All Convex Polyhedra can be Clamped with Parallel Jaw Grippers

We study various classes of polyhedra that can be clamped usingparallel jaw grippers. We show that all n-vertex convex polyhedra can be clamped regardless of the gripper size and present an O(n + k) timealgorithm to compute all positions of a polyhedron that allow a valid clamp where k is the number of antipodal pairs of features. We also observe that all terrain polyhedra and orthogonal polyhedra can beclamped and a valid clamp can be found in linear time. Finally w

All Convex Polyhedra can be Clamped with Parallel Jaw Grippers

We study various classes of polyhedra that can be clamped using parallel jaw grippers. We show that all n-vertex convex polyhedra can be clamped regardless of the gripper size and present an O(n + k) time algorithm to compute all positions of a polyhedron that allow a valid clamp where k is the number of antipodal pairs of features. We also observe that all terrain polyhedra and orthogonal polyhedra can be clamped and a valid clamp can be found in linear time. Finally we show that all polyhedra can be clamped with some size of gripper. 1 Introduction Grasping is an active research area in robotics. Much research has been done on the problem of gripping or immobilizing an object with a multi-fingered hand [4, 8, 12, 13, 16]. Motivated by robot hands consisting of pairs of parallel rectangular plates (known as parallel jaw grippers) researchers have also considered the problem of finding a secure grip of a planar object with a pair of parallel line segments [6, 14, 17, 19]. Each plate i..