Robert's Linkage
Author: Chris Sangwin
Date: 19 Jan 2007

This linkage by Richard Roberts represents the most general "four bar" linkage.  The point P is on the middle link BC, but offset from it.  Here the 4th bar is the link AD, which is also the fixed base.  Notice that with these particular measurements the point P is very close indeed to the straight line between AD.

The complete locus is rather complex, since from a mathematical point of view the linkage could be fliped down, and the point P could be independently flipped up, giving four branches to the locus.

A = Intersect(xAxis, yAxis)
a = 5
c = Circle(A, a)
D = Point(xAxis)
b = 5
d = Circle(D, b)
B = Point(c)
e = 2
f = Circle(B, e)
C = Intersect(d, f, 1)
g = Segment(A, B)
h = Segment(B, C)
i = Segment(C, D)
j = 5
k = Circle(B, j)
l = 5
p = Circle(C, l)
P = Intersect(k, p, 2)
P_1 = Segment(B, P)
n = Segment(P, C)
Q, c_1, b_1, p_1 = Polygon(B, P, C)
loc1 = Locus(P, B)