6.2.1 2D Gear Constraints

The 2D gear constraints provided by Modeler2D cover three elementary cases of a gear-drive relationship. In each case, a simple rotational relationship is enforced between two bodies.

Two gear constraints.

Special gear constraints.

Each gear constraint requires an initial position constant to set the initial relative rotational positions of the two gears. Physically, the constant C specifies which gear teeth are mating when the gears are first assembled, on a continuum.
The following TwoGears2 constraint would be used to model a pair of gears with pitch radii of 4.0 and 6.0, respectively, and local origins at {0, 0}. This method of setting the initial position constant causes the two gears to have angular coordinates of zero simultaneously, regardless of the relative positions of the centers of the gears.
Note that using Angle[gear1, 0, gear2, 0] in the orientation constant would produce invalid results if the centers of the gears were to move relative to each other, because the orientation constant is not constant.

Here is an example of a gear constraint.

In[1]:=

Out[4]=

When an Euler solution method is used in a 2D model (Method -> Euler option for SetSymbols), an extra symbol must be added to the model to keep track of the gross rotations of each gear. This is because the degenerate Euler parameters can only uniquely represent rotations from 0 to 2 pi. The extra symbol can be generated automatically by SetConstraints, or it can be specified with an optional argument to each gear constraint.
These extra symbols, and their initial guesses, are analogous to the extra symbols introduced by all cam constraints and the Modeler2D gear constraints.

Optional arguments for gear constraints with the Euler method.

See the appendix for the optional arguments to other gear constraints.