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Self-balanced unicycle has received the attention of researchers for decades. Over the years, unicycle models with several different assemblies have been introduced by them. A thorough analysis of the dynamics of a unicycle with a frame and a rotating disk is discussed in this research. A torque applied to the rolling wheel maintains the longitudinal stability of the system by moving forward and backward. The rotating disk mounted on the top of the frame maintains the lateral stability of the system by providing a torque. Due to this torque the rolling wheel precess and change its yaw direction. The components of the unicycle assembly are addressed separately for the analysis of the dynamics. First, only the rolling wheel considered. Then, the rolling wheel and the frame are analyzed. Finally, the completed assembly with the rotating disk considered to build the dynamics model. In each of these cases both Newton-Euler and Lagrangian methods are used to obtain the dynamics equations for the unicycle.
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.
Mechanical engineering, an engineering discipline born of the needs of the industrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound issues of productivity and competitiveness that require engineering solu tions, among others. The Mechanical Engineering Series features graduate texts and research monographs intended to address the need for informa tion in contemporary areas of mechanical engineering. The series is conceived as a comprehensive one that will cover a broad range of concentrations important to mechanical engineering graduate edu cation and research. We are fortunate to have a distinguished roster of consulting editors, each an expert in one of the areas of concentration. The names of the consulting editors are listed on the front page of the volume. The areas of concentration are applied mechanics, biomechanics, computa tional mechanics, dynamic systems and control, energetics, mechanics of material, processing, thermal science, and tribology. Professor Leckie, the consulting editor for applied mechanics, and I are pleased to present this volume of the series: Kinematic and Dynamic Simulation of Multibody Systems: The Real-Time Challenge by Professors Garcia de Jal6n and Bayo. The selection of this volume underscores again the interest of the Mechanical Engineering Series to provide our readers with topical monographs as well as graduate texts. Austin Texas Frederick F. Ling v The first author dedicates this book to the memory of Prof F. Tegerizo (t 1988), who introduced him to kinematics.
Formation Control of Multi-Agent Systems: A Graph Rigidity Approach Marcio de Queiroz, Louisiana State University, USA Xiaoyu Cai, FARO Technologies, USA Matthew Feemster, U.S. Naval Academy, USA A comprehensive guide to formation control of multi-agent systems using rigid graph theory This book is the first to provide a comprehensive and unified treatment of the subject of graph rigidity-based formation control of multi-agent systems. Such systems are relevant to a variety of emerging engineering applications, including unmanned robotic vehicles and mobile sensor networks. Graph theory, and rigid graphs in particular, provides a natural tool for describing the multi-agent formation shape as well as the inter-agent sensing, communication, and control topology. Beginning with an introduction to rigid graph theory, the contents of the book are organized by the agent dynamic model (single integrator, double integrator, and mechanical dynamics) and by the type of formation problem (formation acquisition, formation manoeuvring, and target interception). The book presents the material in ascending level of difficulty and in a self-contained manner; thus, facilitating reader understanding. Key features: Uses the concept of graph rigidity as the basis for describing the multi-agent formation geometry and solving formation control problems. Considers different agent models and formation control problems. Control designs throughout the book progressively build upon each other. Provides a primer on rigid graph theory. Combines theory, computer simulations, and experimental results. Formation Control of Multi-Agent Systems: A Graph Rigidity Approach is targeted at researchers and graduate students in the areas of control systems and robotics. Prerequisite knowledge includes linear algebra, matrix theory, control systems, and nonlinear systems.
The market demand for skills, knowledge and adaptability have positioned robotics to be an important field in both engineering and science. One of the most highly visible applications of robotics has been the robotic automation of many industrial tasks in factories. In the future, a new era will come in which we will see a greater success for robotics in non-industrial environments. In order to anticipate a wider deployment of intelligent and autonomous robots for tasks such as manufacturing, healthcare, ent- tainment, search and rescue, surveillance, exploration, and security missions, it is essential to push the frontier of robotics into a new dimension, one in which motion and intelligence play equally important roles. The 2010 International Conference on Intelligent Robotics and Applications (ICIRA 2010) was held in Shanghai, China, November 10–12, 2010. The theme of the c- ference was “Robotics Harmonizing Life,” a theme that reflects the ever-growing interest in research, development and applications in the dynamic and exciting areas of intelligent robotics. These volumes of Springer’s Lecture Notes in Artificial Intel- gence and Lecture Notes in Computer Science contain 140 high-quality papers, which were selected at least for the papers in general sessions, with a 62% acceptance rate Traditionally, ICIRA 2010 holds a series of plenary talks, and we were fortunate to have two such keynote speakers who shared their expertise with us in diverse topic areas spanning the rang of intelligent robotics and application activities.
This research is focused on improving the solutions obtained using theory in contact and impact modeling. A theoretical framework is developed which can simulate the performance of dynamic systems within a real world environment. This environment involves conditions, such as contact, impact and friction. Numerical simulation provides an easy way to perform numerous iterations with varying conditions, which is more cost effective than building equivalent experimental setups. The developed framework will serve as a tool for engineers and scientists to gain some insight on predicting how a system may behave. The current field of research in multibody system dynamics lacks a framework for modeling simultaneous, indeterminate contact and impact with friction. This special class of contact and impact problems is the major focus of this research. This research develops a framework, which contributes to the existing literature. The contact and impact problems examined in this work are indeterminate with respect to the impact forces. This is problematic because the impact forces are needed to determine the slip-state of contact and impact points. The novelty of the developed approach relies on the formation of constraints among the velocities of the impact points. These constraints are used to address the indeterminate nature of the collisions encountered. This approach strictly adheres to the assumptions of rigid body modeling in conjunction with the notion that the configuration of the system does not change in the short time span of the collision. These assumptions imply that the impact Jacobian is constant during the collision, which enforces a kinematic relationship between the impact points. The developed framework is used to address simultaneous, indeterminate contact and impact problems with friction. In the preliminary stages of this research, an iterative method, which incorporated an optimization function was used obtain the solutions for numerical solution to the collision. In an effort to improve the time and accuracy of the results, the iterative method was replaced with an analytical approach and implemented with the constraint formulation to achieve more energetically consistent solutions (i.e. there are no unusual gains in energy after the impact). The details of why this claim is valid will be discussed in more detail in this dissertation. The analytical framework was developed for planar contact and impact problems, while a numerical framework is developed for three-dimensional (3D) problems. The modeling of friction in 3D presents some challenging issues that are well documented in the literature, which make it difficult to apply an analytical framework. Simulations are conducted for a planar ball, planar rocking block problem, Newton's Cradle, 3D sphere, and 3D rocking block. Some examples serve as benchmark problems, in which the results are validated using experimental data.
This book presents suitable methodologies for the dynamic analysis of multibody mechanical systems with joints. It contains studies and case studies of real and imperfect joints. The book is intended for researchers, engineers, and graduate students in applied and computational mechanics.