Spur & rack-and-pinion

Two spur gears meshing is the most basic gear relationship in existence: teeth count sets the speed ratio, and every mesh between two external gears reverses the direction of spin. A rack is simply a spur gear unrolled into a straight bar — meshing a pinion against it turns rotation into straight-line travel, which is how steering racks and 3D-printer axes work.

1. 1Set the driver gear's tooth count and speed. Watch the driven gear spin the opposite way, faster or slower depending on the ratio.
2. 2Switch to the rack view: the same pinion now pushes a straight bar. Its speed along the rack depends only on the pinion's radius and rotation speed.
3. 3Fewer teeth on the driver than the driven gear means torque goes up and speed goes down — and vice versa. You never get both for free.