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."

This volume gathers the latest fundamental research contributions, innovations, and applications in the field of design and analysis of complex robotic mechanical systems, machines, and mechanisms, as presented by leading international researchers at the 1st USCToMM Symposium on Mechanical Systems and Robotics (USCToMM MSR 2020), held in Rapid City, South Dakota, USA on May 14-16, 2020. It covers highly diverse topics, including soft, wearable and origami robotic systems; applications to walking, flying, climbing, underground, swimming and space systems; human rehabilitation and performance augmentation; design and analysis of mechanisms and machines; human-robot collaborative systems; service robotics; mechanical systems and robotics education; and the commercialization of mechanical systems and robotics. The contributions, which were selected by means of a rigorous international peer-review process, highlight numerous exciting and impactful research results that will inspire novel research directions and foster multidisciplinary research collaborations among researchers from around the globe.

21st Century Kinematics focuses on algebraic problems in the analysis and synthesis of mechanisms and robots, compliant mechanisms, cable-driven systems and protein kinematics. The specialist contributors provide the background for a series of presentations at the 2012 NSF Workshop. The text shows how the analysis and design of innovative mechanical systems yield increasingly complex systems of polynomials, characteristic of those systems. In doing so, it takes advantage of increasingly sophisticated computational tools developed for numerical algebraic geometry and demonstrates the now routine derivation of polynomial systems dwarfing the landmark problems of even the recent past. The 21st Century Kinematics workshop echoes the NSF-supported 1963 Yale Mechanisms Teachers Conference that taught a generation of university educators the fundamental principles of kinematic theory. As such these proceedings will provide admirable supporting theory for a graduate course in modern kinematics and should be of considerable interest to researchers in mechanical design, robotics or protein kinematics or who have a broader interest in algebraic geometry and its applications.

This volume gathers the latest fundamental research contributions, innovations, and applications in the field of design and analysis of complex robotic mechanical systems, machines, and mechanisms, as presented by leading international researchers at the 2nd USCToMM Symposium on Mechanical Systems and Robotics (USCToMM MSR), held in Rapid City, South Dakota, USA on May 19-21, 2022. It covers highly diverse topics, including soft, wearable and origami robotic systems; applications to walking, flying, climbing, underground, swimming and space systems; human rehabilitation and performance augmentation; design and analysis of mechanisms and machines; human-robot collaborative systems; service robotics; mechanical systems and robotics education; and the commercialization of mechanical systems and robotics. The contributions, which were selected by means of a rigorous international peer-review process, highlight numerous exciting and impactful research results that will inspire novel research directions and foster multidisciplinary research collaborations among researchers from around the globe.

This volume gathers the latest fundamental research contributions, innovations, and applications in the field of design and analysis of complex robotic mechanical systems, machines, and mechanisms, as presented by leading international researchers at the 1st USCToMM Symposium on Mechanical Systems and Robotics (USCToMM MSR 2020), held in Rapid City, South Dakota, USA on May 14-16, 2020. It covers highly diverse topics, including soft, wearable and origami robotic systems; applications to walking, flying, climbing, underground, swimming and space systems; human rehabilitation and performance augmentation; design and analysis of mechanisms and machines; human-robot collaborative systems; service robotics; mechanical systems and robotics education; and the commercialization of mechanical systems and robotics. The contributions, which were selected by means of a rigorous international peer-review process, highlight numerous exciting and impactful research results that will inspire novel research directions and foster multidisciplinary research collaborations among researchers from around the globe.

21st Century Kinematics focuses on algebraic problems in the analysis and synthesis of mechanisms and robots, compliant mechanisms, cable-driven systems and protein kinematics. The specialist contributors provide the background for a series of presentations at the 2012 NSF Workshop. The text shows how the analysis and design of innovative mechanical systems yield increasingly complex systems of polynomials, characteristic of those systems. In doing so, it takes advantage of increasingly sophisticated computational tools developed for numerical algebraic geometry and demonstrates the now routine derivation of polynomial systems dwarfing the landmark problems of even the recent past. The 21st Century Kinematics workshop echoes the NSF-supported 1963 Yale Mechanisms Teachers Conference that taught a generation of university educators the fundamental principles of kinematic theory. As such these proceedings will provide admirable supporting theory for a graduate course in modern kinematics and should be of considerable interest to researchers in mechanical design, robotics or protein kinematics or who have a broader interest in algebraic geometry and its applications.

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.

This volume gathers the latest fundamental research contributions, innovations, and applications in the field of design and analysis of complex robotic mechanical systems, machines, and mechanisms, as presented by leading international researchers at the 2nd USCToMM Symposium on Mechanical Systems and Robotics (USCToMM MSR), held in Rapid City, South Dakota, USA on May 19-21, 2022. It covers highly diverse topics, including soft, wearable and origami robotic systems; applications to walking, flying, climbing, underground, swimming and space systems; human rehabilitation and performance augmentation; design and analysis of mechanisms and machines; human-robot collaborative systems; service robotics; mechanical systems and robotics education; and the commercialization of mechanical systems and robotics. The contributions, which were selected by means of a rigorous international peer-review process, highlight numerous exciting and impactful research results that will inspire novel research directions and foster multidisciplinary research collaborations among researchers from around the globe.