| Introduction | p. 1 |
| Goal | p. 1 |
| A Brief History of Articulated Robot Hands | p. 2 |
| The 1970s | p. 2 |
| The 1980s | p. 4 |
| Overview | p. 11 |
| Observation of Soft-fingered Grasping and Manipulation | p. 13 |
| Introduction | p. 13 |
| Object Pinching by a Pair of 1-DOF Fingers | p. 14 |
| Rotation of a Pinched Object by External Force | p. 16 |
| Concluding Remarks | p. 17 |
| Elastic Model of a Deformable Fingertip | p. 19 |
| Introduction | p. 19 |
| Static Elastic Model of a Hemispherical Soft Fingertip | p. 21 |
| Fingertip Stiffness | p. 21 |
| Elastic Force | p. 24 |
| Elastic Potential Energy | p. 25 |
| Relationship Between Elastic Force and Elastic Energy | p. 25 |
| Comparison with Hertzian Contact | p. 27 |
| Measurement of Young's Modulus | p. 28 |
| Compression Test | p. 29 |
| Concluding Remarks | p. 32 |
| Fingertip Model with Tangential Deformation | p. 33 |
| Introduction | p. 33 |
| Two-dimensional Elastic Energy Model | p. 34 |
| Derivation of the Energy Equation | p. 34 |
| Local Minimum of Elastic Potential Energy (LMEE) | p. 36 |
| Restoring Moment for a Contacted Object | p. 37 |
| Boundary Condition of Slip Motion | p. 38 |
| Formulation of Geometric Constraints | p. 39 |
| Normal Constraints | p. 39 |
| Tangential Constraints | p. 40 |
| LMEE with Constraints (LMEEwC) | p. 43 |
| Concluding Remarks | p. 43 |
| Variational Formulations in Mechanics | p. 45 |
| Introduction | p. 45 |
| Variational Principles | p. 45 |
| Variational Principle in Statics | p. 45 |
| Variational Principle in Dynamics | p. 48 |
| Numerical Optimization of Energy Functions | p. 51 |
| Nelder-Mead Method | p. 51 |
| Multiplier Method | p. 55 |
| Numerical Integration of Equations of Motion | p. 60 |
| Runge-Kutta Method | p. 60 |
| Constraint Stabilization Method | p. 63 |
| Stabilization of Pfaffian Constraints | p. 66 |
| Concluding Remarks | p. 70 |
| Statics of Soft-fingered Grasping and Manipulation | p. 71 |
| Introduction | p. 71 |
| Static Analysis Based on Force/Moment Equilibrium | p. 71 |
| Internal Energy Function | p. 71 |
| Numerical Analysis | p. 72 |
| Simulation | p. 72 |
| Analysis Without Gravity | p. 72 |
| Analysis Under Gravity | p. 75 |
| Degrees of Freedom Desired for Stable Manipulation | p. 78 |
| Experiments | p. 78 |
| Concluding Remarks | p. 81 |
| Dynamics of Soft-fingered Grasping and Manipulation | p. 83 |
| Introduction | p. 83 |
| Dynamics of Soft-fingered Grasping and Manipulation | p. 83 |
| Simulation of Soft-fingered Grasping and Manipulation | p. 86 |
| Numerical Integration of Lagrange Equations of Motion Under Geometric Constraints | p. 86 |
| Computation of Equations of Motion | p. 87 |
| Simulation Results | p. 91 |
| Experimental Results | p. 95 |
| Discussion | p. 98 |
| Conclusion and Research Perspective | p. 98 |
| Control of Soft-fingered Grasping and Manipulation | p. 101 |
| Introduction | p. 101 |
| Equations of Motion of the Two-fingered Hand | p. 102 |
| Simulations I: Posture Control of a Grasped Object | p. 103 |
| Serially-coupled Two-phased Object Orientation Controller | p. 103 |
| Examples of Failure | p. 106 |
| Available Range of the Biased Torque | p. 108 |
| Passivity Analysis | p. 111 |
| Simulations II: Responses for Time Delay | p. 113 |
| Experiments I: Posture Control of a Grasped Object | p. 118 |
| Object Orientation Control Under Constant Biased Torque (Exp. 1) | p. 119 |
| Open-loop Control of Biased Torque (Exp. 2) | p. 121 |
| Object Orientation Control Under Variable Biased Torque (Exp. 3) | p. 121 |
| Experiments II: Responses for Time Delay | p. 124 |
| Concluding Remarks | p. 132 |
| Geometric and Material Nonlinear Elastic Model | p. 135 |
| Introduction | p. 135 |
| Hertzian Contact and Kao's Elastic Model | p. 135 |
| Identification of Nonlinear Young's Modulus | p. 136 |
| Comparison with Hertzian Contact | p. 138 |
| Force Comparison | p. 139 |
| Concluding Remarks | p. 141 |
| Non-Jacobian Control of Robotic Pinch Tasks | p. 143 |
| Introduction | p. 143 |
| Kinematic Thumb Models in Previous Studies | p. 144 |
| Equations of Motion | p. 147 |
| Simulations | p. 149 |
| A Serial Two-phased Controller | p. 149 |
| Revolute Joint vs. Prismatic Joint (RP Joints) | p. 150 |
| Revolute Joint vs. Revolute Joint (RR Joints) | p. 162 |
| Prismatic 1-DOF Hand (P Joint) | p. 167 |
| Rotational 1-DOF Hand (R Joint) | p. 169 |
| Observations and Discussions | p. 181 |
| Concluding Remarks | p. 183 |
| Three-dimensional Grasping and Manipulation | p. 185 |
| Introduction | p. 185 |
| Quaternions | p. 185 |
| Spatial Geometric Constraints Between an Object and a Fingertip | p. 192 |
| Potential Energy of a Fingertip in Three-dimensional Grasping | p. 197 |
| Grasping and Manipulation by Three 1-DOF Fingers | p. 201 |
| Observation | p. 201 |
| Mathematical Description | p. 202 |
| Lagrange Equations of Motion | p. 207 |
| Simulation | p. 214 |
| Concluding Remarks | p. 217 |
| Conclusions | p. 219 |
| Main Contribution | p. 219 |
| Future Work | p. 221 |
| Static Modeling of Fingertips | p. 223 |
| Contact Plane Formula | p. 223 |
| Spring Constant Formulation | p. 223 |
| Coordinate Conversion to Derive Fingertip Stiffness | p. 224 |
| Approximation Method for a Nonlinear Curve | p. 226 |
| Three-dimensional Modeling of Fingertips | p. 229 |
| Derivatives of Angular Velocity Matrix | p. 229 |
| Bilinear Form of the Outer Product Matrix | p. 230 |
| Derivatives of Relative Angle with Respect to Quaternion Elements | p. 231 |
| Derivatives of Relative Angle with Respect to Finger Angle | p. 232 |
| Derivative of the Arctangent Function | p. 233 |
| References | p. 235 |
| Index | p. 243 |
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