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Hart's Inversor

HartsLinkage

Hart's inversor is 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 while OPP^' is kept parallel to AD. This condition holds automatically if AO/AB=AP/AD=CP^'/BC.

Coxeter (1969, p. 428) shows that if AO=muAB, then

OP×OP^'=mu(1-mu)(AD^2-AB^2).

See also

Linkage, Peaucellier Inversor

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References

Bogomolny, A. "Hart's Inversor." http://www.cut-the-knot.org/Curriculum/Geometry/HartInversor.shtml.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.Mannheim, A. "Sur l'inverseur de Hart." Messenger Math., p. 151, Nov. 1896.Rademacher, H. and Toeplitz, O. The Enjoyment of Mathematics: Selections from Mathematics for the Amateur. Princeton, NJ: Princeton University Press, pp. 124-129, 1957.

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Hart's Inversor

Cite this as:

Weisstein, Eric W. "Hart's Inversor." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HartsInversor.html

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