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David W. Henderson and Daina Taimina
In this picture is the 4bar linkage of model C01
with the link of length 100 held fixed.. Reuleaux designed a stand that
made it possible to hold fixed any of the other three links  the
results are different motions. These different positions of the
C01 linkage are called inversions.
Below we explore the geometry of these four inversions of C01.
First Inversion


See 4bar linkages for a discussion of the eight main types of 4bar linkages. Using the notation from 4bar linkages, we have g = 100, a = 30, h = 94, and b = 39. Thus,
b+h = 133 > 130 = a+g and ag = 70 > 55 = bh
a+h = 124 < 139 = b+g and bg = 61 < 64 = ah.
From the chart in 4bar linkages we have that this is a crankrocker, which means that the input link (on the left) can rotate completely around but the output link on the right will rock back and forth between
and
.


In this inversion fix the link of length 30 as the fixed link g and consider the link of length 94 as the input link a. (The crank handle on the mechanism will no longer function as a crank in this inversion.) We then have g = 30, a = 94, h = 39, and b = 100. Thus,
b+h = 139 > 124 = a+g and ag = 64 > 61 = bh
a+h = 133 > 130 = b+g and bg = 70 > 55 = ah.
From the chart in 4bar linkages we have that this is a double crank, which means that both the input link (length 94) and the output link (length 100) can rotate completely around.
In this inversion fix the link of length 94 as the fixed link g and consider the link of length 39 as the input link a. We then have g = 94, a = 39, h = 100, and b = 30. Thus,
b+h = 130 < 133 = a+g and ag = 55 < 70 = bh
a+h = 139 > 124 = b+g and bg = 64 > 61 = ah.
From the chart in 4bar linkages we have that this is a rockercrank, which means that the output link (length 30) can rotate completely around but the input link (length 39) will rock back and forth between
and
.


In this inversion fix the link of length 39 as the
fixed
link g and consider the link of length 100 as the input link a.
We then have g = 39, a
= 100, h =
30, and b = 94. Thus,
b+h = 124 < 139 = a+g and ag = 61 < 64 = bh
a+h = 130 < 133 = b+g and bg = 55 < 70 = ah.
From the chart in 4bar linkages we have that this is a double crank, which means that both the input link (length 94) and the output link (length 100) can rotate completely around.