Linkages are linked (or constrained) mechanical structures such as those used in robots, excavators, engines, etc. They are also extensively used for character animation in modeling systems.

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.

REFERENCES:

Chuan, J. C. "Machine." http://www.math.ntnu.edu.tw/~jcchuan/demo/gear/machine.html.

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., 1989.

 Erdős, G. "Linkage Designer." http://www.sztaki.hu/~erdos/LinkageDesigner/contents.html.

Kempe, A. B. How to Draw a Straight Line: A Lecture on Linkages. 1977.

King, H. C. "Configuration Spaces of Linkages in ." 23 Nov 1998. http://arxiv.org/abs/math.GT/9811138.

King, H. C. "Semiconfiguration Spaces of Planar Linkages." 20 Oct 1998. http://arxiv.org/abs/math.GT/9810130.

McCarthy, J. M. "Geometric Design of Linkages." http://www.eng.uci.edu/~mccarthy/.

Rademacher, H. and Toeplitz, O. "Producing Rectilinear Motion by Means of Linkages." §18 in The Enjoyment of Mathematics: Selections from Mathematics for the Amateur. Princeton, NJ: Princeton University Press, pp. 119-129, 1957.

Trott, M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, p. 105, 2004. http://www.mathematicaguidebooks.org/.