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E-raamat: 3D Kinematics

  • Formaat: EPUB+DRM
  • Ilmumisaeg: 30-Dec-2018
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319752778
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3D KinematicsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 30-Dec-2018
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319752778
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This book presents an introduction to the analysis of general movements in 3D space, especially for movements of the human body. It is based on the lecture notes of a class on 3D Kinematics, which the author has been holding in the Master Degree Program of his home institution, the University of Applied Sciences Upper Austria. The lecture introduces the mathematics underlying the measurement and analysis of 3D movements. The target audience primarily comprises research experts in the field, but the book may also be beneficial for graduate students alike. 

Arvustused

After reading this book, the reader will be convinced that the intended audience for it consists of scientists and engineers in mechanics and control as well as in graduate and PhD students in the area of mechanics, biomechanics, robotics and mechatronics. (Clementina Mladenova, zbMath 1417.70001, 2019)

1 Introduction
1(10)
1.1 Recording Movement and Orientation
2(1)
1.2 Conventions and Basics
2(3)
1.2.1 Notation
3(1)
1.2.2 Coordinate Systems
3(2)
1.3 Software Packages
5(3)
1.3.1 Python Package scikit-kinematics
5(1)
1.3.2 Matlab 3-D Kinematics Toolbox
6(1)
1.3.3 Source Code for Python and Matlab
7(1)
1.4 Warm-Up Exercises
8(3)
2 Measurement Techniques
11(18)
2.1 Marker-Based Measurements
11(5)
2.1.1 Image Formation
13(3)
2.2 Sensor-Based Measurements
16(13)
2.2.1 Overview
16(1)
2.2.2 Linear Accelerometers
17(3)
2.2.3 Gyroscopes
20(2)
2.2.4 Ultrasound Sensors---Trilateration
22(1)
2.2.5 Magnetic Field Sensors
23(6)
3 Rotation Matrices
29(28)
3.1 Introduction
29(1)
3.2 Rotations in a Plane
30(4)
3.2.1 Rotation in Cartesian Coordinates
31(1)
3.2.2 Rotation in Polar Coordinates
32(1)
3.2.3 Application: Orienting an Object in a Plane
33(1)
3.3 Rotations About Coordinate Axes in 3-D
34(4)
3.3.1 3-D Rotations About Coordinate Axes
34(3)
3.3.2 Rotations of Objects Versus Rotations of Coordinate Systems
37(1)
3.4 Combined Rotations
38(8)
3.4.1 3-D Orientation with Sequential Rotations
40(5)
3.4.2 Gimbal Lock
45(1)
3.5 Homogeneous Coordinates
46(2)
3.5.1 Definition
46(2)
3.6 Applications
48(6)
3.6.1 Two DOF---Targeting an Object in 3-D
48(1)
3.6.2 Two DOF---Projection onto a Flat Surface
49(2)
3.6.3 Three DOF---3-D Orientation Measurements with Search Coils
51(1)
3.6.4 Nested or Cascaded 3-D Rotation Sequences
52(2)
3.6.5 Camera Images
54(1)
3.7 Exercises
54(3)
4 Quaternions and Gibbs Vectors
57(18)
4.1 Representing Rotations by Vectors
57(2)
4.2 Axis-Angle Euler Vectors
59(1)
4.3 Quaternions
59(5)
4.3.1 Background
59(1)
4.3.2 Quaternion Properties
60(1)
4.3.3 Interpretation of Quaternions
61(1)
4.3.4 Unit Quaternions
61(3)
4.4 Gibbs Vectors
64(2)
4.4.1 Properties of Gibbs Vectors
64(2)
4.4.2 Cascaded Rotations with Gibbs Vectors
66(1)
4.4.3 Gibbs Vectors and Their Relation to Quaternions
66(1)
4.5 Applications
66(9)
4.5.1 Targeting an Object in 3-D: Quaternion Approach
66(2)
4.5.2 Orientation of 3-D Acceleration Sensor
68(2)
4.5.3 Calculating Orientation of a Camera on a Moving Object
70(2)
4.5.4 Object-Oriented Implementation of Quaternions
72(3)
5 Velocities in 3-D Space
75(10)
5.1 Equations of Motion
75(1)
5.2 Linear Velocity
76(3)
5.3 Angular Velocity
79(6)
5.3.1 Calculating Angular Velocity from Orientation
79(3)
5.3.2 Calculating Orientation from Angular Velocity
82(3)
6 Analysis of 3-D Movement Recordings
85(14)
6.1 Position and Orientation from Optical Sensors
85(6)
6.1.1 Recording 3-D Markers
85(2)
6.1.2 Orientation in Space
87(1)
6.1.3 Position in Space
88(1)
6.1.4 Velocity and Acceleration
89(1)
6.1.5 Transformation from Camera-to Space-Coordinates
89(1)
6.1.6 Position
90(1)
6.2 Position and Orientation from Inertial Sensors
91(4)
6.2.1 Orientation in Space
91(2)
6.2.2 Position in Space
93(2)
6.3 Applications: Gait Analysis
95(2)
6.4 Exercises
97(2)
7 Multi-sensor Integration
99(16)
7.1 Working with Uncertain Data
100(5)
7.1.1 Uncertain Data in One Dimension
100(2)
7.1.2 Uncertain Data in Multiple Dimensions
102(3)
7.2 Kalman Filter
105(7)
7.2.1 Idea Behind Kalman Filters
105(2)
7.2.2 State Predictions
107(2)
7.2.3 Measurements and Kalman Equations
109(3)
7.2.4 Kalman Filters with Quaternions
111(1)
7.3 Complementary Filters
111(1)
7.3.1 Gradient Descent Approach
112(3)
Appendix A Appendix---Mathematics 115(14)
Appendix B Practical Applications: Denavit-Hartenberg Transformations 129(4)
Appendix C Python and Matlab Programs 133(22)
Appendix D: Human Movement Recordings---Practical Tips 155(6)
Appendix E Exercise Solutions 161(18)
Appendix F Glossary 179(4)
Appendix G Online Resources 183(2)
References 185(4)
Index 189
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