Kinematics mappings and robotics

Simple kinematic mappings have been used in robotics for the specification of robot motion in obstacle avoidance problems. Different kinematic mappings have been highly developed by kinematics researchers for the design of mechanisms, focussed primarily on single degree of freedom motion. It is possible that a more general theory of kinematic mapping will unite this effort. Presented here is a survey of the theory of the kinematic mappings of planar, spherical, and spatial displacements used in mechanical design, together with examples of loci of planar and spherical displacements which satisfy a general constraint.