Motion and Force Prediction of a Pushed Object by Maximum Dissipation Method

Abstract

When an object on a horizontal surface is pushed hard enough to overcome the friction between the object and the surface, the object moves. It was proved by interpreting Kuhn-Tucker’s optimality condition that when a pusher moves an object, the motion and the friction force of the pushed object corresponding to the pusher motion are those that maximize the power dissipated to friction under Coulomb’s friction law. This is different from the principles of maximum and minimum dissipation postulated in the past in that it involves the pusher motion too whereas the principles do not. It allows us to treat the prediction of the motion and the friction force of a pushed object as an optimization problem. Since this optimization can be performed with linear programming within any desired accuracy, it offers us a simple, robust, and fast method to predict the motion and the friction force of a pushed object. The method was verified with an experiment of pushing a wooden block. It was applied to the estimation of the necessary clamping force infixturing for machining.