SpringerBriefs in Applied Sciences and Technology

Dynamics of the Unicycle

Modelling and Experimental Verification

Authors: Niełaczny, Michał, Wiesław, Barnat, Kapitaniak, Tomasz

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  • Presents a three-dimensional model of the complete unicycle–unicyclist system
  • Provides an effective control strategy
  • Includes full experimental verification
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eBook $54.99
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  • ISBN 978-3-319-95384-7
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  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-319-95383-0
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  • Usually dispatched within 3 to 5 business days.
About this book

This book presents a three-dimensional model of the complete unicycle–unicyclist system. A unicycle with a unicyclist on it represents a very complex system. It combines Mechanics, Biomechanics and Control Theory into the system, and is impressive in both its simplicity and improbability. Even more amazing is the fact that most unicyclists don’t know that what they’re doing is, according to science, impossible – just like bumblebees theoretically shouldn’t be able to fly.

This book is devoted to the problem of modeling and controlling a 3D dynamical system consisting of a single-wheeled vehicle, namely a unicycle and the cyclist (unicyclist) riding it. The equations of motion are derived with the aid of the rarely used Boltzmann–Hamel Equations in Matrix Form, which are based on quasi-velocities. The Matrix Form allows Hamel coefficients to be automatically generated, and eliminates all the difficulties associated with determining these quantities. The equations of motion are solved by means of Wolfram Mathematica. To more faithfully represent the unicyclist as part of the model, the model is extended according to the main principles of biomechanics. The impact of the pneumatic tire is investigated using the Pacejka Magic Formula model including experimental determination of the stiffness coefficient.

The aim of control is to maintain the unicycle–unicyclist system in an unstable equilibrium around a given angular position. The control system, based on LQ Regulator, is applied in Wolfram Mathematica.

Lastly, experimental validation, 3D motion capture using software OptiTrack – Motive:Body and high-speed cameras are employed to test the model’s legitimacy. The description of the unicycle–unicyclist system dynamical model, simulation results, and experimental validation are all presented in detail.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-3-319-95384-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-319-95383-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Dynamics of the Unicycle
Book Subtitle
Modelling and Experimental Verification
Authors
Series Title
SpringerBriefs in Applied Sciences and Technology
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-95384-7
DOI
10.1007/978-3-319-95384-7
Softcover ISBN
978-3-319-95383-0
Series ISSN
2191-530X
Edition Number
1
Number of Pages
XI, 77
Number of Illustrations
5 b/w illustrations, 34 illustrations in colour
Topics