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1 | (8) |
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9 | (16) |
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9 | (3) |
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2.2 Forward Kinematic Analysis of Limbs |
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12 | (1) |
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2.3 The Forward Kinematic Model |
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13 | (2) |
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2.4 Application of the Forward Kinematic Model to a Simple Planar Limb |
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15 | (4) |
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2.5 Using the Forward Kinematic Model to Obtain Endpoint Velocities |
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19 | (1) |
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2.6 General Case of the Jacobian in the Context of Screws, Twists, and Wrenches |
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20 | (2) |
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2.7 Using the Jacobian of a Planar System to Find Endpoint Velocities |
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22 | (2) |
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2.8 Exercises and Computer Code |
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24 | (1) |
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24 | (1) |
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25 | (12) |
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3.1 Derivation of the Relationship Between Static Endpoint Forces and Joint Torques |
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25 | (2) |
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3.2 Symbolic Example Finding All Permutations of J for a Planar 2 DOF Limb |
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27 | (1) |
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3.3 Numerical Example Finding All Permutations of J for a Planar 2 DOF Limb |
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28 | (2) |
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3.4 Relationship Between JT and the Equations of Static Equilibrium |
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30 | (1) |
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3.5 Importance of Understanding the Kinematic Degrees of Freedom of a Limb |
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31 | (1) |
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3.6 Analysis of a Planar 3 DOF Limb |
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32 | (2) |
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3.7 Additional Comments on the Jacobian and Its Properties |
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34 | (1) |
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3.8 Exercises and Computer Code |
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35 | (2) |
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36 | (1) |
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37 | (18) |
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38 | (1) |
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4.2 Tendon Routing, Skeletal Geometry, and Moment Arms |
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39 | (2) |
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41 | (2) |
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4.4 Two or More Tendons Acting on a Joint: Under- and Overdetermined Systems |
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43 | (2) |
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4.5 The Moment Arm Matrix for Torque Production |
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45 | (3) |
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4.6 The Moment Arm Matrix for Tendon Excursions |
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48 | (2) |
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4.7 Implications to the Neural Control of Tendon-Driven Limbs |
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50 | (1) |
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4.8 Exercises and Computer Code |
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51 | (4) |
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51 | (4) |
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Part II Introduction to the Neural Control of Tendon-Driven Limbs |
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5 The Neural Control of Joint Torques in Tendon-Driven Limbs Is Underdetermined |
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55 | (16) |
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5.1 Muscle Activation and Redundancy of Neural Control |
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55 | (3) |
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5.2 Linear Programming Applied to Tendon-Driven Limbs |
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58 | (5) |
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5.2.1 Canonical Formulation of the Linear Programming Problem |
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59 | (1) |
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5.2.2 A Classical Example of Linear Programming: The Diet Problem |
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59 | (4) |
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5.3 Linear Programming Applied to Neuromuscular Problems |
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63 | (2) |
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5.4 Geometric Interpretation of Linear Programming |
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65 | (3) |
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5.5 Exercises and Computer Code |
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68 | (3) |
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69 | (2) |
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6 The Neural Control of Musculotendon Lengths and Excursions Is Overdetermined |
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71 | (20) |
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6.1 Forward and Inverse Kinematics of a Limb |
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71 | (1) |
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6.2 Forward Kinematics of a 5 DOF Arm |
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72 | (3) |
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6.3 Inverse Kinematics of a Limb |
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75 | (2) |
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6.3.1 Closed Form Analytical Approach |
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75 | (1) |
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76 | (1) |
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6.3.3 Experimental Approach |
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76 | (1) |
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6.4 The Overdetermined Problem of Tendon Excursions |
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77 | (4) |
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6.4.1 Tendon Excursion Versus Musculotendon Excursion |
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77 | (1) |
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78 | (3) |
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6.4.3 Reflex Mechanisms Interact with Limb Kinematics, Mechanics, and Muscle Properties |
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81 | (1) |
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6.5 Example of a Disc Throw Motion with a 17-Muscle, 5 DOF Arm |
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81 | (2) |
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6.6 Implications to Neural Control and Muscle Redundancy |
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83 | (2) |
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6.7 Exercises and Computer Code |
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85 | (6) |
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85 | (6) |
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Part III Feasible Actions of Tendon-Driven Limbs |
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7 Feasible Neural Commands and Feasible Mechanical Outputs |
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91 | (22) |
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7.1 Mapping from Neural Commands to Mechanical Outputs |
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91 | (3) |
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7.2 Geometric Interpretation of Feasibility |
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94 | (3) |
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7.3 Introduction to Feasible Sets |
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97 | (4) |
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7.4 Calculating Feasible Sets for Tasks with No Functional Constraints |
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101 | (4) |
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7.5 Size and Shape of Feasible Sets |
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105 | (2) |
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7.6 Anatomy of a Convex Polygon, Polyhedron, and Polytope |
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107 | (3) |
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7.7 Exercises and Computer Code |
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110 | (3) |
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110 | (3) |
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8 Feasible Neural Commands with Mechanical Constraints |
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113 | (22) |
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8.1 Finding Unique Optimal Solutions Versus Finding Families of Valid Solutions |
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113 | (3) |
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8.2 Calculating Feasible Sets for Tasks with Functional Constraints |
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116 | (3) |
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8.3 Vertex Enumeration in Practice |
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119 | (5) |
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8.4 A Definition of Versatility |
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124 | (1) |
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8.5 How Many Muscles Should Limbs Have to be Versatile? |
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125 | (2) |
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8.6 Limb Versatility Versus Muscle Redundancy |
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127 | (2) |
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8.7 Exercises and Computer Code |
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129 | (6) |
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129 | (6) |
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Part IV Neuromechanics as a Scientific Tool |
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9 The Nature and Structure of Feasible Sets |
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135 | (24) |
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9.1 Bounding Box Description of Feasible Sets |
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135 | (2) |
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9.2 Principal Components Analysis Description of Feasible Sets |
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137 | (3) |
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9.3 Synergy-Based Description of Feasible Sets |
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140 | (3) |
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9.4 Vectormap Description of Feasible Sets |
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143 | (6) |
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9.5 Probabilistic Neural Control |
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149 | (5) |
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9.6 Exercises and Computer Code |
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154 | (5) |
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154 | (5) |
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159 | (16) |
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159 | (3) |
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10.2 What This Book Did Not Cover |
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162 | (1) |
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163 | (3) |
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10.4 Motion, Force, and Impedance |
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166 | (2) |
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10.5 Agonist Versus Antagonist |
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168 | (1) |
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169 | (3) |
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10.7 Exercises and Computer Code |
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172 | (3) |
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172 | (3) |
Appendix A Primer on Linear Algebra and the Kinematics of Rigid Bodies |
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175 | (16) |
Index |
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191 | |