Compared with the single pin crawler, a double pin caterpillar platform has lower vibration and noise, which is widely used in tracked vehicles. However, its dynamical model is more complex due to its high degrees of freedom and laborious contact detection involved. It is significant to develop an accurate and efficient contact algorithm between tracks and wheels. In this paper, the profiles of the track connector and the tooth groove are discretized into several arc surfaces. The contact between them is characterized as convex and concave. Accordingly, a general mathematical description of the tooth profile is established to describe the real tooth groove geometry. Then a generalized cylindrical contact model is developed to evaluate forces. In the contact detection process, the local frames of the sprocket and tooth groove are employed, resulting in the vector quantities and coordinate transformations describing the contact arc surfaces constantly. This approach can facilitate programming and effectively improve calculation efficiency. Subsequently, a field test was performed to verify the correctness of the dynamical model. To reduce the wear of the sprocket, different cases are simulated, and a reasonable radius of the rubber ring is proposed.