Screw Theory In Robotics

Screw theory is an effective and efficient method used in robotics applications. This book demonstrates how to implement screw theory, explaining the key fundamentals and real-world applications using a practical and visual approach. An essential tool for those involved in the development of robotics implementations, the book uses case studies to analyze mechatronics. Screw theory offers a significant opportunity to interpret mechanics at a high level, facilitating contemporary geometric techniques in solving common robotics issues. Using these solutions results in an optimized performance in comparison to algebraic and numerical options. Demonstrating techniques such as six-dimensional (6D) vector notation and the Product of Exponentials (POE), the use of screw theory notation reduces the need for complex algebra, which results in simpler code, which is easier to write, comprehend, and debug. The book provides exercises and simulations to demonstrate this with new formulas and algorithms presented to aid the reader in accelerating their learning. By walking the user through the fundamentals of screw theory, and by providing a complete set of examples for the most common robot manipulator architecture, the book delivers an excellent foundation through which to comprehend screw theory developments. The visual approach of the book means it can be used as a self-learning tool for professionals alongside students. It will be of interest to those studying robotics, mechanics, mechanical engineering, and electrical engineering.

Robots and Screw Theory describes the mathematical foundations, especially geometric, underlying the motions and force-transfers in robots. The principles developed in the book are used in the control of robots and in the design of their major moving parts. The illustrative examples and the exercises in the book are taken principally from robotic machinery used for manufacturing and construction, but the principles apply equally well to miniature robotic devices and to those used in other industries. The comprehensive coverage of the screw and its geometry lead to reciprocal screw systems for statics and instantaneous kinematics. These screw systems are brought together in a unique way to show many cross-relationships between the force-systems that support a body equivalently to a kinematic serial connection of joints and links. No prior knowledge of screw theory is assumed. The reader is introduced to the screw with a simple planar example yet most of the book applies to robots that move three-dimensionally. Consequently, the book is suitable both as a text at the graduate-course level and as a reference book for the professional. Worked examples on every major topic and over 300 exercises clarify and reinforce the principles covered in the text. A chapter-length list of references gives the reader source-material and opportunities to pursue more fully topics contained in the text.

The importance of screw theory in robotics is recognised but hardly capitalised on. Engineering students rarely get to learn about it in class, so only few postgraduates know how to exploit it. However, in a variety of areas of robotics, the methods and formalisms based on the geometry and algebra of the screws, have proven to be superior to other techniques.The idea of publishing this book came about because there were not enough specialised texts for teaching the screw theory methodologies and advantages through a set of visual and comprehensive examples.This illustrated handbook presents an abstract mathematical formulation for robot KINEMATICS based in the use of the screw theory tools, making an emphasis on modern geometric techniques. Its main objective is to demonstrate that many robotics problems addressed today only with numerical iterative solutions, are solved much better with closed-form geometric solutions based on screw theory.This book will surely spark your excitement about the technological and social prospects for robotics and enable you to develop effective and efficient robot algorithms, solutions and applications. In the end you will realise that, most of the time, a good theory is the fastest way to obtain a better performance, and the only thing you will have to do in exchange is put in some time and commitment in studying the screw theory.The contents of this handbook are used at the "Master in Robotics and Automation" of the UC3M (Universidad Carlos III de Madrid) by the Department of Systems Engineering and Automation.

This book describes the mathematical foundations, especially geometric, underlying the motions and force-transfers in robots. The principles developed can be applied to both control of robots and the design of their major moving parts. Comprehensive coverage of the screw and its geometry bridges the gap between screw theory and traditional mechanics but no prior knowledge of screw theory is assumed. The reader is introduced to the screw with a simple planar example and progresses to robots that move three-dimensionally. Containing many illustrative examples, over 300 exercises, and a chapter list of references it is ideal for graduate students, researchers and professionals in the field of robotics, robot design and development.

This book presents a finite and instantaneous screw theory for the development of robotic mechanisms. It addresses the analytical description and algebraic computation of finite motion, resulting in a generalized type synthesis approach. It then discusses the direct connection between topology and performance models, leading to an integrated performance analysis and design framework. The book then explores parameter uncertainty and multiple performance requirements for reliable, optimal design methods, and describes the error accumulation principle and parameter identification algorithm, to increase robot accuracy. It proposes a unified and generic methodology, and appliesto the invention, analysis, design, and calibration of robotic mechanisms. The book is intended for researchers, graduate students and engineers in the fields of robotic mechanism and robot design and applications./div

A modern and unified treatment of the mechanics, planning, and control of robots, suitable for a first course in robotics.

This work describes the mathematical foundations, especially geometric, underlying the motions and force-transfers in robots. The principles developed can be applied to both control of robots and the design of their major moving parts.

This book contains mechanism analysis and synthesis. In mechanism analysis, a mobility methodology is first systematically presented. This methodology, based on the author's screw theory, proposed in 1997, of which the generality and validity was only proved recently, is a very complex issue, researched by various scientists over the last 150 years. The principle of kinematic influence coefficient and its latest developments are described. This principle is suitable for kinematic analysis of various 6-DOF and lower-mobility parallel manipulators. The singularities are classified by a new point of view, and progress in position-singularity and orientation-singularity is stated. In addition, the concept of over-determinate input is proposed and a new method of force analysis based on screw theory is presented. In mechanism synthesis, the synthesis for spatial parallel mechanisms is discussed, and the synthesis method of difficult 4-DOF and 5-DOF symmetric mechanisms, which was first put forward by the author in 2002, is introduced in detail. Besides, the three-order screw system and its space distribution of the kinematic screws for infinite possible motions of lower mobility mechanisms are both analyzed.