Constrained Motion Interpolation for Planar 6R Closed Chains

This paper deals with the motion interpolation of an object that satisfies the kinematic constraints imposed by planar 6R closed chains. The paper brings together the well-known kinematics of planar 6R closed chains and the freeform rational motions to synthesize the constrained piecewise rational motions in the Cartesian space. The methodology adopted in this paper is based on transforming the kinematic constraints of planar 6R closed chains into geometric constraints and the problem of designing C² continuous rational motions is treated as designing smooth splines in the space of planar displacement matrix parameters. In contrast to another approach of designing smooth splines in the space of planar quaternions, this approach has the advantage of being direct and yields lower degree motions. The results have application in task specification in mechanism synthesis and Cartesian motion planning in robotics.