Ebook: Geometric Design of Linkages

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 workpiece, 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 modelling of robotics and other articulated mechanical systems.

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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 workpiece, 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 modelling of robotics and other articulated mechanical systems.
Content:
Front Matter....Pages i-xxi
Introduction....Pages 1-12
Analysis of Planar Linkages....Pages 13-47
Graphical Synthesis in the Plane....Pages 48-68
Planar Kinematics....Pages 69-85
Algebraic Synthesis of Planar Chains....Pages 86-115
Analysis of Spherical Linkages....Pages 116-139
Spherical Kinematics....Pages 140-161
Algebraic Synthesis of Spherical Chains....Pages 162-188
Analysis of Spatial Chains....Pages 189-214
Spatial Kinematics....Pages 215-239
Algebraic Synthesis of Spatial Chains....Pages 240-265
Platform Manipulators....Pages 266-284
Back Matter....Pages 285-319

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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 workpiece, 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 modelling of robotics and other articulated mechanical systems.
Content:
Front Matter....Pages i-xxi
Introduction....Pages 1-12
Analysis of Planar Linkages....Pages 13-47
Graphical Synthesis in the Plane....Pages 48-68
Planar Kinematics....Pages 69-85
Algebraic Synthesis of Planar Chains....Pages 86-115
Analysis of Spherical Linkages....Pages 116-139
Spherical Kinematics....Pages 140-161
Algebraic Synthesis of Spherical Chains....Pages 162-188
Analysis of Spatial Chains....Pages 189-214
Spatial Kinematics....Pages 215-239
Algebraic Synthesis of Spatial Chains....Pages 240-265
Platform Manipulators....Pages 266-284
Back Matter....Pages 285-319
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