Chapter 6
Solving Algebraic Equations with
C/C++
Background
, A 4bar linkage is a complex mechanism that allows us to convert simple rota
tional input motions (say from a motor or water wheel) to a wide variety of output motions.
The conﬁguration above is known as a
rockercrank
where complete turns of the crank or input
result in a rocking motion in the output link. But how do we determine what input angle maps
to a desired output angle? Consider a general 4bar linkage with the following geometries:
Given the above link lengths and angles, we can derive the relationship between the input angle
and output angle using vector analysis. Consider vectors deﬁned along each link such that:
~a
+
~
b
=
~
c
+
~
d
71
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View Full DocumentCHAPTER 6. SOLVING ALGEBRAIC EQUATIONS WITH C/C++
72
Figure 6.1: A 4bar linkage with input alpha, output beta, and link lengths a, b, c, and d.
We can expand this relationship and ﬁnd that:
a
sin(
α
) +
b
sin(
γ
) =
c
sin(
β
)
a
cos(
α
) +
b
cos(
γ
) =
d
+
c
cos(
β
)
Rearranging.
...
b
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 Fall '08
 Unknown
 Bisection Method, 4 Bar, 0.1 degrees

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