Algodoo

This scene is a proof of concept for accurate global dimensional measurements made from overlapping local measurements. The local measurements are overlapping because the measurement value from the center (yellow circle) sensor is dependent on the two outer (red circle contacts). This results in overlapping simultaneous equations that share variables. This works for both x (tooth pitch) and y (tooth height), resulting in 24 simultaneous equations. The simultaneous equations are solved using the Gauss–Seidel method. This method can be used on racks and, with slight changes in design, spur gears, and face gears. It can also be used for one dimensional straightness or curvature of surface plates, machine beds, and curved surfaces.

Rev A: Made the calculation code more general.
Rev B: Redesigned measurement tool.