The two-wheel balancing system of bicycle implies complex mechanical principles in rural roads and urban streets. As a typical dynamic balance mechanical system, its operation mechanism involves rigid body mechanics, kinematics and control theory and other multidisciplinary knowledge system.
I. Gyroscopic effect and conservation of angular momentum
The gyroscopic effect produced when the wheel rotates is an important factor in maintaining the stability of the vehicle. According to the principle of gyroscopic mechanics, the direction of the angular momentum vector of the rotating wheel follows the right-hand rule, when the vehicle is tilted, the gravitational moment will trigger the in-motion effect, prompting the front wheels to turn to the tilted direction automatically, forming a negative feedback adjustment mechanism. Experimental data show that when the wheel speed reaches 15rad/s, the gyroscopic effect can contribute about 60% of the stabilising moment. When the vehicle is travelling, it constitutes a three-point support structure: the front wheel grounding point (F), the rear wheel grounding point (R) and the cyclist’s centre of mass (G). The stability of this triangular structure depends on the position of the centre of mass projection relative to the support surface. By establishing the kinetic equations, it can be seen that the system is in quasi-static equilibrium when the moment equilibrium condition (M_F + M_R = M_G) is satisfied, and its critical tipping angle is about 12-15 degrees.
A chain drive system transfers force through a sprocket set. The transmission ratio of the standard 21-speed transmission system ranges from 0.7 to 3.2, of which the maximum ratio corresponds to the climbing condition and the minimum ratio is used for high-speed cruising. The energy transfer efficiency test shows that the mechanical efficiency of a good quality chain can reach 98%, while the efficiency of a worn chain link will drop to below 85%.
Tribological Characteristics
The interaction between the tyre and the ground involves static friction and rolling resistance. On dry roads, the coefficient of static friction can reach 0.8-1.0, providing the tangential force required for vehicle starting and braking. The rolling resistance coefficient is approximately 0.002-0.005 and is inversely proportional to tyre pressure. When the road adhesion coefficient is lower than 0.3, the vehicle is prone to skidding instability.
Third, dynamic control theory
The cycling process is essentially a nonlinear time-varying control system. The human body regulates the steering torque (T_δ) and centre of gravity offset (ΔG) through neural feedback to form a closed-loop control. Frequency response analysis shows that the intrinsic frequency of the system is about 0.8-1.2 Hz, and there is a coupling effect with the human step frequency, and this biomechanical synergy is the key to achieve stable cycling.
Modern bicycle engineering has developed multi-body dynamics models, and simulation software such as ANSYS can accurately calculate the stress distribution and modal characteristics under each working condition. However, these complex mathematical models all originate from the simplest physical phenomenon – the dynamic process of two rotating wheels finding equilibrium in a gravity field. This wisdom of transforming basic mechanical principles into practical vehicles is the essence of the fascination of engineering science.
Bicycle Dynamics Explained
