Study on the generalized mathematical model of noncircular gears

The pitch curve of noncircular gears is usually determined by kinematical requirements such as position, velocity, and acceleration. However, it is usually difficult to obtain a tooth profile that complies with kinematical requirements. A Fourier series approximation method is proposed to approximate the pitch curve. Based on the approximated pitch curve, a mathematical model of the tooth profile of noncircular gears is derived. The proposed mathematical model is very flexible with sufficient accuracy and can also be used to process the reverse engineering problem of the existing noncircular gears.