Non-smooth dynamic modeling and simulation of an unmanned bicycle on a curved pavement

doi:10.1007/s10483-022-2811-5

Abstract

Abstract: The non-smooth dynamic model of an unmanned bicycle is established to study the contact-separate and stick-slip non-smooth phenomena between wheels and the ground. According to the Carvallo-Whipple configuration, the unmanned bicycle is reduced to four rigid bodies, namely, rear wheel, rear frame, front fork, and front wheel, which are connected by perfect revolute joints. The interaction between each wheel and the ground is simplified as the normal contact force and the friction force at the contact point, and these forces are described by the Hunt-Crossley contact force model and the LuGre friction force model, respectively. According to the characteristics of flat and curved pavements, calculation methods for contact forces and their generalized forces are presented. The dynamics of the system is modeled by the Lagrange equations of the first kind, a numerical solution algorithm of the dynamic equations is presented, and the Baumgarte stabilization method is used to restrict the drift of the constraints. The correctness of the dynamic model and the numerical algorithm is verified in comparison with the previous studies. The feasibility of the proposed model is demonstrated by simulations under different motion states.

Key words: unmanned bicycle, non-smooth dynamics, LuGre model, contact-impact, stick-slip

2010 MSC Number:

Kaiming ZHANG, Xudong ZHENG, Zhang CHEN, Bin LIANG, Tianshu WANG, Qi WANG. Non-smooth dynamic modeling and simulation of an unmanned bicycle on a curved pavement. Applied Mathematics and Mechanics (English Edition), 2022, 43(1): 93-112.

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