Design, Modeling and Experiments of 3-DOF Electromagnetic Spherical Actuators (Mechanisms and Machine Science, 4)

Preface
Contents
List of Figures
List of Tables
Acronyms
1 Introduction
	1.1 Background and Motivation
	1.2 The State of the Art
	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 (BI r|r=0, BI |r = 0  and BI |r=0)
		2.5.2 Boundary Condition B (BI r|r=Rr=BII r|r=Rr)
		2.5.3 Boundary Condition C (HI |r= Rr=HII |r= Rr and HI |r= Rr=HII |r= Rr)
		2.5.4 Finite Boundary Condition D at r=0 (BIIIr|r=0=, BIII|r=0= and BIII|r=0=)
		2.5.5 Boundary Condition E (BII r|r=Rb=BIII r|r=Rb)
		2.5.6 Boundary Condition F (HII |r= Rb=HIII |r= Rb and HII |r= Rb=HIII |r= Rb)
		2.5.7 Solution of Coefficients nIm and n Im
	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  versus a
		4.2.2 Latitudinal Angle  versus c
		4.2.3 Rotor Radius Rr versus d4
		4.2.4 Rotor Core Radius Rb versus d4
		4.2.5 Relative Permeability r 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