Overview
- Presents a three-dimensional model of the complete unicycle–unicyclist system
- Provides an effective control strategy
- Includes full experimental verification
Part of the book series: SpringerBriefs in Applied Sciences and Technology (BRIEFSAPPLSCIENCES)
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Table of contents (4 chapters)
Keywords
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 aresolved 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.
Authors and Affiliations
Bibliographic Information
Book Title: Dynamics of the Unicycle
Book Subtitle: Modelling and Experimental Verification
Authors: Michał Niełaczny, Barnat Wiesław, Tomasz Kapitaniak
Series Title: SpringerBriefs in Applied Sciences and Technology
DOI: https://doi.org/10.1007/978-3-319-95384-7
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: The Author(s) 2019
Softcover ISBN: 978-3-319-95383-0Published: 16 July 2018
eBook ISBN: 978-3-319-95384-7Published: 02 July 2018
Series ISSN: 2191-530X
Series E-ISSN: 2191-5318
Edition Number: 1
Number of Pages: XI, 77
Number of Illustrations: 5 b/w illustrations, 34 illustrations in colour
Topics: Vibration, Dynamical Systems, Control, Classical Mechanics, Statistical Physics and Dynamical Systems, Biomechanics