CONTENTS Acknowledgements vii 1 Introduction 1 2 Fundamental concepts, methods and classification 4 2.1 Introduction 4 2.2 Kinematics of linkages 10 2.3 Overconstrained linkages 17 2.4 Mechanisms and structures 33 3 Planar double chain linkages 36 3.1 Scissor-like elements and their assemblies 36 3.2 Closed double chain 40 3.3 Supports for double chains 52 3.4 Growth of a double chain 56 3.5 Conclusions 58 4 Spatial rings and domes 62 4.1 Introduction 62 4.2 Kings 64 4.3 Domes 70 4.4 Other design considerations 75 5 Spatial motion structures based on the Bennett linkage 77 5.1 Introduction 77 5.2 Single-layer assembly of Bennett linkages 77 5.3 Multi-layer assemblies of Bennett linkages 88 5.4 Alternative form of Bennett linkage 94 5.5 Physical model of alternative form of Bennett linkage 102 5.6 Assemblies of alternative form linkages 111 5.7 Applications 112 6 Spatial motion structures based on Bricard linkages 117 6.1 Threefold-symmetric Bricard linkages and its assemblies 117 6.2 Alternative forms of threefold-symmetric Bricard linkage 125 6.3 Line and plane symmetric Bricard linkage and its alternative forms 129 7 Layouts of spatial motion structures 136 7.1 Tilings and patterns 136 7.2 Layouts for the Bennett linkage 139 7.3 Assemblies of Myard linkages 145 7.4 Assemblies of threefold-symmetric Bricard linkages 149 7.5 Conclusion and discussion 151 Notes 153 References 154 Index 158