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 …