In this paper we present a novel method for approximating a finite set of n spatial locations with n spherical orientations. This is accomplished by determining a design sphere and the associated orientations on this design sphere which are nearest the n spatial locations. The design sphere and the orientations on it are optimized such that the sum of the distances between each spatial location and its approximating spherical orientation is minimized. The result is a design sphere and n spherical orientations which best approximate a set of n spatial locations. In addition, we include a modification to the method which enables the designer to require that one of the n desired spatial locations be exactly preserved. This method for approximating spatial locations with spherical orientations is directly applicable to the synthesis of spherical mechanisms for motion generation. Here we demonstrate the utility of the method for motion generation task specification in spherical mechanism design. [S1050-0472(00)00204-X]
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December 2000
Technical Papers
Approximating Spatial Locations With Spherical Orientations for Spherical Mechanism Design
David M. Tse,
David M. Tse
Robotics and Spatial Systems Laboratory, Mechanical Engineering Program, Florida Institute of Technology, Melbourne, FL 32901
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Pierre M. Larochelle
Pierre M. Larochelle
Robotics and Spatial Systems Laboratory, Mechanical Engineering Program, Florida Institute of Technology, Melbourne, FL 32901
Search for other works by this author on:
David M. Tse
Robotics and Spatial Systems Laboratory, Mechanical Engineering Program, Florida Institute of Technology, Melbourne, FL 32901
Pierre M. Larochelle
Robotics and Spatial Systems Laboratory, Mechanical Engineering Program, Florida Institute of Technology, Melbourne, FL 32901
Contributed by the Mechanisms Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 1998. Associate Technical Editor: C. M. Gosselin.
J. Mech. Des. Dec 2000, 122(4): 457-463 (7 pages)
Published Online: July 1, 1998
Article history
Received:
July 1, 1998
Citation
Tse , D. M., and Larochelle, P. M. (July 1, 1998). "Approximating Spatial Locations With Spherical Orientations for Spherical Mechanism Design ." ASME. J. Mech. Des. December 2000; 122(4): 457–463. https://doi.org/10.1115/1.1289139
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