Synthesis of Linkages to Trace Plane Curves

Kempe’s universality theorem introduced in 1876 has recently been proven to ensure that given any algebraic curve a mechanism exists that traces the curve. In this paper, we present two methods to simplify Kempe’s linkages. One method uses gear trains, differentials and belt drives to replace his multiplicator, additor and translator linkages. A second method uses the Scotch yoke mechanism and a summing belt drive to generate a mechanical Fourier series that traces the curve. Examples are provided that demonstrate the two approaches.

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