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Intelligent Systems Series......Page 1 Flexible Manipulators: Modeling, Analysis, and Optimum Design ......Page 2 Copyright......Page 3 0ix_Preface......Page 4 3 Modeling of Flexible Manipulators......Page 18 3.1 Introduction......Page 6 References......Page 8 2.1 Earlier Research on Flexible Manipulators......Page 9 2.2 Recent Work on Flexible Manipulators......Page 10 References......Page 15 3.2.1 Problem Statement......Page 20 3.2.2 Kinetic Energy of the Beam......Page 22 3.2.3 Kinetic Energy of the Tip Load......Page 23 6.3 Mechatronic Design of Flexible Manipulators Based on LQR with IHR Programming......Page 24 Variation with Respect to Variable θ......Page 25 Variation with Respect to Variable w......Page 27 3.3.2 Equations of Motion for Euler–Bernoulli Beam Model......Page 29 Variation with Respect to Variable θ......Page 30 Variation with Respect to Variable w......Page 33 Variation with Respect to Variable ϕ......Page 35 3.3.4 Equations of Motion for Timoshenko Beam Model......Page 36 3.4.1 Introduction......Page 37 3.4.3 Timoshenko Model after Linearization......Page 38 Timoshenko Model with Dimensionless Variables......Page 39 Modal Determinant......Page 40 Modal Frequencies and Modal Shapes......Page 42 3.5.2 Finite Modal Model of Euler–Bernoulli Beam......Page 44 3.5.3 Finite Difference Model......Page 50 3.5.4 Finite Element Model......Page 54 References......Page 60 4 Analysis of Flexible Manipulators......Page 62 4.2.1 Introduction......Page 63 4.2.2 Dynamic Models for One-Link Flexible Manipulators......Page 64 Euler–Bernoulli Dynamic Model (Model A)......Page 65 Timoshenko Dynamic Model (Model C)......Page 66 4.2.3 Characteristic Equations for Modal Frequencies and Vibration Modes......Page 67 Euler–Bernoulli Dynamic Model (Model A)......Page 68 Euler–Bernoulli Dynamic Model with Rotary Inertia (Model B)......Page 69 Timoshenko Dynamic Model (Model C)......Page 70 Euler–Bernoulli Dynamic Model with Tip Load (Model D)......Page 72 4.2.4 Asymptotic Behavior of Modal Frequencies and Vibration Modes......Page 73 Euler–Bernoulli Dynamic Model with Rotary Inertia (Model B)......Page 74 6.3.5 Results and Discussion......Page 199 Experimental Verification......Page 75 Vibration Equations......Page 76 Influence of Shear Deformation......Page 77 Influence of Tip Load......Page 79 Numerical Results of System Robustness......Page 229 Euler–Bernoulli Model......Page 83 Actuator Dynamics......Page 233 4.2.7 Step Responses and General Solutions......Page 91 4.3.1 Nonlinear Dynamic Equations of Motion......Page 94 4.3.2 Discretization of Nonlinear Model......Page 95 4.3.3 Stability Analysis......Page 97 References......Page 100 099_Chapter-5-Optimization-of-Flexible-Manipulators......Page 102 6 Mechatronic Design of Flexible Manipulators* ......Page 188 5.1 Optimum Design of Flexible Beams with a New Iteration Approach......Page 103 5.1.1 Introduction......Page 104 5.1.2 Basic Equations......Page 105 5.1.3 Analysis of Singularity at the Free End......Page 107 Case where q=0......Page 108 Case where p=1......Page 109 Case where p ﹥ 1 and q = 0......Page 111 Case where p ﹥ 1 and q ≠ 0......Page 112 Case where p=1 ......Page 114 Cases where p=2 and p=3 ......Page 115 5.2.2 Uniform and Variable Tunnel Cross-Section Designs......Page 119 5.2.3 Composite Material Designs......Page 122 5.3.1 Problem Setup......Page 123 Design Model......Page 125 Optimality Equations......Page 128 Iterative Solution......Page 131 Numerical Results and Discussion......Page 134 Segmentized Formulation......Page 136 Dynamic Programming Solution......Page 140 Adaptive Random Search Solution......Page 141 Numerical Results and Discussion......Page 143 Minimax Optimum Design......Page 145 Two-link Optimum Design......Page 146 5.3.6 Sensitivity Analysis......Page 149 5.4.1 Basic Equations and the Variation Formulation......Page 151 5.4.2 Analytical Approach of Unconstrained Shape Design......Page 154 Scheme: Case where p=1 ......Page 156 Iteration Scheme: Case where p ﹥ 1......Page 158 5.4.3 Optimization Approach of Constrained Shape Design......Page 159 Nonlinear Programming Method: Single Tip Load......Page 160 Minimax Design Method: Multiple Tip Loads......Page 161 Unconstrained Design......Page 162 Constrained Design......Page 165 5.4.5 Sensitivity Analysis of the Optimal Frequency......Page 167 5.5.1 Basic Equations......Page 169 5.5.2 Problem Formulation......Page 171 5.5.3 Solution by Iterations......Page 172 Case where p=1 ......Page 173 Case where p ﹥ 1......Page 174 5.6 Optimum Design of Flexible Manipulators: The Segmentized Solution......Page 175 5.6.1 Basic Equations......Page 177 5.6.2 Segmentized Solutions......Page 178 5.6.3 Optimization Formulations for Linear Mass and Bending Rigidity Distributions......Page 181 Minimum Mass Design Problem......Page 182 Design Formulations for Multiple Loads......Page 183 Strain/Stress and Deflection Constraints......Page 184 References......Page 185 6.1 Introduction......Page 189 Modeling Accuracy and Control Efficiency of Flexible Manipulators......Page 190 6.2.2 What is Mechatronic Design?......Page 191 6.2.3 How Does Mechatronic Design Work?......Page 192 State-space Equations of Flexible Manipulators......Page 193 Output Specifications......Page 195 6.3.2 LQR Formula: Inner Loop Optimizations......Page 196 LQR: Inner Loop Optimization......Page 197 IHR: Outer Loop Optimization......Page 198 6.4.1 State-Space Formulas for H∞ Control Problems......Page 213 6.4.2 Generalized Plant of a Flexible Beam System......Page 215 6.4.3 H∞ Controller Design......Page 218 6.4.4 Simulation Results......Page 219 Sensitivity Analysis......Page 228 6.5 Closed-Loop Design of Flexible Robotic Links......Page 232 6.5.2 Transfer Functions of the Integrated Systems......Page 234 6.5.3 Segmentized Solution for Transfer Functions......Page 235 6.5.4 Optimization Formulations for Mechatronic Design......Page 237 Reference Model Optimization......Page 239 6.6 Concurrent Design......Page 240 6.6.1 General Concepts......Page 241 6.6.2 Existing Representation of Special Concurrent Designs......Page 242 Global Optimization......Page 243 6.7.1 Dynamics of Single-Link Flexible Manipulator Systems......Page 244 6.7.2 Implementation of Concurrent Design......Page 246 6.7.3 Simulation Results......Page 248 References......Page 251 7 Conclusions and Future Research......Page 253 E......Page 255 I......Page 256 O......Page 257 S......Page 258 W......Page 259