Peaucellier's cell
Author: Chris Sangwin
Date: 23 December 2006

This worksheet shows part of Peaucellier's linkage.  This is usually referred to as Peaucellier's Cell.  If you move the point B you will notice that the product of the distances k=OA.OB is constant.  Can you prove this is always the case?  Hence, the distance OA=k/OB.  As a result, the distance OB is "inverted" and this arrangement is often called an inversor.

g = 4
e = 4
b = 4
a = 8
B = Point(xAxis)
d = Circle(B, b)
O = Intersect(xAxis, yAxis)
OB = Distance(O, B)
c = Circle(O, a)
D = Intersect(c, d, 2)
h = Circle(D, g)
C = Intersect(c, d, 1)
f = Circle(C, e)
A, E = Intersect(f, h)
OA = Distance(O, A)
i = Segment(O, D)
j = Segment(B, D)
l = Segment(C, O)
m = Segment(C, A)
n = Segment(A, D)
k: OB OA
p = Segment(B, C)