Rotational-Translational Couplings

Convert Between Rotational and Translation Motion

In general, mechanical systems mix rotational and translational motion. Rotational dynamics and motion about an axis couples to translational dynamics and motion (velocity v, momentum p, force F) at some distance (moment arm r) from the rotational pivot through a constraint that captures only motion normal to the moment arm.

While most driveline components involve rotational motion around fixed axes, certain key components transform translational and rotational motions from one to the other. Such components map motion along lines and motion around circles to one another.

The rack-and-pinion is an example of a mixed-motion gear constraint. Tires and propellers use contact friction to change driven rotational motion into forward or backward linear motion.

Use Simscape and Simscape Driveline Elements to Couple Rotation and Translation

Simscape™ and Simscape Driveline™ components that couple rotational and translational motion have mixed mechanical conserving ports of both rotational and translational type. Such blocks include wheels, tires, and certain gears:

For an example of rotational-translational coupling with Tire (Magic Formula), see the model in Complete Vehicle Model.