A Method for Relatively Accurate Quantitative Calculation of the Motion Decoupling Performance of Parallel Mechanisms

Abstract Excellent motion decoupling performance (MDP) of parallel mechanisms (PMs) will give them significant advantages in kinematics/dynamics modeling, real-time control, and other aspects. However, current methods for evaluating the MDP of PMs remain at a qualitative level. This paper address the issue of quantitative calculation of MDP of PMs. Firstly, two novel concepts, i.e., the correlation matrix of input-output parameters and the motion decoupling coefficient for quantifying the motion decoupling performance are proposed based on the input-output qualitative expression established of a PM. Secondly, building on the two concepts, a new quantitative method for assessing the MDP of PMs is presented, which includes three steps, i.e., in the first step, deriving a input-output qualitative expression describing the relationship between the input parameters and the pose of moving platform is performed by conducting the topological characteristics-based analysis. As the second step, this qualitative expression is formulated as a correlation matrix. In the third step, the motion decoupling coefficient is quantitatively calculated from the correlation matrix to measure the MDP of PMs. This method enables a clear comparison of MDP across PMs with different topology, facilitating the selection of PMs with superior motion control capabilities and simplifying subsequent kinematic and dynamic modeling. Lastly, the validity and universality of the proposed method are demonstrated through four examples including 7 over-constrained PMs, including the quantitative calculation of MDP for four 3-DOF specific PMs and for a family of three 4-DOF PMs.