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Mathematics of the Slider Cranks
>

2. Inversions of the Slider Crank

Notice that the above analysis 1. Generic Slider Crank looks
at relative
positions and does not specify which part of the mechanism is grounded,
that is
held fixed so it cannot move. The different ways of grounding a
mechanism are
called *inversions *of the mechanism*. *The slider crank
has four
inversions that correspond to fixing (preventing from moving) either
the link *CE*,
the slider *B*, the link *CA*, or the link *AB*.** **

** **

**a. Fixing the link CE**.

This
is the inversion is illustrated in movies **C05**b
and C05. (Note that in C05 there is a circular slider
replacing the crank *CA*.)

In
this mode *CE* is held fixed and *A* rotates around *C*
along a
circle and *B* slides back and forth along *CE* according
to equation
(**) derived in 1. Generic
Slider Crank.

** **

**b. Fixing the slider B**.

This is the inversion of

In this
mode the slider *B* is held fixed and *CE* slides back and
forth thru
the slider according to Equation
(**). The point *A* is rotating back and forth along
an arc of
a circle with center at *B* and radius *b* with the angle
described by Equation (*).

**c. Fixing the
link CA**. In this mode

The slider *B *slides back and forth
along the
rotating *CE* according to Equation
(**). In polar coordinates (with the origin at *C*)
then the
position of *B* is described by **
.
**

**d. Fixing the
link AB. **

This
is the inversion (**D02**) pictured here. In this mode *A* and
*B*
are both held fixed but the slider is allowed to swivel. The position
of *C*
in polar coordinates (with center at *B*) is described by

**
**

**
**,

which, if we use (*) to express the angle in terms of , becomes

.

Go to:

1. Generic
Slider Crank (**C02**)

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

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