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TECHNICAL PAPERS

A Closed-Form Approach to Coupler-Curves of Multi-Loop Mechanisms

[+] Author and Article Information
A. K. Dhingra, A. N. Almadi, D. Kohli

Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53201

J. Mech. Des 122(4), 464-471 (Aug 01, 1999) (8 pages) doi:10.1115/1.1290394 History: Received August 01, 1999
Copyright © 2000 by ASME
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References

Roberts,  S., 1875, “On Three-bar Motion in Plane Space,” Proc. R. Soc. London, Ser. A, 7, pp. 14–23.
Kempe,  A. B., 1876, “On a General Method of Describing Plane Curves of the Nth degree by Linkwork,” Proc. R. Soc. London, Ser. A, 7, pp. 213–216.
Blechschmidt,  J. L., and Uicker,  J. J., 1986, “Linkage Synthesis Using Algebraic Curves,” J. Mech. Trans. Auto. Des., 108, pp. 543–548.
Primrose,  E. J. F., Freudenstein,  F., and Roth,  B., 1967, “Six-Bar Motion, Part 1: The Watt Mechanism,” Arch. Ration. Mech. Anal., 24, pp. 22–41.
Semple, J. G., and Roth, L., 1949, Algebraic Geometry, Oxford Univ. Press.
Primrose,  E. J. F., Freudenstein,  F., and Roth,  B., 1967, “Six-Bar Motion, Part 3: Extension of the Six-Bar Techniques to Eight-Bar and 2n-Bar Mechanisms,” Arch. Ration. Mech. Anal., 24, pp. 73–77.
Wunderlich,  W., 1963, “Höhere Koppelkurven,” Ost. Ing., Arch., 17, pp. 162–165.
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Oxford Univ. Press, New York, NY.
Nolle,  H., 1974–75, “Linkage Coupler Curve Synthesis: A Historical Review-Part I: Developments up to 1875,” Mech. Mach. Theory , 9, pp. 147–168, “Part II: Developments After 1875,” 9, pp. 325–348.“Part III: Spatial Synthesis and Optimization,” 10, pp. 41–55.
Roberts,  S., 1871, “On the Motion of a Plane Under Certain Conditions,” Proc. R. Soc. London, Ser. A, 3, pp. 286–318.
Mourrain, B., 1996, “Enumeration Problems in Geometry, Robotics, and Vision,” in Algorithms in Algebraic Geometry and Applications, 143 of Progress in Mathematics, Gonzalez, L., and Recio, T., eds, pp. 285–306, Birkhauser.
Wampler, C. W., 1996, “Isotropic Coordinates, Circularity, and Bezout Numbers: Planar Kinematics from a New Perspective,” Proc. of 1996 ASME DETC, Paper No. 96-DETC/MECH-1210.
Almadi, A. N., 1996, “On New Foundations of Kinematics Using Classical and Modern Algebraic Theory and Homotopy,” Ph.D. thesis, University of Wisconsin, Milwaukee.

Figures

Grahic Jump Location
8-link 1-DOF kinematic chains
Grahic Jump Location
8-link mechanism with coupler point attached to link 7
Grahic Jump Location
Stephenson-III six-link mechanism
Grahic Jump Location
Cascaded mechanism extended in Stephenson pattern
Grahic Jump Location
8-link mechanism with coupler point attached to link 1

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