This paper addresses the problem of synthesizing robust optimal clamping schemes on three-dimensional parts with planar faces, with and without friction. Given a work part 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 external disturbing wrenches is also given. The frictionless case is considered first, and a new linear program is formulated to provide clamp locations that minimize the maximum clamping force. A transformation of the solution is presented that permits the extraction of both, the optimal positions of the clamps and the magnitude of the corresponding maximum clamping force. Friction is introduced next, and a linear program is presented that minimizes the maximum normal clamping force. We also extend the earlier formulations to support the case of frictionless clamping contacts on cylindrical faces. The result is a nonlinear (but convex) optimization problem that can be easily solved. Finally, we discuss a linear algebraic technique to find the directions, and associated relative motion rates, along which the clamps can be moved while maintaining the clamping forces constant. These lines of constant clamping force, as we name them, identify an equivalence set of clamping schemes (such that the maximum clamping force, given a set of disturbing wrenches, stays invariant).
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August 2002
Technical Papers
Optimal Placement of Fixture Clamps: Minimizing the Maximum Clamping Forces
Rodrigo A. Marin,
Rodrigo A. Marin
Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801
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Placid M. Ferreira
Placid M. Ferreira
Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801
Search for other works by this author on:
Rodrigo A. Marin
Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801
Placid M. Ferreira
Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801
Contributed by the Manufacturing Engineering Division for publication in the Journal of Manufacturing Science and Engineering. Manuscript received Dec. 2000; Revised Sept. 2001. Associate Editor: E. DeMeter.
J. Manuf. Sci. Eng. Aug 2002, 124(3): 686-694 (9 pages)
Published Online: July 11, 2002
Article history
Received:
December 1, 2000
Revised:
September 1, 2001
Online:
July 11, 2002
Citation
Marin , R. A., and Ferreira, P. M. (July 11, 2002). "Optimal Placement of Fixture Clamps: Minimizing the Maximum Clamping Forces ." ASME. J. Manuf. Sci. Eng. August 2002; 124(3): 686–694. https://doi.org/10.1115/1.1469520
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