New bounds on the number of frictionless fingers requied to immobilize

Using a novel second-order mobility theory that was recently developed by the authors, this article develops new lower bounds on the number of frictionless fingers required to immobilize generic planar objects. We show that any generic smooth or polygonal planar object can be immobilized with three convex fingers or fixtures that have sufficiently flat curvature. Further, if it is possible to specify the fingertip curvature, then any generic smooth or polygonal object can be immobilized with two, possibly concave, fingers. © 1995 John Wiley & Sons, Inc.