This research addresses the analysis of the quasi static motion of systems of contacting bodies. A robotic system in contact with the local environment can in some sense be characterized dynamically as a system of interacting rigid and flexible bodies. Some of these bodies are actively controlled while others respond in a passive manner. If the accelerations of these bodies are very small, then it is often useful to assume that acceleration to be zero in the analysis of the motion of the passive bodies. This type of system is said to be quasi static, and the law of static equilibrium is assumed to hold. Mechanical systems amenable to quasi static modeling are those for which the motion is dominated by the effects of contacts, i.e., a robot hand assembling workpieces into a fixture. The approach used here is based on Peshkin's Minimum Power Principle which states that the instantaneous motion of the passive bodies is that which simultaneously minimizes power dissipation and satisfies kinematic constraints imposed by contact with active bodies. Application of this principle results in an algorithm which can determine the velocities of the system's passive bodies and the contact forces as functions of time. The algorithm is less computationally intensive than traditional solution of the system differential equations, and integration of the algorithm into existing mechanical assembly CAD/CAM systems will allow proposed assembly procedures to be evaluated for contact forces, joint torques required, and stability and jamming conditions before beginning assembly.
