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TECHNICAL PAPERS

An Introduction to Burmester Field Theory

[+] Author and Article Information
John R. Mlinar

3M Company, Automation Technologies Dept., St. Paul, MN 55144

Arthur G. Erdman

University of Minnesota, Department of Mechanical Engineering, Minneapolis, MN 55455

J. Mech. Des 122(1), 25-30 (Jan 01, 2000) (6 pages) doi:10.1115/1.533553 History: Received December 01, 1998; Revised January 01, 2000
Copyright © 2000 by ASME
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References

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Sabada, S., Srinivasan, U., Kinzel, G. L., and Waldron, K. J., “Automatic Synthesis of Four-Bar Mechanisms for Four-Position Motion-Generation,” Proceedings of the 20th Biennial ASME Mechanisms Conference, (Trends and Developments Machine and Robotics), DE-Vol. 15-2, ASME 1988, pp. 121–128.
Venkataraman, S. C., Kinzel, G. L., and Waldron, K. J., “Optimal Synthesis of Four-Bar Linkages for Four-Position Rigid-Body Guidance with Selective Tolerance Specifications,” Mechanism Design and Synthesis, DE-Vol. 46, ASME 1992, pp. 651–659.
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Mirth, J. A., “Quasi-Precision Position Synthesis of Four-Bar Linkages,” ASME DE-Vol. 70, 1994, pp. 215–220.
Holte, J. E., “Two Precision Positions of Planar Mechanisms with Approximate Position and Velocity Constraints,” Ph.D. Dissertation, University of Minnesota, Minneapolis, Minnesota, 1996.
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Kaufman,  R. E., 1973, “KINSYN Phase II: A Human Engineered Computer System for Kinematic Design and a New Least-Squares Synthesis Operator,” Mech. Mach. Theory, 8, pp. 469–478.
Erdman,  A. G., and Chase,  T. R., 1985, “New Software Synthesizes Complex Mechanisms,” Mach. Design, 57, No. 19, pp. 107–113.
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Courant, R., Differential and Integral Calculus, Vol. 2, Revised Edition, Nordemann Publishing Company, New York, 1937, pp. 171–179.
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Keller,  R. E., 1965, “Sketching Rules for the Curves of Burmester Mechanism Synthesis,” ASME J. Eng. Ind., 87, May, pp. 155–160.
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Luck,  K., 1994, “Computer-Aided Mechanism Synthesis Based on the Burmester Theory,” Mech. Mach. Theory, 29, No. 6, pp. 877–886.
Waldron, K. J., and Strong, R. T., “Improved Precision Position Mechanism Synthesis,” October 1979b, Final Report TR-12, Department of Mechanical Engineering, University of Houston.
Mlinar, J. R., and Erdman, A. G., “Burmester Field Envelopes for Multiple Design Parameters,” 1998 ASME Design Engineering Technical Conference, paper DETC98/MECH-5917, September, 1998.

Figures

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Ground-pivot Burmester-field plot
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Pole location on the perpendicular bisector
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Sketch of a Burmester field showing nonanchor poles
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Sketch of Burmester fields with shared nonanchor poles
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Definition of the direction of fc
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Parameter-limit curves B1 and Bn with fc direction at the points S and T
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Parameter-limit curves B1 and Bn with fc direction at the points S and T
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Center-point Burmester field with various segments of the envelope labeled
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Center-point Burmester field with various segments of the envelope labeled
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Center-point Burmester field where envelope consists of only parameter limit curves
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Opposite-pole quadrilateral showing angles used in Burmester curve derivation

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