Influence of passive joint damping on modal space decoupling for a class of symmetric spatial parallel mechanisms

In this study, we analyze the influence of passive joint viscous friction on modal space decoupling for a class of symmetric spatial parallel mechanisms. The Jacobian matrix relating the platform movements to each passive joint velocity is first gained by vector analysis and the passive joint damping matrix is then derived by applying the Kane method. Next, an analytic formula index measuring the damping non-proportionality is proposed using classical modal analysis of dynamic equations in task space. Based on the index, a new optimal design method is found which establishes the kinematics parameters for minimizing the non-proportional part of damping and achieves optimal fault tolerance for modal space decoupling. To illustrate the effectiveness of the theory, the new method was used to redesign two configurations of an actual group manipulator.