Inverse Kinematic Solutions of a Rolling Disk Between Two Planar Manipulators

Abstract

Abstract This paper describes the inverse kinematic solutions of a disk rolling between two planar manipulators. The problem, in essence, is to compute the joint angles of the manipulator links given the position and orientation of the rolling disk. An algebraic technique is used to find out the inverse solutions of the manipulator links and the maximum possible number of these solutions for a given position and orientation of the rolling disk. This problem is worthy of presentation due to the following reasons: (1) the inverse solutions are obtained after including the constraints of rolling between the disk and the manipulators, (2) the upper bound on the number of inverse solutions with rolling constraints is much higher than that demonstrated for structurally similar closed-chain manipulators without rolling, (3) the joint solutions are a function of the initial assembly configuration of the mechanism, (4) these solutions have potential use in the development of path-planning algorithms for planar manipulators with rolling constraints. From our study, we conclude that a disk manipulated by two planar 2R robots has a maximum of 24 feasible sets of joint angles for a given position and orientation of the disk.