Constrained motion interpolation for planar open kinematic chains

This paper deals with the problem of motion interpolation of an object as part of planar open kinematic chains. Instead of synthesizing the interpolating motions in the joint space of a planar chain, this paper presents a method for synthesizing smooth motions in the workspace of the chain. The resulting motions are piecewise rational and therefore more compatible with the existing NURBS based CAD systems. The paper brings together the well-known kinematics of planar two- and three-DOF kinematic chains with revolute and/or prismatic joints and the recently developed freeform rational motions to study the problem of synthesizing constrained rational motions. Both C¹ and C² continuous interpolations are considered. The results have applications in Cartesian motion planning in robotics and task specification for the task driven design of robots and mechanisms.