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Article

Fourier Methods for Kinematic Synthesis of Coupled Serial Chain Mechanisms

[+] Author and Article Information
Xichun Nie

Department of Mechanical Engineering, Center for Intelligent Machines, McGill University, 3480 University Street, No. 421, Montreal, Quebec, Canadaemail: xichun_nie@hotmail.com

Venkat Krovi

Department of Mechanical and Aerospace Engineering, State University of New York at Buffalo, 318 Jarvis Hall, Buffalo, NYemail: vkrovi@eng.buffalo.edu

J. Mech. Des 127(2), 232-241 (Mar 25, 2005) (10 pages) doi:10.1115/1.1829726 History: Received December 05, 2003; Revised June 02, 2004; Online March 25, 2005
Copyright © 2005 by ASME
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References

Krovi, V., 1998, “Design and Virtual Prototyping of User-Customized Assistive Devices,” Ph.D. thesis, Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA.
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Clarendon Press, Oxford.
Nie, X., and Krovi, V., 2001, “Design of Passive Reconfigurable Manipulation Assistive Aids,” DETC2001/DAC-21087, Proceedings of the 2001 ASME Design Engineering Technical Conferences, Pittsburgh, PA.
Nie, X., 2001, “Design of Reconfigurable Manipulation Assist Aids by Fourier Methods,” M.Eng. thesis, Department of Mechanical Engineering, McGill University, Montreal, Canada.
Sandor, G. N., 1964, “On the Existence of a Cycloidal Burmester Theory in Planar Kinematics,” Trans. ASME, 31, J. Appl. Mech., 86 , pp. 694–699.
Wunderlich, W., 1970, “Chapter 33: Hohere Radlinien,” Ebene Kinematik, B.I-Hochschultaschenbucher, No. 447/447A, Mannheim, Germany.
Kaufman,  R. E., and Sandor,  G. N., 1969, “Bicycloidal Crank: A New Four-Link Mechanism,” Trans. ASME, J. Eng. Ind.,91, pp. 91–96.
Tsai,  L.-W., 1995, “Design of Tendon-Driven Manipulators,” ASME J. Mech. Des., 117, pp. 80–86.
Rosheim,  M., 1997, “In the Footsteps of Leonardo,” IEEE Rob. Autom. Mag., 4, pp. 12–14.
Leaver,  S., McCarthy,  J. M., and Bobrow,  J., 1988, “The Design and Control of a Robot Finger for Tactile Sensing,” J. Rob. Syst., 5, pp. 567–581.
Figliolini, G., and Ceccarelli, M., 1998, “A Motion Analysis for One D.O.F. Anthropomorphic Finger Mechanism,” DETC98/MECH-5985, Proceedings of the 1998 ASME Design Engineering Technical Conferences, Atlanta, GA.
Hong,  D. W., and Cipra,  R. J., 2003, “A Method for Representing the Configuration and Analyzing the Motion of Complex Cable-Pulley Systems,” ASME J. Mech. Des., 125, pp. 332–341.
Sandor, G. N., and Erdman, A. G., 1984, Advanced Mechanism Design: Analysis and Synthesis, Vol. 2, Prentice-Hall, Englewood Cliffs, NJ.
Rao, S. S., 2004, Mechanical Vibrations, 4th ed., Prentice-Hall, Upper Saddle River, NJ.
Thomson, W. T., and Dahleh, M. D., 1998, Theory of Vibration With Applications, 5th ed., Prentice-Hall, Upper Saddle River, NJ.
Lin,  C.-C., 2002, “Finite Element Analysis of a Computer Hard Disk Drive Under Shock,” ASME J. Mech. Des., 124, pp. 121–125.
Yu,  S. D., and Xi,  F., 2003, “Free Vibration Analysis of Planar Flexible Mechanisms,” ASME J. Mech. Des., 125, pp. 764–772.
Yuan,  L., and Rastegar,  J., 2004, “Kinematics Synthesis of Linkage Mechanisms With Cam Integrated Joints for Controlled Harmonic Content of the Output Motion,” ASME J. Mech. Des., 126, pp. 135–142.
Rastegar,  J., and Yuan,  L., 2002, “A Systematic Method for Kinematics Synthesis of High-Speed Mechanisms With Optimally Integrated Smart Materials,” ASME J. Mech. Des., 124, pp. 14–20.
Ullah,  I., and Kota,  S., 1997, “Optimal Synthesis of Mechanisms for Path Generation Using Fourier Descriptors and Global Search Methods,” ASME J. Mech. Des., 119, pp. 504–510.
Oppenheim, A. V., and Schafer, R. W., 1992, Discrete-Time Signal Processing, Prentice Hall, Englewood Cliffs, NJ.
Angeles, J., and Liu, Z., 1993, in Modern Kinematics: Developments in the Last Forty Years, edited by A. G. Erdman, John Wiley & Sons, New York.
Chedmail, P., 1998, “Chapter I-5: Optimization of Multi-DOF Mechanisms,” Computational Methods in Mechanical Systems: Mechanism Analysis, Synthesis and Optimization, Springer, Berlin.
Krovi,  V., Ananthasuresh,  G. K., and Kumar,  V., 2002, “Kinematic and Kinetostatic Synthesis of Planar Coupled Serial Chain Mechanisms,” ASME J. Mech. Des., 124(2), pp. 301–312.
Krovi,  V., Ananthasuresh,  G. K., and Kumar,  V., 2001, “Kinematic Synthesis of Spatial R-R Dyads for Path Following With Applications to Coupled Serial Chain Mechanisms,” ASME J. Mech. Des., 123, pp. 359–366.
Zhou,  H., and Cheung,  H. M., 2001, “Optimal Synthesis of Crank-Rocker Linkages for Path Generation Using the Orientation Structural Error of the Fixed Link,” Mech. Mach. Theory, 36, pp. 973–982.
Zhou,  H., and Ting,  K.-L., 2002, “Adjustable Slider-Crank Linkages for Multiple Path Generation,” Mech. Mach. Theory, 37, pp. 499–509.
Vanderplaats, G. N., 1982, “Chapter 3: Unconstrained Optimization in N Variables,” Numerical Optimization Techniques in Engineering Design: With Applications, McGraw-Hill, New York.
Farin, G., 1997, Curves and Surfaces for Computer-Aided Geometric Design: A Practical Guide, 4th ed., Academic Press, San Diego, CA.
Pang, Y.-W., 1999, “Fourier Methods for Synthesis of Coupled Serial Chain Mechanisms,” Honors thesis, Department of Mechanical Engineering, McGill University, Montreal, Canada.

Figures

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(a) Three-link single degree-of-freedom coupled serial chain (SDCSC) mechanism; (b) typical end-effector paths of SDCSC mechanisms
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Potential use of a passive manipulation assist device based on the SDCSC configuration to form a “virtual reconfigurable manipulation guide-rail” in an industrial setting
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(a) Geometric curve sampled with two different parameterizations (circles denote sampling locations); and (b) DFT transforms of the two sampled sets
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Flowchart of the Fourier-based optimization
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GUI-based designer interface aids the designer in specifying and synthesizing SDCSC mechanisms (shown for a desired square end-effector path)
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Improved path tracing of a rectangular-path with increasing numbers of links: (a) two-link, (b) three-link, (c) four-link, and (d) five-link
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Path tracing for a rectangular path (a) without and (b) with suitable dwell at corners
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Six assembly configurations of a three-link SDCSC mechanism synthesized by the Fourier-based synthesis method trace identical end-effector paths with different speeds
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Reconfigurable 3-link SDCSC mechanism: (a) parametric CAD model; and (b) fabricated physical prototype

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