Immobilizing 2D serial chains in form closure grasps

The immobilization of non-rigid objects is a relatively unexplored area in grasp mechanics. This paper considers the immobilization of 2D serial chains of n hinged polygons at a given placement using frictionless point fingers. The paper sets the problem in the context of classical grasping theory by showing that chain immobilization can only be achieved with equilibrium grasps. In earlier work we described an immobilization procedure for serial chains of n≠3 polygons using n+2 frictionless point fingers. However, the immobilization of three-link chains remained an open problem. This paper establishes that three-link chains can usually be immobilized with five point fingers, but certain three-link chains can only be immobilized with six point fingers. The paper then considers the robust immobilization of serial chains under small contact placement errors. We describe a procedure for robust immobilization of n-link chains that requires only one extra contact for the entire chain, using a total of n+3 frictionless point fingers. The immobilization procedures and the exceptional three-link chains are illustrated with example.