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.

Computational Geometry
School of Computer Science

Bose, P, Bremner, D. (David), & Toussaint, G. (Godfried). (1996). All convex polyhedra can be clamped with parallel jaw grippers. Computational Geometry, 6(5), 291–302. doi:10.1016/0925-7721(95)00052-6