Gripping Parts at Concave Vertices

A simple gripper with two vertical cylindrical jaws can make contact with external or internal concavities in polygonal and polyhedral parts to align and grip parts in form closure. Such grippers are inexpensive, lightweight, and their small footprint facilitates access and insertion for industrial applications. We refer to this as a v-grip. We begin by defining 2D v-grips, where a pair of frictionless point jaws makes contact with a pair of polygonal part concavities to achieve form-closure. We define a v-grip quality metric based on the maximum possible change in the part’s orientation when jaw position is relaxed infinitesimally. For a polygonal part with polygonal holes, we give an algorithm for computing and ranking 2D v-grips. We also extend the definition to jaws with non-zero radii. In 3D, v-grips are achieved with a pair of frictionless vertical cylinders. We define 3D v-grips and give a numerical algorithm for computing all 3D vgrips of a polyhedral part. If n is the number of vertices that describe the part and k is the number of concave vertices, we can compute all 2D v-grips in O(n+k) time. Computing offsets for jaws with non-zero radii takes O(n log n) time. A ranked list of 2D v-grips based on the quality metric can be computed in an additional O(k log k) time. We find all 3D v-grips in O(n k) time. A Java implementation of the 2D v-grip algorithm is available online for testing.