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Geometric Construction of Piecewise Line-Symmetric Spherical Motions Using Quaternion Biarcs

[+] Author Affiliations
Carlos A. Trujillo, Q. J. Ge

State University of New York at Stony Brook, Stony Brook, NY

Paper No. DETC2006-99647, pp. 275-281; 7 pages
  • ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1: 32nd Design Automation Conference, Parts A and B
  • Philadelphia, Pennsylvania, USA, September 10–13, 2006
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4255-X | eISBN: 0-7918-3784-X
  • Copyright © 2006 by ASME


This paper employs quaternion biarcs to interpolate a set of orientations with angular velocity constraints. The resulting quaternion curve represents a piecewise spherical line-symmetric rational motion with C1 continuity. Since a quaternion arc corresponds to the motion of the planet gear in a special spherical epicyclic gear train, each segment of the quaternion biarcs can be realized with such an epicyclic gear train. Quaternion biarcs may be used to approximate B-spline quaternion curves that represent rational spherical motions that have applications in robot path planning, CAD/CAM, mechanism design, and computer graphics.

Copyright © 2006 by ASME
Topics: Motion , Construction



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