Development of derivation of inverse Jacobian matrices for 195 6-DOF GSP mechanisms

One of the key issues in robotics is finding high-performance manipulator structures. To evaluate the performance of a parallel manipulator, researchers mostly use kinematic performance indices (such as condition number, minimum singular value, dexterity, and manipulability), which are based on inverse Jacobian matrices. Driving the inverse Jacobian matrix of even one parallel manipulator is a very cumbersome process. However, in this paper, general equations for the inverse Jacobian matrices of 195 GSP mechanisms are symbolically derived by considering 4 basic leg types having 1 angular and 4 distance constraints. With the help of these general equations, the development of the inverse Jacobian matrix for a GSP mechanism can be achieved by defining only the leg connection points on the base and moving platforms with minimum cost. Having derived the inverse Jacobian matrices, one can directly compute kinematic performance indices to measure and compare the manipulator performance of the 195 GSP mechanism. These analyses may yield new high-performance GSP mechanisms for use in engineering, medical device design, and other applied branches. Two different mechanisms (symmetrical and asymmetrical) are given as examples to describe the methodology for deriving the inverse Jacobian matrices. Finally, 2 numerical examples are given for illustrating the practical applications of the procedure.

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