Comparison of Limit Surface Approach with other Approaches in Fixture Planning with Friction

A fixture planning module is being developed as part of a computational system for concurrent product and process design. In general, three kinds of constraints such as geometric, kinematic, force constraints are considered to provide an appropriate fixturing for a given machining process. Since many fixture arrangements rely on friction to hold a part, the ability to reason about friction is an important component of fixture planning. Limit surface in force/moment space are introduced as a convenient formalism to check whether parts will slip and to help in specifying clamping forces. In this paper, the use of limit surfaces obtained either by scanning over the space of possible motions or by Minkowski sums is compared with other four approaches to establishing the relationships among applied forces and moments and the corresponding direction of sliding motion. Since the other approaches in the literature have only been applied to planar examples, the discussion in this paper will be confined to the case of a planar pressure distribution.