Abstract
Bicycles are driven by manpower, therefore, the brake safety is considered to be the most crucial index for high-quality bicycles. This paper focused on establishing mathematical model and then conducting parametric analysis of the riding dynamics for both rigid and fully suspended bicycle frames. The key factors for improving the brake performance of a bicycle can be obtained from the analyses of various friction coefficients of road surfaces, the types of bicycle frames, and the methods of brake forces applied. This paper employed the linear motion (1D), 2-D and 3-D turning conditions to establish the physical models of riding dynamics of the rigid bicycle frame and then derive the mathematical equations, which was used as a foundation of parametric analysis for linear brake and turning movement. Regarding the analysis of a fully suspended bicycle, a theoretical model that consisted of a front wheel, a rear wheel and a frame equipped with suspensions was established first. After that, the Lagrange method was used to derive the equations of motion for the bicycle, which led to the analysis of various riding parameters. Regarding the simulation and analysis of brake safety, the issues of riding and brake safety on rigid and fully suspended bicycles were discussed based on the results derived from the theoretical derivation. In the paper, the distribution curve of ideal brake force was used to obtain the optimal ratio of braking force for front and rear wheels, so ideal synchronization brake could be achieved and the brake performance of a bicycle could be improved. In addition, the simulation of dynamic response to linear riding of suspension bicycle also used the concept of ideal synchronization brake to improve the difficulty of excessive brake force. Discussion was implemented on braking force for front and rear wheels in using time delay during applying brake force, which prevents dead lock on one wheel. The simulation results obtained can be used as reference of practical engineering design on the ideal synchronization brake.