| Preface to the Second Edition |
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xiii | |
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xv | |
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1 | (8) |
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8 | (1) |
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Chapter 2 Compliances of Basic Flexible-Hinge Segments |
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9 | (64) |
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2.1 Straight-Axis Flexible-Hinge Segments |
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9 | (37) |
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2.1.1 Generic Compliances |
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10 | (4) |
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2.1.1.1 In-Plane Load, Displacement Vectors and Compliance Matrix |
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14 | (1) |
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2.1.1.2 Out-of-Plane Load, Displacement Vectors and Compliance Matrix |
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15 | (3) |
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2.1.2 Geometric Configurations |
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18 | (1) |
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2.1.2.1 Straight-Line Profile Segments |
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18 | (7) |
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2.1.2.2 Curvilinear-Profile Segments |
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25 | (21) |
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2.2 Curvilinear-Axis Flexible-Hinge Segments |
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46 | (15) |
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2.2.1 Generic Compliances |
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46 | (2) |
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2.2.1.1 In-Plane Compliances |
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48 | (2) |
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2.2.1.2 Out-of-Plane Compliances |
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50 | (3) |
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2.2.2 Geometric Configurations |
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53 | (1) |
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2.2.2.1 Circular-Axis Hinge Segment |
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53 | (3) |
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2.2.2.2 Elliptical-Axis Hinge Segment |
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56 | (2) |
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2.2.2.3 Parabolic-Axis Hinge Segment |
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58 | (1) |
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2.2.2.4 Corner-Filleted Hinge Segments |
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59 | (2) |
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Appendix A2 Closed-Form Compliances |
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61 | (10) |
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A2.1 Straight-Axis Segments |
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61 | (1) |
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A2.1.1 Rectangular Cross-Section of Constant Out-of-Plane Width w and Minimum In-Plane Thickness t |
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61 | (4) |
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A2.1.2 Circular Cross-Section |
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65 | (3) |
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A2.2 Curvilinear-Axis Segments of Constant Cross-Section |
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68 | (1) |
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A2.2.1 Circular-Axis Segment |
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68 | (1) |
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A2.2.2 Parabolic-Axis Segment |
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69 | (2) |
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71 | (2) |
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Chapter 3 Compliances of Straight-Axis Flexible Hinges |
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73 | (68) |
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3.1 Compliance Matrix Transformations |
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73 | (9) |
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3.1.1 Compliance Matrix Translation |
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73 | (1) |
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3.1.1.1 Series Connection |
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74 | (3) |
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3.1.1.2 Parallel Connection |
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77 | (1) |
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3.1.2 Compliance Matrix Rotation |
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78 | (1) |
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3.1.2.1 In-Plane Rotation |
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79 | (1) |
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3.1.2.2 Out-of-Plane Rotation |
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80 | (2) |
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3.2 Series-Connection Flexible Hinges |
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82 | (45) |
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3.2.1 Flexible Hinges without Transverse Symmetry |
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83 | (1) |
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3.2.1.1 Compliance Matrices through Addition and Rotation |
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83 | (6) |
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3.2.1.2 Geometric Configurations |
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89 | (2) |
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3.2.2 Transversely Symmetric Flexible Hinges |
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91 | (1) |
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3.2.2.1 Generic Compliance Matrices |
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91 | (7) |
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3.2.2.2 Hinge Configurations: Finite Element Confirmation of Analytical Compliances |
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98 | (11) |
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3.2.2.3 Hinge Configurations: Internal Comparison |
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109 | (8) |
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3.2.2.4 Two-Axis Flexible Hinges |
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117 | (6) |
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3.2.3 Folded, Spatially Periodic Flexible Hinges |
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123 | (4) |
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3.3 Parallel-Connection Flexible Hinges |
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127 | (8) |
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3.3.1 Two-Member Flexible Hinge with Symmetry Axis |
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129 | (1) |
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3.3.1.1 In-Plane Compliance Matrix |
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129 | (1) |
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3.3.1.2 Out-of-Plane Compliance Matrix |
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130 | (2) |
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3.3.2 Two-Member Flexible Hinge with Identical and Geometrically Parallel Segments |
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132 | (1) |
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3.3.3 The Crossed-Leaf Spring |
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133 | (2) |
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Appendix A3 Independent Closed-Form Compliances |
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135 | (3) |
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A3.1 Flexible Hinges of Rectangular Cross-Section with Constant Out-of-Plane Width w and Minimum In-Plane Thickness t |
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135 | (1) |
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A3.1.1 Right Circular Hinge |
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135 | (1) |
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A3.1.2 Right Elliptical Hinge |
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136 | (1) |
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A3.2 Flexible Hinges of Circular Cross-Section |
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137 | (1) |
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A3.2.1 Right Circular Hinge |
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137 | (1) |
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A3.2.2 Right Elliptical Hinge |
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137 | (1) |
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138 | (3) |
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Chapter 4 Compliances of Curvilinear-Axis Flexible Hinges |
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141 | (48) |
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4.1 Compliance Matrix Transformations |
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141 | (4) |
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4.1.1 In-Plane Compliances |
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142 | (1) |
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4.1.2 Out-of-Plane Compliances |
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143 | (2) |
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4.2 Series-Connection Flexible Hinges |
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145 | (34) |
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4.2.1 Compliance Matrices of Flexible Hinges without Symmetry |
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145 | (1) |
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4.2.1.1 In-Plane Compliance Matrix |
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146 | (1) |
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4.2.1.2 Out-of-Plane Compliance Matrix |
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146 | (2) |
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4.2.2 Compliance Matrices of Flexible Hinges with Symmetry Axis |
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148 | (1) |
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4.2.2.1 Generic Hinge and Compliance Matrices |
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149 | (4) |
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4.2.2.2 Flexible-Hinge Configurations |
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153 | (8) |
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4.2.3 Compliance Matrices of Flexible Hinges with Antisymmetry Axis |
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161 | (1) |
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4.2.3.1 Generic Hinge and Compliance Matrices |
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161 | (2) |
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4.2.3.2 Flexible-Hinge Configuration |
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163 | (4) |
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4.2.4 Folded Flexible Hinges |
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167 | (1) |
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4.2.4.1 Straight-Line (Rectangular) Envelope |
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168 | (4) |
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4.2.4.2 Curvilinear-Line Envelope |
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172 | (2) |
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4.2.4.3 Radial Folded Hinge with Rigid Connectors |
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174 | (5) |
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4.3 Parallel-Connection Flexible Hinges |
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179 | (7) |
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4.3.1 In-Plane Compliance Matrix |
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181 | (1) |
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4.3.2 Out-of-Plane Compliance Matrix |
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182 | (4) |
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186 | (3) |
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Chapter 5 Quasi-Static Response of Serial Flexible-Hinge Mechanisms |
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189 | (68) |
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5.1 Planar (2D) Mechanisms |
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190 | (58) |
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5.1.1 Serial Chain with One Flexible Hinge and One Rigid Link |
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190 | (1) |
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5.1.1.1 Rigid-Link Load and Displacement Transformation |
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190 | (4) |
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194 | (3) |
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5.1.1.3 Overconstrained Chains |
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197 | (5) |
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5.1.2 Multiple-Link, Flexible-Hinge Serial Chains |
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202 | (2) |
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5.1.2.1 Fixed-Free Chains |
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204 | (22) |
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5.1.2.2 Overconstrained Chains |
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226 | (8) |
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5.1.3 Displacement-Amplification Mechanisms Reducible to Serial Flexible Chains |
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234 | (1) |
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5.1.3.1 Mechanisms with Two Symmetry Axes |
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235 | (8) |
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5.1.3.2 Mechanisms with One Symmetry Axis |
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243 | (5) |
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5.2 Spatial (3D) Mechanisms |
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248 | (7) |
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5.2.1 Rigid-Link Load and Displacement Transformation |
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248 | (1) |
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249 | (1) |
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250 | (2) |
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5.2.2 Fixed-Free Serial Chain |
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252 | (3) |
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255 | (2) |
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Chapter 6 Quasi-Static Response of Parallel Flexible-Hinge Mechanisms |
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257 | (62) |
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6.1 Planar (2D) Mechanisms |
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257 | (54) |
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6.1.1 Load on Rigid Link Common to All Flexible Chains |
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258 | (1) |
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6.1.1.1 Suspension Mechanism with Two Identical, Symmetrical and Collinear, Straight-Axis Flexible Chains |
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259 | (3) |
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6.1.1.2 Folded Chains with Curvilinear-Axis Hinges |
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262 | (2) |
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6.1.1.3 Mechanisms with Identical, Symmetrical and Non-Collinear Flexible Chains |
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264 | (21) |
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6.1.2 Load on Rigid Link Common to All Flexible Chains and Loads on Flexible Chains |
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285 | (1) |
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6.1.2.1 Generic Compliance-Matrix Model |
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285 | (3) |
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6.1.2.2 Displacement-Amplification Mechanisms |
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288 | (11) |
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6.1.2.3 Mechanisms with Radial Symmetry - xyQ Stages |
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299 | (5) |
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6.1.3 Branched Flexible Planar Mechanisms and Substructuring |
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304 | (7) |
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6.2 Spatial (3D) Mechanisms |
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311 | (3) |
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314 | (5) |
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Chapter 7 Dynamics of Flexible-Hinge Mechanisms |
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319 | (78) |
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319 | (5) |
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7.1.1 Degrees of Freedom (DOF) |
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320 | (1) |
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7.1.2 Time-Domain Free Undamped Response |
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321 | (1) |
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7.1.3 Time-Domain Free Damped Response |
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322 | (1) |
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7.1.4 Time-Domain Forced Response |
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323 | (1) |
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7.1.5 Steady-State and Frequency-Domain Responses for Harmonic Forcing |
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324 | (1) |
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7.2 Inertia (Mass) Matrix |
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324 | (27) |
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7.2.1 Heavy Rigid Links and Massless Flexible Hinges |
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324 | (1) |
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7.2.2 Heavy Rigid Links and Heavy Flexible Hinges |
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325 | (1) |
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7.2.2.1 Fixed-Free Flexible Hinges |
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325 | (11) |
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7.2.2.2 Free-Free Flexible Hinges |
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336 | (15) |
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351 | (2) |
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7.3.1 Viscous Damping from Rigid Links |
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352 | (1) |
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7.3.2 Proportional Viscous Damping from Rigid Links and Flexible Hinges |
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352 | (1) |
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353 | (24) |
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7.4.1 Planar (2D) Mechanisms |
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353 | (1) |
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7.4.1.1 Fixed-Free Chain with One Flexible Hinge and One Rigid Link |
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353 | (5) |
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7.4.1.2 Fixed-Free Chain with Multiple Flexible Hinges and Rigid Links |
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358 | (8) |
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7.4.1.3 Overconstrained Chain with Multiple Flexible Hinges and Rigid Links |
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366 | (7) |
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7.4.2 Spatial (3D) Mechanisms |
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373 | (4) |
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377 | (17) |
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7.5.1 Planar (2D) Mechanisms |
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377 | (1) |
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7.5.1.1 Straight-Axis Chain with Two Identical Flexible Hinges and One Rigid Link |
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377 | (3) |
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7.5.1.2 Mechanisms with Multiple Single-Hinge Chains |
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380 | (3) |
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7.5.1.3 Mechanisms with Multiple Chains Formed of Serially Connected Rigid Links and Flexible Hinges |
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383 | (8) |
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7.5.2 Spatial (3D) Mechanisms |
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391 | (3) |
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394 | (3) |
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Chapter 8 Finite Element Analysis of Flexible-Hinge Mechanisms |
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397 | (74) |
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8.1 Straight-Axis Line Elements |
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397 | (25) |
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397 | (1) |
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398 | (3) |
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8.1.1.2 Torsional Loading |
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401 | (1) |
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402 | (8) |
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8.1.1.4 In-Plane and Out-of-Plane Element Matrices |
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410 | (3) |
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8.1.1.5 Inertia Matrices of Rigid Elements |
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413 | (3) |
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416 | (1) |
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8.1.2.1 Axial Effects and Torsion |
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416 | (2) |
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418 | (4) |
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8.2 Circular-Axis Line Elements |
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422 | (16) |
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8.2.1 Long Elements and the Euler-Bernoulli Model |
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422 | (1) |
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8.2.1.1 In-Plane Matrices |
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422 | (7) |
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8.2.1.2 Out-of-Plane Matrices |
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429 | (3) |
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8.2.2 Short Elements and the Timoshenko Model |
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432 | (1) |
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8.2.2.1 In-Plane Matrices |
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432 | (2) |
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8.2.2.2 Out-of-Plane Matrices |
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434 | (4) |
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8.3 Flexible-Hinge Mechanisms |
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438 | (28) |
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8.3.1 Global-Frame Element Stiffness and Inertia Matrices |
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438 | (1) |
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8.3.1.1 Straight-Axis Flexible Hinges |
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438 | (2) |
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8.3.1.2 Circular-Axis Flexible Hinges |
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440 | (2) |
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8.3.2 The Assembling Process |
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442 | (4) |
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8.3.3 Quasi-Static Response |
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446 | (13) |
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8.3.4 Natural Response and Frequencies |
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459 | (3) |
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8.3.5 Time-Domain Response |
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462 | (4) |
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466 | (5) |
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Chapter 9 Miscellaneous Topics |
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471 | (70) |
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9.1 Stress Concentration in Flexible Hinges and Flexible-Hinge Mechanisms |
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471 | (19) |
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9.1.1 Stress Concentrators |
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471 | (2) |
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9.1.2 In-Plane Stress Concentration |
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473 | (10) |
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9.1.3 Out-of-Plane Stress Concentration |
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483 | (7) |
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9.2 Rotation Precision of Flexible Hinges |
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490 | (5) |
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9.2.1 Straight-Axis Flexible Hinges |
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490 | (2) |
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9.2.2 Circular-Axis Flexible Hinges |
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492 | (3) |
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9.3 Flexible-Hinge Compliance Thermal Sensitivity |
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495 | (11) |
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9.3.1 Straight-Axis Flexible Hinges |
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495 | (1) |
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9.3.1.1 Rectangular Cross-Section |
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495 | (5) |
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9.3.1.2 Circular Cross-Section |
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500 | (1) |
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9.3.2 Circular-Axis Flexible Hinges |
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500 | (1) |
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9.3.2.1 Rectangular Cross-Section |
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501 | (5) |
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9.3.2.2 Circular Cross-Section |
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506 | (1) |
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9.4 Straight-Axis Layered Flexible Hinges |
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506 | (12) |
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9.4.1 Constant-Width Flexible Hinges with Transverse Geometry and Material Symmetry |
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507 | (5) |
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9.4.2 Constant-Thickness Flexible Hinges |
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512 | (6) |
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9.5 Piezoelectric Actuation and Sensing in Flexible-Hinge Mechanisms |
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518 | (19) |
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9.5.1 Active Layered (Piezoelectric) Flexible Hinges |
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519 | (1) |
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519 | (5) |
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524 | (3) |
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9.5.2 Block (Piezoelectric) Actuation and Sensing |
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527 | (1) |
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527 | (7) |
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534 | (3) |
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537 | (4) |
| Index |
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541 | |