Passive force analysis with elastic contacts for fixturing and grasping

Unlike active force closure, which is a property for the multi-finger robotic hand grasping, passive force closure are involved in the grasping systems with constraining devices that cannot freely control the contact forces, such as the whole-arm grasping and manufacturing fixture. In passive grasping, the contact forces rely on the physical compliance of the system which is usually described by complex contact mechanics models. The purpose of this paper is to study the properties of a type of contact model, the linear elastic contact model, so that it is possible to determine the passive force closure condition and to understand the essential characteristics of the passive grasping. The formula to solve the passive grasping forces is derived. Properties of the passive grasping is studied. The kinematic compatibility equation which describes the requirement of the coordination of contact forces is discovered, which is unique to the passive grasping. The algorithm to find the range of the preload to guarantee the passive force closure is deduced. The algorithm is demonstrated with two examples.