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1 Kinematics of Rigid Bodies |
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1 | (60) |
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1.1 Position and Displacement of a Point |
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1 | (7) |
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1.1.1 The Function arctan2 |
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1 | (1) |
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1.1.2 Points in Cartesian Coordinates |
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2 | (1) |
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1.1.3 Points in Cylindrical Coordinates |
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3 | (2) |
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1.1.4 Points in Spherical Coordinates |
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5 | (3) |
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1.2 Pose and Displacement of a Body |
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8 | (5) |
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8 | (1) |
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1.2.2 Finite Displacement of a Body |
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9 | (3) |
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1.2.3 Continuous Displacement of a Body |
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12 | (1) |
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1.3 Operations in Vector Space |
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13 | (13) |
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18 | (7) |
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25 | (1) |
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1.4 Sequences of Translations and Rotations |
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26 | (3) |
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1.4.1 Rotation Before Translation |
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26 | (1) |
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1.4.2 Translation Before Rotation |
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27 | (1) |
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28 | (1) |
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1.5 Position and Orientation of a Body |
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29 | (9) |
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1.5.1 Rotation Angle and Vector |
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29 | (2) |
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1.5.2 The Angles Between Pairs of Coordinate Axes |
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31 | (1) |
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1.5.3 Euler Orientation Angles |
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32 | (2) |
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1.5.4 Orientation Angles YPR |
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34 | (2) |
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1.5.5 Invariants of Rotation Matrices |
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36 | (2) |
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1.6 Linear and Angular Velocity of a Body |
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38 | (8) |
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1.6.1 Rotation Before Translation |
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38 | (2) |
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1.6.2 Translation Before Rotation |
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40 | (2) |
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1.6.3 Angular Velocity and Time Derivatives of the Euler Angles |
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42 | (2) |
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1.6.4 Angular Velocity and Time Derivatives of the YPR Angles |
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44 | (2) |
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1.7 Linear and Angular Acceleration of a Body |
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46 | (5) |
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1.7.1 Rotation Before Translation |
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46 | (2) |
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1.7.2 Translation Before Rotation |
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48 | (1) |
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1.7.3 Angular Acceleration and Time Derivatives of the Euler Angles |
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49 | (1) |
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1.7.4 Angular Acceleration and Time Derivatives of the YPR Angles |
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50 | (1) |
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1.8 Homogeneous Transformations |
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51 | (10) |
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1.8.1 Rotation Before Translation |
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52 | (3) |
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1.8.2 Translation Before Rotation |
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55 | (2) |
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1.8.3 Characteristics of a Planar Motion |
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57 | (4) |
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61 | (30) |
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2.1 Joints and Degrees of Freedom |
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62 | (12) |
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62 | (3) |
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2.1.2 Types of Mechanisms |
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65 | (6) |
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2.1.3 Degrees of Freedom in Mechanisms |
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71 | (3) |
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2.2 Parameters and Variables of a Kinematic Pair |
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74 | (7) |
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2.2.1 Cylindrical Joint in a Cartesian Space |
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75 | (1) |
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2.2.2 Scalar Parameters of a Kinematic Pair |
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76 | (2) |
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2.2.3 Vector Parameters of a Kinematic Pair |
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78 | (3) |
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2.3 Parameters and Variables of a Mechanism |
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81 | (10) |
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2.3.1 Denavit and Hartenberg Parameters of a Mechanism |
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82 | (3) |
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2.3.2 Vector Parameters of a Mechanism |
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85 | (6) |
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91 | (60) |
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92 | (29) |
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3.1.1 Orientation and Position of a Mechanism |
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92 | (8) |
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3.1.2 Angular and Translational Velocities of a Mechanism |
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100 | (10) |
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3.1.3 Angular and Translational Accelerations of a Mechanism |
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110 | (11) |
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121 | (9) |
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3.2.1 Equations of Direct Kinematics |
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122 | (1) |
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123 | (5) |
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128 | (2) |
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130 | (18) |
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3.3.1 Algebraic Solutions to the Inverse Kinematics Problem |
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137 | (4) |
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3.3.2 Numerical Solutions to the Inverse Kinematics Problem |
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141 | (7) |
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3.4 Serial Mechanisms with Fixed Rotational Axes |
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148 | (3) |
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4 Evaluation of Mechanisms |
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151 | (34) |
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151 | (17) |
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4.1.1 Reachable Workspace |
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152 | (4) |
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4.1.2 Determination of Reachable Workspace Based on Direct Kinematics |
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156 | (2) |
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4.1.3 Determination of Reachable Workspace Based on Inverse Kinematics |
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158 | (4) |
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4.1.4 Dexterous Workspace |
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162 | (2) |
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4.1.5 Selection of Mechanism with a Desired Workspace |
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164 | (4) |
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4.2 Kinematic Flexibility and Kinematic Singularity |
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168 | (10) |
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4.2.1 Kinematic Flexibility |
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169 | (2) |
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4.2.2 Kinematic Singularity |
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171 | (7) |
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4.3 Manipulability and Kinematic Index |
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178 | (7) |
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5 Singular Planes and Dexterous Robot Mechanisms |
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185 | (22) |
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5.1 Decoupled Singularities of Robots with Spherical Wrists |
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186 | (1) |
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5.2 Singularities of Serial Robot Arms |
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187 | (13) |
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5.2.1 Singular Planes of the Articulated Arm |
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187 | (5) |
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5.2.2 Singular Planes of the Spherical Arm |
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192 | (3) |
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5.2.3 Singular Plane of the Cylindrical Arm |
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195 | (4) |
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5.2.4 Singular Plane of the Scara Arm |
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199 | (1) |
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5.3 Singularities of Spherical Wrists |
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200 | (1) |
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5.4 Singularity Metrics of Industrial Robots |
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201 | (1) |
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5.4.1 Pointing Singularities |
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201 | (1) |
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5.5 Singularity Free Pointing Systems |
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202 | (5) |
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5.5.1 Singularity Free Robot Wrists |
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205 | (1) |
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5.5.2 Singularity Free Robot Arms |
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205 | (2) |
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207 | (32) |
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6.1 Independent Solution of Primary and Secondary Tasks |
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210 | (4) |
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6.2 Combined Solution of Primary and Secondary Tasks |
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214 | (10) |
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214 | (1) |
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6.2.2 Primary Task with Higher Priority |
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215 | (3) |
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6.2.3 Null Space of Primary Task |
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218 | (1) |
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6.2.4 Best Weighting Matrix |
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219 | (3) |
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6.2.5 Best Solution of Secondary Task |
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222 | (2) |
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6.3 Use of Kinematic Redundancy |
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224 | (15) |
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6.3.1 Kinematic Flexibility and Self-motion Curves of a 3R Mechanism |
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224 | (4) |
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6.3.2 Examples of Kinematic Redundancy |
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228 | (3) |
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6.3.3 Inverse Kinematic Solution of a Non-redundant Mechanism |
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231 | (2) |
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233 | (6) |
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239 | (34) |
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7.1 Characteristics of Parallel Mechanisms |
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240 | (5) |
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7.1.1 Components of Parallel Mechanisms |
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241 | (2) |
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7.1.2 Stewart-Gough Platform |
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243 | (1) |
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243 | (2) |
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7.2 Connectivity of Legs and Degrees of Freedom |
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245 | (5) |
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7.2.1 Mechanisms with v1 = v2 = ... = vK = λ |
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247 | (1) |
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7.2.2 Mechanisms with v1 = v2 = ... = vK = F |
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248 | (1) |
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7.2.3 Mechanisms with v1 = F and v2 = v3 = ... = vK = λ |
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249 | (1) |
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7.2.4 Mechanisms with v1 = v2 = ... = vK |
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249 | (1) |
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250 | (17) |
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7.3.1 Parameters and Variables of a Parallel Mechanism |
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251 | (1) |
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252 | (6) |
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258 | (5) |
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7.3.4 Kinematic Singularities |
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263 | (3) |
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7.3.5 Overconstrained and Redundant Parallel Mechanisms |
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266 | (1) |
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7.4 Some Examples of Parallel Mechanisms |
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267 | (6) |
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273 | (18) |
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275 | (5) |
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280 | (6) |
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286 | (5) |
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291 | (22) |
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9.1 Robot Grasp with Two Fingers |
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292 | (5) |
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9.2 Robot Grasp with Multiple Fingers |
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297 | (5) |
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302 | (11) |
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10 Kinematic Model of the Human Hand |
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313 | (14) |
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10.1 Kinematic Model of the Finger |
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314 | (3) |
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10.2 Inverse Kinematics of the Finger |
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317 | (2) |
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10.3 Kinematic Model of the Thumb |
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319 | (3) |
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10.4 Inverse Kinematics of the Thumb |
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322 | (2) |
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10.5 Thumb and Fingers Pose with Respect to Palm |
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324 | (3) |
References |
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327 | (4) |
Index |
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331 | |