Abstract - A new approach to the kinematic analysis of object motion constrained by mechanical contacts is presented. The constraints by mechanical contacts are generally described by a set of linear inequalities. In task planning, it is often necessary for the planner to treat the inequalities. Thus, we develop an efficient mathematical tool based on the theory of polyhedral convex cones in order to treat the inequalities in a simple and systematic manner. We apply the method to the planning of hybrid position/force control.