The application of the finite rotation and displacement method for a manipulator of a sequential structure with kinematic pairs of the fifth class

An algorithm for a unified approach to the solution of the inverse kinematics problem for manipulators of a sequential structure with an arbitrary number of links connected by kinematic pairs of the fifth class is developed. The algorithm is based on the application of theorems on the finite angle of rotation and displacement for each degree of mobility of the manipulator, which makes it possible to optimally use each degree of mobility when the gripper moves to specified position and orientation parameters when solving the inverse kinematics problem. A computer program was written and an IKP was solved for a particular manipulator using the developed algorithm and using the pseudo-inverse Jacobi matrix for the Moore-Penrose transformation. Comparative estimates of the solutions are given.