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Hart's Inversor


A linkage which draws the inverse of a given curve. It can also convert circular to linear motion. The rods satisfy $AB=CD$ and $BC=DA$, and $O$, $P$, and $P'$ remain Collinear. Coxeter (1969, p. 428) shows that if $AO=\mu AB$, then

OP\times OP' = \mu(1-\mu)(AD^2-AB^2).

See also Peaucellier Inversor


Courant, R. and Robbins, H. What is Mathematics?: An Elementary Approach to Ideas and Methods. Oxford, England: Oxford University Press, p. 157, 1978.

Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, pp. 82-83, 1969.

Rademacher, H. and Toeplitz, O. The Enjoyment of Mathematics: Selections from Mathematics for the Amateur. Princeton, NJ: Princeton University Press, pp. 124-129, 1957.

© 1996-9 Eric W. Weisstein