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Author: J. M. McCarthy
Publisher: MIT Press (MA)
ISBN: 9780262132527
Category : Computers
Languages : en
Pages : 130
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Book Description
Introduction to Theoretical Kinematics provides a uniform presentation of the mathematical foundations required for studying the movement of a kinematic chain that makes up robot arms, mechanical hands, walking machines, and similar mechanisms. It is a concise and readable introduction that takes a more modern approach than other kinematics texts and introduces several useful derivations that are new to the literature. The author employs a unique format, highlighting the similarity of the mathematical results for planar, spherical, and spatial cases by studying them all in each chapter rather than as separate topics. For the first time, he applies to kinematic theory two tools of modern mathematics - the theory of multivectors and the theory of Clifford algebras - that serve to clarify the seemingly arbitrary nature of the construction of screws and dual quaternions. The first two chapters formulate the matrices that represent planar, spherical, and spatial displacements and examine a continuous set of displacements which define a continuous movement of a body, introducing the "tangent operator." Chapter 3 focuses on the tangent operators of spatial motion as they are reassembled into six-dimensional vectors or screws, placing these in the modern setting of multivector algebra. Clifford algebras are used in chapter 4 to unify the construction of various hypercomplex "quaternion" numbers. Chapter 5 presents the elementary formulas that compute the degrees of freedom or mobility, of kinematic chains, and chapter 6 defines the structure equations of these chains in terms of matrix transformations. The last chapter computes the quaternion form of the structure equations for ten specific mechanisms. These equations define parameterized manifolds in the Clifford algebras, or "image spaces," associated with planar, spherical, and spatial displacements. McCarthy reveals a particularly interesting result by showing that these parameters can be mathematically manipulated to yield hyperboloids or intersections of hyperboloids.
Author: J. M. McCarthy
Publisher: MIT Press (MA)
ISBN: 9780262132527
Category : Computers
Languages : en
Pages : 130
Get Book Here
Book Description
Introduction to Theoretical Kinematics provides a uniform presentation of the mathematical foundations required for studying the movement of a kinematic chain that makes up robot arms, mechanical hands, walking machines, and similar mechanisms. It is a concise and readable introduction that takes a more modern approach than other kinematics texts and introduces several useful derivations that are new to the literature. The author employs a unique format, highlighting the similarity of the mathematical results for planar, spherical, and spatial cases by studying them all in each chapter rather than as separate topics. For the first time, he applies to kinematic theory two tools of modern mathematics - the theory of multivectors and the theory of Clifford algebras - that serve to clarify the seemingly arbitrary nature of the construction of screws and dual quaternions. The first two chapters formulate the matrices that represent planar, spherical, and spatial displacements and examine a continuous set of displacements which define a continuous movement of a body, introducing the "tangent operator." Chapter 3 focuses on the tangent operators of spatial motion as they are reassembled into six-dimensional vectors or screws, placing these in the modern setting of multivector algebra. Clifford algebras are used in chapter 4 to unify the construction of various hypercomplex "quaternion" numbers. Chapter 5 presents the elementary formulas that compute the degrees of freedom or mobility, of kinematic chains, and chapter 6 defines the structure equations of these chains in terms of matrix transformations. The last chapter computes the quaternion form of the structure equations for ten specific mechanisms. These equations define parameterized manifolds in the Clifford algebras, or "image spaces," associated with planar, spherical, and spatial displacements. McCarthy reveals a particularly interesting result by showing that these parameters can be mathematically manipulated to yield hyperboloids or intersections of hyperboloids.
Author: O. Bottema
Publisher: Courier Corporation
ISBN: 0486663469
Category : Science
Languages : en
Pages : 594
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Book Description
Classic, comprehensive treatment covers Euclidean displacements; instantaneous kinematics; two-position, three-position, four-and-more position theory; special motions; multiparameter motions; kinematics in other geometries; and special mathematical methods.
Author: Oleg Vinogradov
Publisher: CRC Press
ISBN: 1420042335
Category : Science
Languages : en
Pages : 306
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Book Description
The study of the kinematics and dynamics of machines lies at the very core of a mechanical engineering background. Although tremendous advances have been made in the computational and design tools now available, little has changed in the way the subject is presented, both in the classroom and in professional references. Fundamentals of Kinematics and Dynamics of Machines and Mechanisms brings the subject alive and current. The author's careful integration of Mathematica software gives readers a chance to perform symbolic analysis, to plot the results, and most importantly, to animate the motion. They get to "play" with the mechanism parameters and immediately see their effects. The downloadable resources contain Mathematica-based programs for suggested design projects. As useful as Mathematica is, however, a tool should not interfere with but enhance one's grasp of the concepts and the development of analytical skills. The author ensures this with his emphasis on the understanding and application of basic theoretical principles, unified approach to the analysis of planar mechanisms, and introduction to vibrations and rotordynamics.
Author: J. Michael McCarthy
Publisher: Springer Science & Business Media
ISBN: 1441978925
Category : Science
Languages : en
Pages : 466
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Book Description
This book is an introduction to the mathematical theory of design for articulated mechanical systems known as linkages. The focus is on sizing mechanical constraints that guide the movement of a work piece, or end-effector, of the system. The function of the device is prescribed as a set of positions to be reachable by the end-effector; and the mechanical constraints are formed by joints that limit relative movement. The goal is to find all the devices that can achieve a specific task. Formulated in this way the design problem is purely geometric in character. Robot manipulators, walking machines, and mechanical hands are examples of articulated mechanical systems that rely on simple mechanical constraints to provide a complex workspace for the end- effector. The principles presented in this book form the foundation for a design theory for these devices. The emphasis, however, is on articulated systems with fewer degrees of freedom than that of the typical robotic system, and therefore, less complexity. This book will be useful to mathematics, engineering and computer science departments teaching courses on mathematical modeling of robotics and other articulated mechanical systems. This new edition includes research results of the past decade on the synthesis of multi loop planar and spherical linkages, and the use of homotopy methods and Clifford algebras in the synthesis of spatial serial chains. One new chapter on the synthesis of spatial serial chains introduces numerical homotopy and the linear product decomposition of polynomial systems. The second new chapter introduces the Clifford algebra formulation of the kinematics equations of serial chain robots. Examples are use throughout to demonstrate the theory.
Author: Jens Wittenburg
Publisher: Springer
ISBN: 3662484870
Category : Technology & Engineering
Languages : en
Pages : 697
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Book Description
The book deals with kinematics of mechanisms. It focuses on a solid theoretical foundation and on mathematical methods applicable to the solution of problems of very diverse nature. Applications are demonstrated in a large number of fully worked-out problems. In kinematics a wide variety of mathematical tools is applicable. In this book, wherever possible vector equations are formulated instead of lengthy scalar coordinate equations. The principle of transference is applied to problems of very diverse nature. 15 chapters of the book are devoted to spatial kinematics and three chapters to planar kinematics. In Chapt. 19 nonlinear dynamics equations of motion are formulated for general spatial mechanisms. Nearly one half of the book is dealing with position theory and the other half with motion. The book is intended for use as reference book for researchers and as textbook in advanced courses on kinematics of mechanisms.
Author: Constantine Pozrikidis
Publisher: Oxford University Press
ISBN: 0199752079
Category : Computers
Languages : en
Pages : 1274
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Book Description
This book discusses the fundamental principles and equations governing the motion of incompressible Newtonian fluids, and simultaneously introduces numerical methods for solving a broad range of problems. Appendices provide a wealth of information that establishes the necessary mathematical and computational framework.
Author: Stephen Childress
Publisher: American Mathematical Soc.
ISBN: 0821848887
Category : Science
Languages : en
Pages : 218
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Book Description
This book gives an overview of classical topics in fluid dynamics, focusing on the kinematics and dynamics of incompressible inviscid and Newtonian viscous fluids, but also including some material on compressible flow. The topics are chosen to illustrate the mathematical methods of classical fluid dynamics. The book is intended to prepare the reader for more advanced topics of current research interest.
Author: Cho W. S. To
Publisher: Morgan & Claypool Publishers
ISBN: 1681731878
Category : Technology & Engineering
Languages : en
Pages : 198
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Book Description
Introduction to Kinematics and Dynamics of Machinery is presented in lecture notes format and is suitable for a single-semester three credit hour course taken by juniors in an undergraduate degree program majoring in mechanical engineering. It is based on the lecture notes for a required course with a similar title given to junior (and occasionally senior) undergraduate students by the author in the Department of Mechanical Engineering at the University of Calgary from 1981 and since 1996 at the University of Nebraska, Lincoln. The emphasis is on fundamental concepts, theory, analysis, and design of mechanisms with applications. While it is aimed at junior undergraduates majoring in mechanical engineering, it is suitable for junior undergraduates in biological system engineering, aerospace engineering, construction management, and architectural engineering.
Author: C. H. Chiang
Publisher:
ISBN: 9781575241555
Category : Links and link-motion
Languages : en
Pages : 0
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Book Description
This text describes examples of the spherical mechanism that are seen in everyday life, such as the universal joint, a swiveling electric fan and a pair of bevel gears. The subject has received massive impetus from robotics, where many of the results of the theory find their application.
Author: William Rees Sears
Publisher: Amer Inst of Aeronautics &
ISBN: 9781600867736
Category : Science
Languages : en
Pages : 203
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Book Description
Formally published for the first time, Professor William R. Sears classic work, "Introduction to Theoretical Aerodynamics and Hydrodynamics, "reflects many years of continual evolution as a course study guide at the Graduate School of Aeronautical Engineering at Cornell University, with updates prepared by his former students to enhance ease of use by todays students. Instructors will find this a superb textbook for a first course in ideal aerodynamics and/or hydrodynamics. Because Sears was a master of connecting mathematical concepts with physical fluid dynamic quantities, readers will find fundamental concepts directly connected to practical applications in the numerous step-by-step examples found throughout the book. SPECIAL FEATURES
