A Multibody Model for Riderless Bicycle Dynamics Considering Tire Characteristics

A multibody model for riderless bicycle dynamics considering tire characteristics is presented. A riderless bicycle is regarded as a multibody system consisting of four rigid bodies: rear wheel, frame, front fork, and front wheel. Every two bodies are connected with a revolute joint. The mass center coordinates and Euler angles of the rigid bodies are used as the generalized coordinates to describe their positions and orientations. The system equations of motion are obtained using Lagrange equations of the first kind. Due to the existence of the three revolute constraints and the use of dependent generalized coordinates, the Lagrange multipliers are employed to account for revolute reaction forces. As for the contact between the wheel and the ground, many studies regarded the wheel as a rigid body with a knife edge, which lead to the nonholonomic constraints between the wheel and the ground. However, this hypothesis may cause deviations when the bicycle travels at a high speed or takes a sharp turn. In reality, the tire is deformed due to the forces acting between the ground and the wheel which leads to the slip phenomenon and stiffness characteristic. To study the bicycle dynamics under extreme conditions better, a dynamic tire force model including the longitudinal slip, side slip, and camber force is presented. The resulting motion equations are differential-algebraic equations (DAEs) and the Baumgarte constraint stabilization method is used to solve the DAEs. Simulations according to different working conditions like accelerating and braking with tire properties are presented, where many interesting dynamic characteristics of the riderless bicycle are revealed.