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El. knyga: Design, Modeling and Experiments of 3-DOF Electromagnetic Spherical Actuators

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A spherical actuator is a novel electric device that can achieve 2/3-DOF rotational motions in a single joint with electric power input. It has advantages such as compact structure, low mass/moment of inertia, fast response and non-singularities within the workspace. It has promising applications in robotics, automobile, manufacturing, medicine and aerospace industry.

This is the first monograph that introduces the research on spherical actuators systematically.  It broadens the scope of actuators from conventional single-axis to multi-axis, which will help both beginners and researchers to enhance their knowledge on electromagnetic actuators. Generic analytic modeling methods for magnetic field and torque output are developed, which can be applied to the development of other electromagnetic actuators. A parametric design methodology that allows fast analysis and design of spherical actuators for various applications is proposed. A novel non-contact high-precision 3-DOF spherical motion sensing methodology is developed and evaluated with experiments, which shows that it can achieve one order of magnitude higher precision than conventional methods. The technologies of nondimensionalization and normalization are introduced into magnetic field analysis the first time, and a benchmark database is established for the reference of other researches on spherical actuators.



Recenzijos

From the reviews:

This monograph aims to present a generic methodology for modeling, design, and experimental investigation of three degree-of-freedom (3-DOF) permanent magnet spherical actuators. The book is primarily intended for researchers and developers working on spherical actuators, sensors, and instruments. (IEEE Control Systems Magazine, February, 2012)

List of Figures xv
List of Tables xix
1 Introduction 1(28)
1.1 Background and Motivation
1(4)
1.2 The State of the Art
5(12)
1.3 Objective and Scope of the Study
17(5)
1.4 Book Organization
22(1)
References
22(7)
2 Magnetic Field Modeling 29(18)
2.1 Introduction
29(1)
2.2 Configuration of Rotor Poles
30(2)
2.3 Magnetic Scalar Potential
32(3)
2.3.1 Relations Between H and B for Three Regions
32(1)
2.3.2 Laplace's Equations for Three Regions
33(2)
2.3.3 Genera] Solution of Laplace's Equation
35(1)
2.4 Spherical Harmonic Expansion of M0r
35(2)
2.5 Boundary Conditions
37(6)
2.5.1 Boundary Condition A or Far Field Boundary Condition (blr|->infinity = 0, B1theta|r->infinity = 0))
38(1)
2.5.2 Boundary Condition B (Blr|r=Rr = B r|Rr)
38(2)
2.5.3 Boundary Condition C (HIΦ|r=Rr = Hφ|r=Rr and HItheta|r=R = Htheta|Rr)
40(1)
2.5.4 Finite Boundary Condition D at r = 0(B r|0 not = to infinity, B theta|r=0 not = to infinity and Bφ|r = not = to infinity)
41(1)
2.5.5 Boundary Condition E(B |r=Rb = B r|r=Rb)
41(1)
2.5.6 Boundary Condition F (H φ|r=Rb = H φ|r = Rb and H theta|r = Rb = H theta|r = rb)
41(1)
2.5.7 Solution of Coefficients ximnl and kmnl
42(1)
2.6 Solutions of Scalar Potential and Flux Density
43(1)
2.7 Simplification of Magnetic Field Model
44(1)
2.8 Summary
45(1)
References
45(2)
3 Torque Modeling 47(22)
3.1 Introduction
47(3)
3.2 Formulation of Actuator Torque
50(12)
3.2.1 Torque Generating Component of Flux Density
50(1)
3.2.2 Torque Model for a Single Coil
50(6)
3.2.3 Torque Model for Complete Set of Coils
56(1)
3.2.4 Orientation Dependance of Torque Model
57(5)
3.3 Solution of Inverse Electromagnetics
62(4)
3.3.1 Nonsingularity of the Workspace
62(3)
3.3.2 Minimum Right-inverse Solution of Electromagnetics
65(1)
3.4 Summary
66(1)
References
67(2)
4 Prototype Development 69(30)
4.1 Introduction
69(6)
4.1.1 Prototype of PM Spherical Actuator
70(1)
4.1.2 Equations for Actuator Design
70(5)
4.2 Rotor Pole Design
75(5)
4.2.1 Longitudinal Angle α versus a
75(1)
4.2.2 Latitudinal Angle β versus c
76(1)
4.2.3 Rotor Radius Rr versus d4
77(1)
4.2.4 Rotor Core Radius Rb, versus d4
77(1)
4.2.5 Relative Permeability μr versus d4
78(1)
4.2.6 Result of PM Pole Design
79(1)
4.3 Coil Pole Design
80(13)
4.3.1 Geometric Parameters of Coil
81(5)
4.3.2 Increase Number of Winding Turns
86(7)
4.3.3 Material of Coil Frame
93(1)
4.4 Stator
93(2)
4.5 Spherical Bearing
95(1)
4.6 Summary
96(1)
References
97(2)
5 Experimental Investigation 99(34)
5.1 Measurement of PM Rotor Magnetic Field
100(14)
5.1.1 Flux Density Measurement Apparatus
101(6)
5.1.2 Flux Density Data Processing
107(5)
5.1.3 Visualization and Analysis of Experimental Result
112(2)
5.2 Measurement of Actuator Torque Output
114(16)
5.2.1 Experiment on Torque Generated by a Single Coil
116(7)
5.2.2 Experiment on Torque Generated by Multiple Coils
123(7)
5.3 Summary
130(1)
References
130(3)
6 Three Degree-of-freedom Optical Orientation Measurement 133(20)
6.1 Introduction
133(1)
6.2 Operating Principle
134(2)
6.3 Algorithm for Computing Rotation Angles
136(2)
6.3.1 Definition of Coordinate Systems
136(1)
6.3.2 Calculation of Tilting Angles
137(1)
6.3.3 Calculation of Spinning Angle
138(1)
6.4 Experimental Measurement
138(11)
6.4.1 Experimental Measurement on Apparatus 1
138(7)
6.4.2 Experimental Measurement on Apparatus 2
145(4)
6.5 Conclusion
149(1)
References
150(3)
7 Conclusions 153(6)
7.1 Accomplishments and Contributions
153(3)
7.2 Recommendation for Future Research
156(2)
References
158(1)
Index 159
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