Sylvester, Kempe and Cayley developed the geometry associated with the theory of linkages in the 1870s. Kempe proved that every finite segment of an algebraic curve can be generated by a linkage in the manner of Watt's Curve.
See also Hart's Inversor, Kempe Linkage, Pantograph, Peaucellier Inversor, Sarrus Linkage, Watt's Parallelogram
References
Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., 1989.