Chebyshev's linkage - alternative form
Author: Chris Sangwin
Date: 22 Dec 2006

It is indeed curious that more than one linkage can generate a particular curve.  Have a play with the GeoGebra applet below, in which the two forms of Chebyshev's linkage are superimposed.

Move the point C', and compare the movement of ABCD and A'B'C'P

e = 2.5
A = (-2, 0)
D = (2, 0)
A' = (0, 0)
a = 1
c = Circle(D, a)
C' = Point(c)
b = 2.5
d = Circle(A', b)
f = Circle(C', e)
B' = Intersect(d, f, 1)
g = Ray(C', B')
h = 5
k = Circle(C', h)
P = Intersect(k, g, 1)
i = Segment(C', P)
j = Segment(A', B')
l = Segment(D, C')
m = 5
p = Circle(A, m)
n = 5
q = Circle(D, n)
o = 1
r = Circle(P, o)
B = Intersect(p, r, 2)
s = Ray(B, P)
C = Intersect(r, s, 1)
t = Segment(C, B)
a_1 = Segment(A, B)
b_1 = Segment(C, D)
loc1 = Locus(P, C')