Differential Kinematics of Spherical and Spatial Motions Using Kinematic Mapping

This paper develops the basic framework for studying differential kinematics of spherical and spatial motions using a mapping of spatial kinematics. Relationships are derived relating the intrinsic properties of the image curves corresponding to a mapping of spherical and spatial kinematics and the instantaneous invariants of the corresponding spherical and spatial motions. In addition, in the case of spherical motions, the equations for the inflection cone and cubic cone of stationary geodesic curvature, important in spherical mechanism synthesis, are derived in terms of the curvature and torsion of corresponding image curves. Similar relationships defining the polhodes of spherical motions and their curvature at the reference instant are recast as well. A simple example involving a special spherical four-bar motion is also presented.