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.
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