An explicit solution of forward and inverse kinematics for a serial manipulator with insufficient intersection joints based on finite and instantaneous screw theory

Abstract

To satisfy the requirements of large workspace, high capability, and low inertia demanded by the high precision and high stiffness aerospace equipment, serial manipulator with insufficient intersection joints is proposed in this article based on finite and instantaneous screw theory. Due to the specific topology structure with no intersecting joints at both ends, the explicit solution of forward and inverse kinematics for the serial manipulator with insufficient intersection joints proposed in this article is extremely difficult. Therefore, an analytical method based on finite and instantaneous screw theory is proposed for this serial manipulator, and the explicit kinematic solution is derived in this article. According to particular calculation principle of finite and instantaneous screw theory, the finite motion of this serial manipulator is described. Based on this description, the product of exponentials formula of the kinematics of the serial manipulator with insufficient intersection joints is established on the basic of finite and instantaneous screw theory for the first time, and a novel subproblem is arose during the decomposition of product of exponentials formula. Regarding this issue, an innovative approach to this subproblem is proposed by introducing the new Paden–Kahan subproblem with elimination, and the explicit solution for the inverse kinematics is derived. Finally, the numerical examples are simulated, and the correctness of the method proposed in this article is verified.