Hart's Cell
Author: Chris Sangwin
Date: 23 December 2006

This arrangements of linkages forms the basis of Hart's linkage for a straight line.

Move the points B and C.  As you do this notice the lengths FE and FG.

Also notice FE' which is calculated as (AB+BC)/FE.  In a sense, this is the "inverse" of FE.  Hence, this cell is also called an "inversor".

How does an inversor cell help to generate an exact straight line motion?

A = Intersect(xAxis, yAxis)
a = 8
c = Circle(A, a)
B = Point(c)
b = 4
d = Circle(B, b)
C = Point(d)
e = 8
f = Circle(C, e)
g = 4
h = Circle(A, g)
D = Intersect(f, h, 1)
i = Segment(A, B)
j = Segment(B, C)
k = Segment(C, D)
l = Segment(D, A)
m = 2
p = Circle(A, m)
E = Intersect(h, i, 1)
F = Intersect(p, l, 1)
n = 2
q = Circle(C, n)
o = 4
r = Circle(C, o)
G = Intersect(r, k, 1)
H = Intersect(q, j, 1)
s = Segment(F, H)
FG = Segment(F, E)
FE = Segment(F, G)
FE': 12 / FE