Design, Modeling and Experiments of 3-DOF Electromagnetic Spherical Actuators

List of Figures.- List of Tables.- 1 Introduction.- 1.1 Background and Motivation.- 1.2 The State of the.- 1.3 Objective and Scope of the Study.- 1.4 Book Organization.- References.- 2 Magnetic Field Modeling.- 2.1 Introduction.- 2.2 Configuration of Rotor Poles.- 2.3 Magnetic Scalar Potential.- 2.3.1 Relations Between H and B for Three Regions.- 2.3.2 Laplace’s Equations for Three Regions.- 2.3.3 General Solution of Laplace’s Equation.- 2.4 Spherical Harmonic Expansion of M0r.- 2.5 Boundary Conditions.- 2.5.1 Boundary Condition A or Far Field Boundary Condition (BIrjr!¥ = 0, BIq jr!¥ = 0 and BIf jr!¥ = 0).- 2.5.2 Boundary Condition B (BIrjr=Rr = BIIrjr=Rr ).- 2.5.3 Boundary Condition C (HIf jr=Rr = HIIf jr=Rr and HIq jr=Rr = HIIq jr=Rr ).- 2.5.4 Finite Boundary Condition D at r = 0 (BIIIrjr=0 6= ¥, BIIIq jr=0 6= ¥ and BIIIf jr=0 6= ¥).- 2.5.5 Boundary Condition E (BIIrjr=Rb = BIIIrjr=Rb ).- 2.5.6 Boundary Condition F (HIIf jr=Rb = HIIIf jr=Rb and HIIq jr=Rb = HIIIq jr=Rb ).- 2.5.7 Solution of Coefficients x mnI and kmnI.- 2.6 Solutions of Scalar Potential and Flux Density.- 2.7 Simplification of Magnetic Field Model.- 2.8 Summary.- References.- 3 Torque Modeling.- 3.1 Introduction.- 3.2 Formulation of Actuator Torque.- 3.2.1 Torque Generating Component of Flux Density.- 3.2.2 Torque Model for a Single Coil.- 3.2.3 Torque Model for Complete Set of Coils.- 3.2.4 Orientation Dependance of Torque Model.- 3.3 Solution of Inverse Electromagnetics.- 3.3.1 Nonsingularity of the Workspace.- 3.3.2 Minimum Right-inverse Solution of Electromagnetics.- 3.4 Summary.- References.- 4 Prototype Development.- 4.1 Introduction.- 4.1.1 Prototype of PM Spherical Actuator.- 4.1.2 Equations for Actuator Design.- 4.2 Rotor Pole Design.- 4.2.1 Longitudinal Angle a versus a.- 4.2.2 Latitudinal Angle b versus c.- 4.2.3 Rotor Radius Rr versus d4.- 4.2.4 Rotor Core Radius Rb versus d4.- 4.2.5 Relative Permeability mr versus d4.- 4.2.6 Result of PM Pole Design.- 4.3 Coil Pole Design.- 4.3.1 Geometric Parameters of Coil.- 4.3.2 Increase Number of Winding Turns.- 4.3.3 Material of Coil Frame.- 4.4 Stator.- 4.5 Spherical Bearing.- 4.6 Summary.- References.- 5 Experimental Investigation.- 5.1 Measurement of PM Rotor Magnetic Field.- 5.1.1 Flux Density Measurement Apparatus.- 5.1.2 Flux Density Data Processing.- 5.1.3 Visualization and Analysis of Experimental Result.- 5.2 Measurement of Actuator Torque Output.- 5.2.1 Experiment on Torque Generated by a Single Coil.- 5.2.2 Experiment on Torque Generated by Multiple Coils.- 5.3 Summary.- References.- 6 Three Degree-of-freedom Optical Orientation Measurement.- 6.1 Introduction.- 6.2 Operating Principle.- 6.3 Algorithm for Computing Rotation Angles.- 6.3.1 Definition of Coordinate Systems.- 6.3.2 Calculation of Tilting Angles.- 6.3.3 Calculation of Spinning Angle.- 6.4 Experimental Measurement.- 6.4.1 Experimental Measurement on Apparatus 1.- 6.4.2 Experimental Measurement on Apparatus 2.- 6.5 Conclusion.- References.- 7 Conclusions.- 7.1 Accomplishments and Contributions.- 7.2 Recommendation for Future Research.- References.- Index.