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Optimal placement of fixture clamps

This paper addresses the problem of synthesizing optimal clamping schemes on 3D parts with planar and cylindrical faces, with and without friction. Given a workpart with a pre-defined deterministic 3-2-1 location scheme, a set of polygonal convex regions on its faces are defined as areas of admissible clamp positions. A known set of one or more external disturbing wrenches are also given. The frictionless case is first considered, and a new linear program is formulated that minimizes the maximum clamping force. A transformation of the solution is presented that permits the extraction of the optimal positions of the clamps as well. Friction is introduced next, and a linear program is presented that minimizes the maximum normal clamping force. We extend the frictionless formulation to support the case of clamping contacts on cylindrical faces, resulting in a nonlinear convex formulation. Finally, we discuss a linear algebraic technique to find the lines of constant clamping force, along which the clamps can be moved while maintaining the clamping force constant.