Theory for Worm and Wheel
The worm and wheel node connects a worm gear with a spur or helical gear in such a way that at the contact point they have no relative motion along the line of action. The remaining displacements and rotations of both the gears are independent of each other.
When friction is included on a worm and wheel node, frictional forces in the plane perpendicular to the line of action are added on both the gears.
Figure 3-14: Sketch of a worm and wheel pair where line of action is computed by the clockwise rotation of the tangent.
The degrees of freedom at the worm and wheel are θwm and θwh. They are defined as the rotation of the worm and wheel about the first axis of their respective local coordinate system.
Figure 3-15: The sketch of a worm and wheel pair where line of action is computed by the counterclockwise rotation of the tangent.
In the worm and wheel node, the configuration is always neither parallel nor intersecting and the contact model is point contact.
The rest of the theory for the worm and wheel node is similar to the Theory for Gear Pairs.
The gear pair node connects a wheel with pinion whereas the worm and wheel node connects a worm with wheel. To get worm and wheel node specific equations, replace wheel with worm and pinion with wheel everywhere.