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Peaucellier Inversor

PeaucelliersCell

A linkage with six rods which draws the inverse of a given curve. When a pencil is placed at P, the inverse is drawn at P^' (or vice versa). If a seventh rod (dashed) is added (with an additional pivot), P is kept on a circle and the locus traced out by P^' is a straight line. It therefore converts circular motion to linear motion without sliding, and was discovered in 1864. Another linkage which performs this feat using hinged squares had been published by Sarrus in 1853 but ignored. Coxeter (1969, p. 428) shows that

OP×OP^'=OA^2-PA^2.

See also

Hart's Inversor, Kempe Linkage, Linkage

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References

Bogomolny, A. "Peaucellier Linkage." http://www.cut-the-knot.org/pythagoras/invert.shtml.Courant, R. and Robbins, H. What Is Mathematics?: An Elementary Approach to Ideas and Methods. Oxford, England: Oxford University Press, p. 156, 1978.Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, pp. 82-83, 1969.Durell, C. V. Modern Geometry: The Straight Line and Circle. London: Macmillan, p. 117, 1928.Ogilvy, C. S. Excursions in Geometry. New York: Dover, pp. 46-48, 1990.Rademacher, H. and Toeplitz, O. The Enjoyment of Mathematics: Selections from Mathematics for the Amateur. Princeton, NJ: Princeton University Press, pp. 121-126, 1957.Sarrus. Comptes Rendus de l'Académie de Paris 36, 1036, 1853.Smith, D. E. A Source Book in Mathematics. New York: Dover, p. 324, 1994.Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, p. 139, 1999.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 120 and 181-182, 1991.

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Peaucellier Inversor

Cite this as:

Weisstein, Eric W. "Peaucellier Inversor." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PeaucellierInversor.html

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