The analysis of equilateral grip of a prismatic and convex workpiece

Certain facets of the gripping problem in robotics are discussed. A gripper with a single degree of freedom is considered, which consists of three equal-length fingers. The set of workpieces under consideration are modeled by prismatic and convex polyhedra. This leads to a planar-geometric formulation. The computational geometric problem of inscribing, in a given convex polygon, an equilateral triangle that is locally minimal, is addressed. Feasibility and the (computational) geometric construction of the solution are emphasized