Kempe's universality theorem

"[5] Kempe recognized that his results demonstrate the existence of a drawing linkage but it would not be practical.

He states It is hardly necessary to add, that this method would not be practically useful on account of the complexity of the linkwork employed, a necessary consequence of the perfect generality of the demonstration.

There is still, however, a wide field open to the mathematical artist to discover the simplest linkworks that will describe particular curves.

[6] Several approaches have been taken to simplify the drawing linkages that result from Kempe's universality theorem.

[9] Specializing the curves to those defined by trigonometric polynomials has provided another way to obtain simpler drawing linkages.