Reconfiguration of a Rolling Sphere: A Problem in Evolute-Involute Geometry

The task of complete reconfiguration of a rolling sphere is recast as a problem in planar geometry. Based on our specific choice of coordinate system, two control points are defined that equivalently represent the configuration of the sphere. Under the applied control inputs, the trajectories of these control points are shown to form an evolute-involute pair. The objective of complete reconfiguration is then captured within integral conditions over the path of the control points. A class of solution to the geometric problem is derived and a three step algorithm for complete reconfiguration is proposed. The solution is computationally in-expensive and is confirmed by simulation results.Copyright © 2004 by ASME