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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 C05b 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 C02 pictured here.
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 C
and A are both held fixed and the link CE rotates in a
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
1. Generic Slider Crank (C02)
3. Offset Slider Cranks (D01, C04)
4. Topological Extensions of the Slider Crank (D14, D07, D08, C06)