Evaluation on Configuration Stiffness of Overconstrained 2R1T Parallel Mechanisms

Currently, two rotations and one translation (2R1T) three-degree-of-freedom (DOF) parallel mechanisms (PMs) are widely applied in five-DOF hybrid machining robots. However, there lacks an effective method to evaluate the configuration stiffness of mechanisms during the mechanism design stage. It is a challenge to select appropriate 2R1T PMs with excellent stiffness performance during the design stage. Considering the operational status of 2R1T PMs, the bending and torsional stiffness are considered indices to evaluate PMs' configuration stiffness. Then a specific method is proposed to calculate these stiffness indices. At first, each branch's different types of structural and driving stiffness are judged initially, and their specific values are defined. Then the rigid-flexible coupled force model of the over-constrained 2R1T PM is established, and the proposed evaluation method is used to analyze the configuration stiffness of the five 2R1T PMs in the entire workspace. Finally, the driving force and constraint force of each branch in the whole working space are calculated to further explain the stiffness evaluating results by using the proposed method above. Obtained results demonstrate that the bending and torsional stiffness of the 2RPU/UPR/RPR mechanism along the x- and y-directions are larger than the other four mechanisms.