Single degree-of-freedom coupled serial chain (SDCSC) mechanisms are a class of mechanisms that can be realized by coupling successive joint rotations of a serial chain linkage, by way of gears or cable-pulley drives. Such mechanisms combine the benefits of single degree-of-freedom design and control with the anthropomorphic workspace of serial chains. Our interest is in creating articulated manipulation-assistive aids based on the SDCSC configuration to work passively in cooperation with the human operator or to serve as a low-cost automation solution. However, as single-degree-of-freedom systems, such SDCSC-configuration manipulators need to be designed specific to a given task. In this paper, we investigate the development of a synthesis scheme, leveraging tools from Fourier analysis and optimization, to permit the end-effectors of such manipulators to closely approximate desired closed planar paths. In particular, we note that the forward kinematics equations take the form of a finite trigonometric series in terms of the input crank rotations. The proposed Fourier-based synthesis method exploits this special structure to achieve the combined number and dimensional synthesis of SDCSC-configuration manipulators for closed-loop planar path-following tasks. Representative examples illustrate the application of this method for tracing candidate square and rectangular paths. Emphasis is also placed on conversion of computational results into physically realizable mechanism designs.
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March 2005
Article
Fourier Methods for Kinematic Synthesis of Coupled Serial Chain Mechanisms
Xichun Nie,
Xichun Nie
Department of Mechanical Engineering, Center for Intelligent Machines, McGill University, 3480 University Street, No. 421, Montreal, Quebec, Canada
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Venkat Krovi
Venkat Krovi
Department of Mechanical and Aerospace Engineering, State University of New York at Buffalo, 318 Jarvis Hall, Buffalo, NY
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Xichun Nie
Department of Mechanical Engineering, Center for Intelligent Machines, McGill University, 3480 University Street, No. 421, Montreal, Quebec, Canada
Venkat Krovi
Department of Mechanical and Aerospace Engineering, State University of New York at Buffalo, 318 Jarvis Hall, Buffalo, NY
Contributed by the Mechanisms and Robotics Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 5, 2003; revised June 2, 2004. Associate Editor: Q. J. Ge.
J. Mech. Des. Mar 2005, 127(2): 232-241 (10 pages)
Published Online: March 25, 2005
Article history
Received:
December 5, 2003
Revised:
June 2, 2004
Online:
March 25, 2005
Citation
Nie, X., and Krovi, V. (March 25, 2005). "Fourier Methods for Kinematic Synthesis of Coupled Serial Chain Mechanisms ." ASME. J. Mech. Des. March 2005; 127(2): 232–241. https://doi.org/10.1115/1.1829726
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