Characteristics analysis of joint space inverse mass matrix for the optimal design of a 6-DOF parallel manipulator

An optimal design method for the Gough–Stewart platform manipulators based on dynamic isotropy is proposed. First, a dynamic isotropy measure is derived from the analysis of the natural frequencies of a Stewart platform at a neutral pose using the inverse of the joint space mass matrix. Next, considering a specific Gough–Stewart platform (SGSP), it is found that, when the payload inertia matrix is diagonal, the neutral pose joint space inverse generalized mass matrix is a symmetric Centro symmetric matrix. Using this property, we derive symbolic expressions for the Eigen values and Eigenvectors and discuss and present various predominant definitions in terms of the Eigen values. We show that one can obtain spatial isotropy based on dynamics whereas it is impossible to get spatial isotropy from kinematics and statics. Finally, we present an optimal design method based on the dynamic isotropy for SGSP. We also give a numerical example to illustrate the design procedure.