Roulettes of the Fixed Axis Gear Trains and Their Application in Machining Polygon Prisms

The mathematic model of the roulettes of a fixed axis gear train composed of a couple of gears by transforming coordinates is built firstly, and a series of roulettes are drawn, then the factors which influence their characteristics and shapes are found. The mathematic model of the roulettes of a general fixed axis gear trains is built according to the transmission characteristics of the fixed axis gear train. Parts can be machined to polygon prisms by the property of roulettes that their central shapes are regular polygon prisms if tolerance is permitted. A square is given as an example to analyze error. An experiment and the prototype of its control system are shown in the end