This paper develops methods for the exact analysis and representation of the swept volume of a circular cylinder undergoing rational Be´zier and B-spline motions. Instead of following the traditional approach of analyzing the point trajectory of an object motion for swept volume analysis, this paper develops a new method for swept volume analysis by studying the plane trajectory of a rational motion. It brings together recent work in swept volume analysis, plane representation of developable surfaces, as well as computer aided synthesis of freeform rational motions. The results have applications in design and approximation of freeform surfaces as well as tool path planning for 5-axis machining of freeform surfaces.
On the Exact Representation of the Boundary Surfaces of the Swept Volume of a Cylinder Undergoing Rational Be´zier and B-Spline Motions
Contributed by the Mechanisms Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received Jun. 1999. Associate Editor: G. S. Chirikjian.
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Xia, J., and Ge, Q. J. (June 1, 1999). "On the Exact Representation of the Boundary Surfaces of the Swept Volume of a Cylinder Undergoing Rational Be´zier and B-Spline Motions ." ASME. J. Mech. Des. June 2001; 123(2): 261–265. https://doi.org/10.1115/1.1357539
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