This paper describes a mechanism design methodology that draws plane curves which have finite Fourier series parameterizations, known as trigonometric curves. We present three ways to use the coefficients of this parameterization to construct a mechanical system that draws the curve. One uses Scotch yoke mechanisms for each of the terms in the coordinate trigonometric functions, which are then added using a belt or cable drive. The second approach uses two-coupled serial chains obtained from the coordinate trigonometric functions. The third approach combines the coordinate trigonometric functions to define a single-coupled serial chain that draws the plane curve. This work is a version of Kempe's universality theorem that demonstrates that every plane trigonometric curve has a linkage which draws the curve. Several examples illustrate the method including the use of boundary points and the discrete Fourier transform to define the trigonometric curve.
Design of Mechanisms to Draw Trigonometric Plane Curves
Manuscript received October 20, 2016; final manuscript received January 13, 2017; published online March 9, 2017. Assoc. Editor: Venkat Krovi.
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Liu, Y., and Michael McCarthy, J. (March 9, 2017). "Design of Mechanisms to Draw Trigonometric Plane Curves." ASME. J. Mechanisms Robotics. April 2017; 9(2): 024503. https://doi.org/10.1115/1.4035882
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