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Mathematics of the Slider Cranks
>

1. Generic Slider Crank

This is the generic slider crank (**C02**):

In this picture a crank *CA* is constrained
to rotate
around the point *C*. Link *AB* is the connecting rod and *B
*is
the slider that slides along *CE*. We have fixed lengths *AC*
= *a * and *AB* = *b*. The length *CB*
= *x* varies as the crank is moved. When *CA* is rotating
around *C*
we can describe its position with respect to the angle
*ACB* =
that we measure from *CB*
counterclockwise from * CB* to *CA*.
How can we determine the length of *CB*,
when the crank is moving (that is, when *AC* is being rotated
around *C*)?

Let us use some geometry and basic trigonometry
here. Let us
construct *AD* perpendicular to* CB*; then, from the right
triangle *ACD*,
we can determine

.

Note that when
> 90° then *D*
is to the right
of *C* and *CD* is negative and
when
> 180°
then *A* is above
*CE* and *AD*
is negative.

Also, notice that

(*) .

By the Pythagorean Theorem,

.

Thus,

(**) .

Go to:

2. Inversions
of the Slider Crank (**C02**, **C05**, **D2**)

3. Offset
Slider Cranks (**D01**, **C04**)

4. Topological
Extensions of the Slider Crank (**D14**, **D07**, **D08**,
**C06**)