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TECHNICAL PAPERS

Graphical Technique to Locate the Center of Curvature of a Coupler Point Trajectory

[+] Author and Article Information
Gordon R. Pennock, Edward C. Kinzel

School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907-2088 USA

J. Mech. Des 126(6), 1000-1005 (Feb 14, 2005) (6 pages) doi:10.1115/1.1798091 History: Received September 23, 2003; Revised February 13, 2004; Online February 14, 2005
Copyright © 2004 by ASME
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References

Hrones, J. A., and Nelson, G. L., 1951, Analysis of the Four-Bar Linkage; Its Application to the Synthesis of Mechanisms, The Technology Press, MIT Press, Cambridge, MA.
Erdman, A. G., 1993, Modern Kinematics, Developments in the Last Forty Years, Wiley, Wiley Series in Design Engineering, New York.
Beyer, R., 1963, The Kinematic Synthesis of Mechanisms, Chapman and Hall, London, England.
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Clarendon Press, Oxford, England.
Erdman, A. G., Sandor, G. N., and Kota, S., 2001, Mechanism Design, Vol. 1, 4th ed., Prentice-Hall, Upper Saddle River, New Jersey.
Uicker, J. J., Jr., Pennock, G. R., and Shigley, J. E., 2003, Theory of Machines and Mechanisms, 3rd ed., Oxford University, New York.
Hain, K., 1967, Applied Kinematics, 2nd ed., McGraw-Hill, New York.
Dijksman, E. A., 1976, Motion Geometry of Mechanisms, Cambridge University Press, Cambridge, England.
Hall, A. S., Jr., 1986, Kinematics and Linkage Design, Waveland Press, Prospect Heights, Illinois (Originally published by Prentice-Hall, Inc., 1961).
Waldron, K. J., and Kinzel, G. L., 1999, Kinematics, Dynamics, and Design of Machinery, Wiley, New York.
Pennock, G. R., and Sankaranarayanan, H., 2003, “Path Curvature of a Geared Seven-Bar Mechanism,” Mechanism and Machine Theory, Vol. 38, No. 12, October, Pergamon Press, Great Britain, pp. 1345–1361.
Pennock,  G. R., and Kinzel,  E. C., 2004, “Path Curvature of the Single Flier Eight-Bar Linkage,” ASME J. Mech. Des., 126, pp. 470–477.
Pennock,  G. R., and Raje,  N. N., 2004, “Curvature Theory for the Double Flier Eight-Bar Linkage,” Mech. Mach. Theory, 39(7), pp. 665–679.
Sandor,  G. N., Xu,  Y., and Weng,  T.-C., 1990, “A Graphical Method for Solving the Euler-Savary Equation,” Mech. Mach. Theory, 25(2), pp. 141–147.
Yang,  A. T., Pennock,  G. R., and Hsia,  L. M., 1994, “Instantaneous Invariants and Curvature Analysis of a Planar Four-Link Mechanism,” ASME J. Mech. Des., 116(4), pp. 1173–1176.

Figures

Grahic Jump Location
Coupler curve and the osculating circle
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Instant centers, collineation axis 1 and ray 3
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(a) The construction circle and collineation axis 2, (b) a proof of the geometric construction
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Instant centers I25 and I15
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Center of curvature of the trajectory of point C
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Purely graphical technique to locate the pole tangent
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Center of curvature of the path trajectory point C
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Inflection circle and center of curvature of trajectory of point C
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Single flier eight-bar linkage
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(a) Equivalent four-bar linkage for the coupler link, (b) inflection circle and osculating circle for the coupler link

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