/sup\u003e. The patellofemoral JCF has been modelled based on the quadriceps tendon and patellar tendon forces while the tibiofemoral JCF was modelled as a result of the opposing posterior cruciate ligament and patellar tendon forces\u003csup\u003e[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]\u003c/sup\u003e. The maximally used quadriceps during the CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e, together with their diminished ability to transfer tension to the patellar tendon while in knee flexion\u003csup\u003e[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]\u003c/sup\u003e (the posture which is prolonged during CMJ\u003csub\u003eArms\u003c/sub\u003e), may explain the similar tibiofemoral and patellofemoral vertical impulses during both jumps.\u003c/p\u003e \u003cp\u003eThe results of the participant-level PCA where only one to three fDOF were required to describe the main characteristics of both the CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e, suggests that a large number of constraints exist in individual CMJ motor control strategies. On average, only one additional fDOF was needed to define the 3D JCF and muscle forces separately for all 18 participants in the CMJ\u003csub\u003eNoArms\u003c/sub\u003e (three total fDOF) and two additional fDOF were needed for CMJ\u003csub\u003eArms\u003c/sub\u003e (four total fDOF). This shows that there was a high degree of similarity between participants in their proximal-to-distal movement pattern, suggesting that underlying mechanical constraints exist within our musculoskeletal system, enforcing this movement pattern\u003csup\u003e[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/sup\u003e. At the maximum depth of the countermovement before the propulsion phase, the quadriceps are able to generate more force about the femur through the quadriceps tendon than about the tibia through the patellar tendon due to the knee flexion and geometry of patella\u003csup\u003e[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]\u003c/sup\u003e. This enhances the proximal-to-distal strategy in which the femur extends prior to the tibia in vertical jumping\u003csup\u003e[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]\u003c/sup\u003e. The biarticulate muscles, apart from creating a rotational effect not only on their proximal and distal segments, but also on their intermediate segment\u003csup\u003e[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]\u003c/sup\u003e, are able to transfer energy from their proximal-to-distal segment\u003csup\u003e[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]\u003c/sup\u003e. Therefore, the biarticulate muscles and the geometry of the patella define additional constraints on the system through mechanical coupling during vertical jumps, reinforcing the proximal-to-distal delay and reducing the load on the central control system\u003csup\u003e[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eWhile the lower limb segments exhibit mechanical coupling, the anatomy of the upper limb is not mechanically linked and constrained to that of the lower limb. Thus, the inclusion of an arm swing exhibited greater variability both within (participant-level fDOF) and between (group-level fDOF) participants' movement strategies. The higher variation for CMJ\u003csub\u003eArms\u003c/sub\u003e can also be seen in the stabilization muscles with varying activation and peak timings in CMJ\u003csub\u003eArms\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e3\u003c/span\u003e, muscle groups 5\u0026ndash;7). Theoretically, simply prolonging the proximal-to-distal strategy in CMJ\u003csub\u003eArms\u003c/sub\u003e could have been defined by only three fDOF at a group level, particularly as the peaks in PC2 and PC3 are already delayed in CMJ\u003csub\u003eArms\u003c/sub\u003e compared to CMJ\u003csub\u003eNoArms\u003c/sub\u003e. However, CMJ\u003csub\u003eArms\u003c/sub\u003e required the inclusion of PC4 to describe the force-time curve of the vastus lateralis as some participants exhibited double curves or multiple peaks in the knee extensor force-time curve, while others exhibited a smoother single curve. Similar patterns have been found in knee extensor NJM, where a smoother curve resulted in improved jump performance, compared to knee NJMs consisting of multiple peaks\u003csup\u003e[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e. The CMJ\u003csub\u003eArms\u003c/sub\u003e also required an additional use of PC3 in muscle group 1 (including the biceps femoris), which describes a slight increase in muscle force late in the CMJ propulsion phase. This may have been caused by the delayed peak of the knee extensor requiring additional antagonistic co-contraction of the biarticulate biceps femoris for stability at the knee joint to avoid hyperextension on take-off\u003csup\u003e[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe effect of increased variability and number of fDOF on jump performance can be seen more clearly on a participant level. Participants exhibiting two fDOF had a higher vertical external impulse compared to those who only had one fDOF (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) as it would represent the majority of muscles working simultaneously. At a participant level, two fDOF are sufficient to define a proximal-to-distal strategy as the PC score curves are able to follow the individual\u0026rsquo;s strategy more closely than at a group level and reduces the need for more generic PC curves. The addition of the third fDOF at participant level may indicate excessive variation and reduced coordination within the individual\u0026rsquo;s motor strategy, resulting in decreased performance. However, the sample size of participants exhibiting one and three fDOFs is too small to make conclusive comparisons between the groups.\u003c/p\u003e \u003cp\u003eVertical jumping is present in many sports with different demands and constraints. It may not be possible for the potential benefits of a prolonged ground contact time in CMJ\u003csub\u003eArms\u003c/sub\u003e to be fully utilized, such as when fast reaction is required, or when speed is determined by music\u0026rsquo;s tempo in dance. However, the lack of direct mechanical coupling between the arms and the lower extremity, as described by the additional fDOF, emphasises the importance of training CMJ\u003csub\u003eArms\u003c/sub\u003e to improve the individual\u0026rsquo;s jump performance. Possible sources of variation in CMJ\u003csub\u003eArms\u003c/sub\u003e which may effect and improve jump height include arm swing timing and technique\u003csup\u003e[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]\u003c/sup\u003e. Individual\u0026rsquo;s dynamic core flexion strength has been shown to affect the musculoskeletal ability to transfer the energy generated from the arms to the distal segments\u003csup\u003e[\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]\u003c/sup\u003e. Due to the contribution of shoulder musculature to the vertical energy generated by the arm swing, it has been suggested that shoulder flexor strength may also alter performance in CMJ\u003csub\u003eArms\u003c/sub\u003e\u003csup\u003e[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]\u003c/sup\u003e, although further research is needed. Therefore, training a specific optimal technique, and increasing shoulder and dynamic core flexion strength may be crucial to reduce variation within the individual\u0026rsquo;s movement strategy and improve jump performance.\u003c/p\u003e \u003cp\u003eAs noted by Cleather and Cushion\u003csup\u003e[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]\u003c/sup\u003e, even though the motor strategies used in both CMJs can be described by three or four fDOF, it does not imply that every participant\u0026rsquo;s motor strategy is the same. In fact, the PC combination for each participant and each muscle can be easily identified from the PCA\u0026rsquo;s coefficient matrix, resulting in different curve profiles, peak timings and motor strategies from the same PCs. The small number of fDOF present simply indicate that the muscle forces and JCFs are tightly constrained during CMJs and that individual strategies can be defined by a linear combination of the same PCs\u003csup\u003e[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]\u003c/sup\u003e, as can be seen from the multiple curves resulting from different combinations of the CMJ\u0026rsquo;s PCs (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Future research may explore whether additional constraints are present between the lower extremity, trunk and upper limb segments through a full-body musculoskeletal model and PCA. Jump performance can also be investigated to identify the movement characteristics describing the most effective arm swing technique to improve jump height.\u003c/p\u003e \u003cp\u003eA strength of this study is the inclusion of time normalisation in the vertical impulse analysis. This allowed for a distinction between solely the difference in time or a combined difference of time and vertical force as the main contribution for change in impulse between CMJ\u003csub\u003eNoArms\u003c/sub\u003e and CMJ\u003csub\u003eArms\u003c/sub\u003e. Another strength is the comparison of the muscle group principal component combinations between jumps in real time, clearly indicating the similarities and differences in the timings of the proximal-to-distal strategy. This detail is lost when comparing muscle activity in normalised time\u003csup\u003e[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]\u003c/sup\u003e. Although Kov\u0026aacute;cs et al.\u003csup\u003e[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]\u003c/sup\u003e found the same sequence of muscle peak timings using electromyography, no differences were found in muscle peak timings between the jumps. This can be misleading as true differences in peak timing may still exist due to the prolonged CMJ\u003csub\u003eArms\u003c/sub\u003e, while the difference found in the vastus lateralis activation between 38\u0026ndash;56% of CMJ\u003csub\u003eArms\u003c/sub\u003e and CMJ\u003csub\u003eNoArms\u003c/sub\u003e may not be significant in real time. The principal impulse for each muscle group also closely represented the sum of the group\u0026rsquo;s muscle impulses, with a strong positive correlation. This demonstrates further the usefulness of PCA as a data reduction method to simplify the understanding of complex motor control strategies. However, it is important to keep in mind that this technique is based solely on linear relationships between the DOF. Therefore, the number of fDOF may be overestimated as non-linear relationships may still exist in the identified fDOF and thus may not be entirely independent\u003csup\u003e[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/sup\u003e. It should also be noted that the muscle groups categorization and cut-off coefficients for the group\u0026rsquo;s PC combination were based on the interpretation of the group\u0026rsquo;s composite muscle force curves. Even though a rigorous method was followed for these steps, muscle group categorization and cut-off coefficients were determined using mainly a qualitative visual inspection of the curves. In addition, individual strategies may have varied and slightly different muscle group categorizations and PC linear combinations may have emerged between participants. There were several possible ways to interpret the results of this study, however the method followed was chosen due to the similarity in movement strategies found previously between participants for CMJ\u003csub\u003eArms\u003c/sub\u003e and CMJ\u003csub\u003eNoArms\u003c/sub\u003e\u003csup\u003e[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/sup\u003e, suggesting that an in-depth group analysis was suitable to compare muscle forces between jumps.\u003c/p\u003e \u003cp\u003eIn conclusion, jump performance improved with an added arm swing as it increased the ground contact time, resulting in higher vertical impulses. The increased ground contact time to perform the arm swing was mainly used by the lower extremity to decrease the hip extension velocity, allowing the hip muscles to generate higher forces, and to delay knee extension, enhancing the proximal-to-distal strategy. The PCA has shown that muscle activation and joint kinetics in the lower limb exhibit very similar patterns within and between individuals. This suggests that the underlying anatomy, such as biarticulate muscles and the patella, provide mechanical constraints and coupling during a CMJ, reducing the load on the central control system\u003csup\u003e[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/sup\u003e. The inclusion of an arm swing required an additional fDOF (four in total) to describe the main characteristics of the movement, suggesting that the arms are not directly mechanically coupled with the lower extremity, resulting in additional variation within individual motor strategies.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eData Availability\u003c/p\u003e\n\u003cp\u003eThe datasets collected by Cushion et al.\u003csup\u003e[\u003c/sup\u003e\u003csup\u003e12\u003c/sup\u003e\u003csup\u003e]\u003c/sup\u003e which were analysed during this study are available from the corresponding author on reasonable request.\u003c/p\u003e\n\u003cp\u003eAcknowledgments\u003c/p\u003e\n\u003cp\u003eThe research work disclosed in this publication is partially funded by the ENDEAVOUR II Scholarships Scheme (Malta). Project may be co-funded by the ESF+ 2021-2027.\u003c/p\u003e\n\u003cp\u003eAuthor Contributions\u003c/p\u003e\n\u003cp\u003eC.C. wrote the manuscript, completed the data analysis and prepared all figures. J.S. and D.C. supervised and contributed to the writing of the manuscript, data analysis and preparation of all figures. E.C. performed the data collection. All authors were involved in conceptualization of the study, and reviewed the manuscript.\u003c/p\u003e\n\u003cp\u003eAdditional Information\u003c/p\u003e\n\u003cp\u003eCompeting Interests Statement\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eLi, Z.-M. Functional degrees of freedom. \u003cem\u003eMotor Control\u003c/em\u003e \u003cstrong\u003e10\u003c/strong\u003e, 301\u0026ndash;310 (2006). \u003c/li\u003e\n\u003cli\u003eLatash, M.L. The bliss (not the problem) of motor abundance (not redundancy). \u003cem\u003eExp. 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Dynamic core flexion strength is important for using arm-swing to improve countermovement jump height. \u003cem\u003eAppl. Sci\u003c/em\u003e. \u003cstrong\u003e10\u003c/strong\u003e, 7676; 10.3390/app10217676 (2020). \u003c/li\u003e\n\u003cli\u003eCleather, D. \u0026amp; Cushion, E. Muscular coordination during vertical jumping. \u003cem\u003eJ. Human Perf. Health\u003c/em\u003e \u003cstrong\u003e2019\u003c/strong\u003e, a1-10; 10.29359/JOHPAH.1.4.01 (2019).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"principal component analysis, motor control strategy, mechanical coupling, degrees of freedom, proximal-to-distal, arm swing","lastPublishedDoi":"10.21203/rs.3.rs-4142464/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4142464/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAn abundance of degrees of freedom (DOF) exist when executing a countermovement jump (CMJ). This research aims to simplify the understanding of this complex system by comparing jump performance and independent functional DOF (fDOF) present in CMJs without (CMJ\u003csub\u003eNoArms\u003c/sub\u003e) and with (CMJ\u003csub\u003eArms\u003c/sub\u003e) an arm swing. Principal component analysis was used on 39 muscle forces and 15 3-dimensional joint contact forces obtained from kinematic and kinetic data, analyzed in FreeBody (a segment-based musculoskeletal model). Jump performance was greater in CMJ\u003csub\u003eArms\u003c/sub\u003e with the increased ground contact time resulting in higher external (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.012), hip (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001) and ankle (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.009) vertical impulses, and slower hip extension enhancing the proximal-to-distal joint extension strategy. This allowed the hip muscles to generate higher forces and greater time-normalized hip vertical impulse (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.006). Three fDOF were found for the muscle forces and 3-dimensional joint contact forces during CMJ\u003csub\u003eNoArms\u003c/sub\u003e, while four fDOF were present for CMJ\u003csub\u003eArms\u003c/sub\u003e. This suggests that the underlying anatomy provides mechanical constraints during a CMJ, reducing the demand on the control system. The additional fDOF present in CMJ\u003csub\u003eArms\u003c/sub\u003e suggests that the arms are not mechanically coupled with the lower extremity, resulting in additional variation within individual motor strategies.\u003c/p\u003e","manuscriptTitle":"A countermovement jump with an arm swing is defined by four functional degrees of freedom and an enhanced proximal-to-distal delay.","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-04 17:20:56","doi":"10.21203/rs.3.rs-4142464/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-07-11T08:04:56+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"38884904769630059060527319797799977707","date":"2024-06-17T22:23:29+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-15T11:58:13+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-13T06:16:51+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"19603992107729194698469373299296010308","date":"2024-06-05T13:50:59+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"76895497935944066060786291400051541329","date":"2024-06-04T09:22:54+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-06-04T08:07:40+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-05-27T11:24:29+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-03-29T13:16:15+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-03-29T13:05:57+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-03-21T09:47:32+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"085056e2-fa3d-474d-9270-3fca8a9b0a64","owner":[],"postedDate":"April 4th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":30173820,"name":"Health sciences/Anatomy/Musculoskeletal system"},{"id":30173821,"name":"Physical sciences/Engineering/Biomedical engineering"}],"tags":[],"updatedAt":"2024-09-09T16:17:42+00:00","versionOfRecord":{"articleIdentity":"rs-4142464","link":"https://doi.org/10.1038/s41598-024-70194-z","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2024-09-02 16:08:22","publishedOnDateReadable":"September 2nd, 2024"},"versionCreatedAt":"2024-04-04 17:20:56","video":"","vorDoi":"10.1038/s41598-024-70194-z","vorDoiUrl":"https://doi.org/10.1038/s41598-024-70194-z","workflowStages":[]},"version":"v1","identity":"rs-4142464","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4142464","identity":"rs-4142464","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}