According to Camus’ theorem, for a single degree-of-freedom (DOF) three-body system with the three instant centers staying coincident, a point embedded on a body traces a pair of conjugated curves on the other two bodies. This paper discusses a fundamental issue not addressed in Camus’ theorem in the context of higher order curvature theory. Following the Aronhold–Kennedy theorem, in a single degree-of-freedom three-body system, the three instant centers must lie on a straight line. This paper proposes that if the line of the three instant centers is stationary (i.e., slide along itself) on the line of the instant centers, a point embedded on a body traces a pair of conjugated curves on the other two bodies. Another case is that if the line of the three instant centers rotates about a stationary point, the stationary point embedded on a body also traces a pair of conjugated curves on the other two bodies. The paper demonstrates the use of instantaneous invariants to synthesize such a three-body system leading to a conjugate curve-pair generation. It is a supplement or extension of Camus’ theorem. Camus’ theorem may be regarded as a special singular case, in which all three instant centers are coincident.
Extended Camus Theory and Higher Order Conjugated Curves
Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received February 2, 2019; final manuscript received May 22, 2019; published online July 12, 2019. Assoc. Editor: Raffaele Di Gregorio.
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Chan, C. L., and Ting, K. (July 12, 2019). "Extended Camus Theory and Higher Order Conjugated Curves." ASME. J. Mechanisms Robotics. October 2019; 11(5): 051009. https://doi.org/10.1115/1.4043924
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