英國自行車動力學與控制dissertationBicycle Dynamics and Control

Introduction

This paper treats bicycles from the perspective of control. Models of differentcomplexity are presented starting with simple ones and ending with more real-istic models generated from multibody software. Models that capture essentialbehavior such as self-stabilization and demonstrate the dif?culties with rearwheel steering are presented. Experiences of using bicycles in control educationare presented with suggestions for fun and thought-provoking experiments withproven student attraction. The paper also describes design of adapted bicyclesfor children with disabilities and clinical experiences of their use.The bicycle is used everywhere, for transportation, exercise, and recreation.The bicycle’s evolution over time was a product of necessity, ingenuity, materi-als, industrialization, invention, imagination, and yet with comparatively littletheoretical insight. The bicycle is ef?cient, highly maneuverable, and yet it rep-resents a tantalizing enigma. Learning to ride a bicycle is an acquired skill,often acquired with some dif?culty, and yet once mastered the skill becomes subconscious and second nature, literally just "as easy as riding a bike."Bicycles have interesting dynamic behavior. They are statically unstable, likeinverted pendulums, but can under certain conditions be stable in forward mo-tion. They also exhibit non-minimum phase steering behavior. There are alsononlinearities due to geometry and tire-road interactions.Bicycles have intrigued scientists ever since they appeared in the middle ofthe nineteenth century and there is a considerable literature on bicycles. Thebook by Sharp is a classic from 1896 that has recently been reprinted [1], thebooks [2], [3] give a broad engineering perspective. There are early papers fromthe 19th century [4] - [8]. Famous scientists like Rankine [4], Klein and Som-merfeld have analyzed bicycles [9]. It is notable that Klein and Sommerfeld wereparticularly interested in the effect of gyroscopic action of the front wheel. Pa-pers on bicycles appear regularly in literature [10] - [22]. The ?rst publicationsof differential equations describing the motion of an idealized bicycle appearedtowards the end of the 19th century. Notable are Whipple [7], Carvallo [8], [23],who derived equations of motion, linearized around the vertical equilibrium con-?guration, from Lagranges equations. During the early 20th century severalauthors studied the problems of bicycle self stability, balancing, and steering thebicycle, with variable success. The paper [24] presented one of the ?rst computersimulations of a nonlinear bicycle model. Neˇ?mark and Fufaev [25] derived acomprehensive set of linear models by approximating potential and kinetic en-ergy by quadratic terms and applying Lagrange’s equations to these expressions.They used different wheel models, ideal disks as well as pneumatic tires. Theirmodel is elaborated in the book [26]. Modeling of bicycles became a popular topicfor dissertations in the later half of the last century, [27] - [33]. Simple models ofbicycle dynamics are given in the text books [34], [35] and [36]. Nonlinear modelsare presented in [21], [37], [38] and [39].#p#分頁標題#e#

Geometry and Coordinate Systems

Simple Second Order Models
Rear-wheel Steering
Bicycles in Education
ManeuveringBicycles in EducationAdapted Bicycles for Teaching Children with Disabilities
More Complicated Models
Conclusions

1. References

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