10.2.2 Finding Equilibrium Velocity

To find the equilibrium velocity of a mechanism, a FreeSystem object is built that contains a new set of equations of motion with one or more constraints removed from the model.

Velocity equilibrium.

The driving constraint is dropped from the slider-crank model to give the model one degree of freedom.

This drops the constraint that controls rotation of the crank.

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This solves the FreeSystem object. Note that the angular velocity of the crank 2d is less than the driven angular velocity of 2 pi.

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To find the equilibrium velocity at a sequence of positions through a full cycle of the mechanism, the InitialCondition option is used to pass SolveFree a new set of initial conditions at each position where the equilibrium velocity is to be found. Thus, it is not necessary to create a new FreeSystem object for each solution point.

An option for SetFree and SolveFree.

This generates a list of 20 rules to be used as initial conditions for the equilibrium velocity solution.

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This solves the FreeSystem object at each initial condition in postab.

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Here is a plot of the equilibrium velocity of the crank through a full cycle of the mechanism.

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