info prev up next book cdrom email home

Hart's Inversor

\begin{figure}\begin{center}\BoxedEPSF{Harts_Linkage.epsf}\end{center}\end{figure}

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

\begin{displaymath}
OP\times OP' = \mu(1-\mu)(AD^2-AB^2).
\end{displaymath}

See also Peaucellier Inversor


References

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
1999-05-25