The Design of Mechanisms to Draw Plane Curves
This dissertation develops a mechanism design procedures to draw algebraic plane curves. In 1876, Alfred B. Kempe published a proof that showed how to construct a linkage system obtained from the equation of an algebraic curve that draws the curve. He admitted that his approach lead to complex devices and recommended further study to achieve practical designs. Kempe's result, now called the Kempe Universality Theorem, was proven with modern mathematical precision by John Milson and Michael Kapovich in 2000. The resulting designs remain complex due to the generality of the proof. In this dissertation the focus is on the design of practical linkage systems that draw algebraic curves, trigonometric curves and Bezier curves. We also explore the realization of these linkage systems using solid models and additive manufacturing.