This paper brings together line geometry, kinematic geometry of line-symmetric motions, and computer aided geometric design to develop a method for geometric design of rational Be´zier line-symmetric motions. By taking advantage of the kinematic geometry of a line-symmetric motion, the problem of synthesizing a rational Be´zier line-symmetric motion is reduced to that of designing a rational Be´zier ruled surface. In this way, a recently developed de Casteljau algorithm for line-geometric design of ruled surfaces can be applied. An example is presented in which the Bennet motion is represented as a rational Be´zier line-symmetric motion whose basic surface is a hyperboloid.
Rational Be´zier Line-Symmetric Motions
Contributed by the Mechanisms and Robotics Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 19, 2002; revised March 1, 2004. Associate Editor: D. C. H. Yang.
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Li, S., and Ge, Q. J. (March 25, 2005). "Rational Be´zier Line-Symmetric Motions ." ASME. J. Mech. Des. March 2005; 127(2): 222–226. https://doi.org/10.1115/1.1798251
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