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E-raamat: Parallel Robots: Mechanics and Control

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(K.N. Toosi University of Technology, Tehran, Iran)
  • Formaat: 533 pages
  • Ilmumisaeg: 20-Feb-2013
  • Kirjastus: CRC Press Inc
  • ISBN-13: 9781466555778
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Parallel Robots: Mechanics and ControlSuurem pilt
  • Formaat: 533 pages
  • Ilmumisaeg: 20-Feb-2013
  • Kirjastus: CRC Press Inc
  • ISBN-13: 9781466555778
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Parallel structures are more effective than serial ones for industrial automation applications that require high precision and stiffness, or a high load capacity relative to robot weight. Although many industrial applications have adopted parallel structures for their design, few textbooks introduce the analysis of such robots in terms of dynamics and control. Filling this gap, Parallel Robots: Mechanics and Control presents a systematic approach to analyze the kinematics, dynamics, and control of parallel robots. It brings together analysis and design tools for engineers and researchers who want to design and implement parallel structures in industry.

Covers Kinematics, Dynamics, and Control in One Volume

The book begins with the representation of motion of robots and the kinematic analysis of parallel manipulators. Moving beyond static positioning, it then examines a systematic approach to performing Jacobian analysis. A special feature of the book is its detailed coverage of the dynamics and control of parallel manipulators. The text examines dynamic analysis using the Newton-Euler method, the principle of virtual work, and the Lagrange formulations. Finally, the book elaborates on the control of parallel robots, considering both motion and force control. It introduces various model-free and model-based controllers and develops robust and adaptive control schemes. It also addresses redundancy resolution schemes in detail.

Analysis and Design Tools to Help You Create Parallel Robots

In each chapter, the author revisits the same case studies to show how the techniques may be applied. The case studies include a planar cable-driven parallel robot, part of a promising new generation of parallel structures that will allow for larger workspaces. The MATLAB® code used for analysis and simulation is available online. Combining the analysis of kinematics and dynamics with methods of designing controllers, this text offers a holistic introduction for anyone interested in designing and implementing parallel robots.
Preface xi
1 Introduction
1(22)
1.1 What Is a Robot?
1(2)
1.2 Robot Components
3(3)
1.3 Robot Degrees-of-Freedom
6(4)
1.4 Robot Classification
10(11)
1.4.1 Serial Robots
10(3)
1.4.2 Parallel Robots
13(1)
1.4.2.1 The Stewart-Gough Platform
14(3)
1.4.2.2 The Delta Robot
17(1)
1.4.3 Cable-Driven Parallel Robots
18(3)
1.5 The Aims and Scope of This Book
21(2)
2 Motion Representation
23(36)
2.1 Spatial Motion Representation
23(19)
2.1.1 Position of a Point
24(1)
2.1.2 Orientation of a Rigid Body
24(1)
2.1.2.1 Rotation Matrix
25(2)
2.1.2.2 Rotation Matrix Properties
27(4)
2.1.2.3 Screw Axis Representation
31(4)
2.1.2.4 Euler Angles
35(7)
2.2 Motion of a Rigid Body
42(2)
2.3 Homogeneous Transformations
44(9)
2.3.1 Homogeneous Coordinates
44(1)
2.3.2 Homogeneous Transformation Matrix
45(2)
2.3.3 Screw Displacement
47(2)
2.3.4 Transformation Arithmetics
49(1)
2.3.4.1 Consecutive Transformations
49(3)
2.3.4.2 Inverse Transformation
52(1)
Problems
53(6)
3 Kinematics
59(52)
3.1 Introduction
59(2)
3.2 Loop Closure Method
61(1)
3.3 Kinematic Analysis of a Planar Manipulator
62(7)
3.3.1 Mechanism Description
62(1)
3.3.2 Geometry of the Manipulator
63(1)
3.3.3 Inverse Kinematics
63(2)
3.3.4 Forward Kinematics
65(1)
3.3.5 Simulations
66(3)
3.4 Kinematic Analysis of Shoulder Manipulator
69(8)
3.4.1 Mechanism Description
69(2)
3.4.2 Geometry of the Manipulator
71(2)
3.4.3 Inverse Kinematics
73(1)
3.4.4 Forward Kinematics
74(1)
3.4.5 Simulations
75(2)
3.5 Kinematic Analysis of Stewart-Gough Platform
77(18)
3.5.1 Mechanism Description
77(1)
3.5.2 Geometry of the Manipulator
78(1)
3.5.3 Inverse Kinematics
79(1)
3.5.4 Forward Kinematics
80(1)
3.5.4.1 Background Literature
80(2)
3.5.4.2 Analytical Solution
82(5)
3.5.4.3 Numerical Solution
87(1)
3.5.5 Simulations
88(1)
3.5.5.1 Analytical Solution
89(2)
3.5.5.2 Numerical Solution
91(4)
Problems
95(16)
4 Jacobians: Velocities and Static Forces
111(56)
4.1 Introduction
111(1)
4.2 Angular and Linear Velocities
112(6)
4.2.1 Angular Velocity of a Rigid Body
112(1)
4.2.1.1 Angular Velocity and Rotation Matrix Rate
113(1)
4.2.1.2 Angular Velocity and Euler Angles Rate
114(1)
4.2.2 Linear Velocity of a Point
114(2)
4.2.3 Screw Coordinates
116(2)
4.3 Jacobian Matrices of a Parallel Manipulator
118(1)
4.4 Velocity Loop Closure
119(1)
4.5 Singularity Analysis of Parallel Manipulators
120(2)
4.5.1 Inverse Kinematic Singularity
121(1)
4.5.2 Forward Kinematic Singularity
121(1)
4.5.3 Combined Singularity
122(1)
4.6 Jacobian Analysis of a Planar Manipulator
122(5)
4.6.1 Velocity Loop Closure
122(3)
4.6.2 Singularity Analysis
125(1)
4.6.3 Sensitivity Analysis
126(1)
4.7 Jacobian Analysis of Shoulder Manipulator
127(5)
4.7.1 Velocity Loop Closure
128(1)
4.7.1.1 Jacobian of the Actuated Limbs
128(1)
4.7.1.2 Jacobian of the Passive Limb
129(1)
4.7.2 Singularity Analysis
130(2)
4.8 Jacobian Analysis of the Stewart-Gough Platform
132(7)
4.8.1 Velocity Loop Closure
132(2)
4.8.2 Singularity Analysis
134(1)
4.8.2.1 Background Literature
134(2)
4.8.2.2 A 3-6 Stewart-Gough Platform
136(3)
4.9 Static Forces in Parallel Manipulators
139(8)
4.9.1 Free-Body Diagram Approach
139(1)
4.9.2 Virtual Work Approach
140(2)
4.9.3 Static Forces of a Planar Manipulator
142(2)
4.9.4 Static Forces of Shoulder Manipulator
144(2)
4.9.5 Static Forces of the Stewart-Gough Platform
146(1)
4.10 Stiffness Analysis of Parallel Manipulators
147(12)
4.10.1 Stiffness and Compliance Matrices
148(1)
4.10.2 Transformation Ellipsoid
149(2)
4.10.3 Stiffness Analysis of a Planar Manipulator
151(2)
4.10.4 Stiffness Analysis of Shoulder Manipulator
153(2)
4.10.5 Stiffness Analysis of the Stewart-Gough Platform
155(4)
Problems
159(8)
5 Dynamics
167(102)
5.1 Introduction
167(2)
5.2 Dynamics of Rigid Bodies: A Review
169(11)
5.2.1 Acceleration of Rigid Bodies
169(1)
5.2.1.1 Angular Acceleration of a Rigid Body
170(1)
5.2.1.2 Linear Acceleration of a Point
170(1)
5.2.2 Mass Properties
171(1)
5.2.2.1 Center of Mass
172(1)
5.2.2.2 Moments of Inertia
172(1)
5.2.2.3 Principal Axes
173(1)
5.2.2.4 Inertia Matrix Transformations
173(1)
5.2.3 Momentum and Kinetic Energy
174(1)
5.2.3.1 Linear Momentum
174(1)
5.2.3.2 Angular Momentum
175(1)
5.2.3.3 Kinetic Energy
176(1)
5.2.4 Newton-Euler Laws
177(1)
5.2.5 Variable-Mass Systems
178(2)
5.3 Newton-Euler Formulation
180(41)
5.3.1 Dynamic Formulation of a Planar Manipulator: Constant Mass Treatment
181(1)
5.3.1.1 Acceleration Analysis
181(1)
5.3.1.2 Dynamic Formulation of the Limbs
182(2)
5.3.1.3 Dynamic Formulation of the Moving Platform
184(1)
5.3.1.4 Forward Dynamics Simulation
185(5)
5.3.1.5 Inverse Dynamics Simulation
190(3)
5.3.2 Dynamic Formulation of a Planar Manipulator: Variable-Mass Treatment
193(1)
5.3.2.1 Acceleration Analysis
193(3)
5.3.2.2 Dynamic Analysis of the Limbs
196(3)
5.3.3 Dynamic Formulation of the Stewar-Gough Platform
199(1)
5.3.3.1 Acceleration Analysis
199(3)
5.3.3.2 Dynamic Formulation of the Limbs
202(4)
5.3.3.3 Dynamic Formulation of the Moving Platform
206(1)
5.3.4 Closed-Form Dynamics
207(1)
5.3.4.1 Closed-Form Dynamics of the Limbs
207(2)
5.3.4.2 Closed-Form Dynamics of the Moving Platform
209(1)
5.3.4.3 Closed-Form Dynamics of the Stewart-Gough Manipulator
210(1)
5.3.4.4 Forward Dynamics Simulations
211(4)
5.3.4.5 Inverse Dynamics Simulation
215(6)
5.4 Virtual Work Formulation
221(11)
5.4.1 D'Alembert's Principle
221(1)
5.4.2 Principle of Virtual Work
222(3)
5.4.3 Dynamic Formulation of a Planar Manipulator: Constant Mass Treatment
225(2)
5.4.4 Formulation Verification
227(1)
5.4.5 Dynamic Formulation of a Planar Manipulator: Variable Mass Treatment
228(1)
5.4.6 Dynamic Formulation of the Stewart-Gough Platform
229(3)
5.5 Lagrange Formulation
232(28)
5.5.1 Generalized Coordinates
232(2)
5.5.2 Lagrange Equations of the Second Kind
234(2)
5.5.3 Lagrange Equations of the First Kind
236(1)
5.5.4 Dynamic Formulation Properties
237(1)
5.5.4.1 Mass Matrix Properties
238(1)
5.5.4.2 Linearity in Parameters
239(1)
5.5.4.3 Coriolis and Centrifugal Vector Properties
239(4)
5.5.5 Dynamic Formulation of a Planar Manipulator
243(2)
5.5.5.1 Dynamic Formulation of the Limbs
245(4)
5.5.5.2 Dynamic Formulation of the Moving Platform
249(1)
5.5.5.3 Dynamic Formulation of the Whole Manipulator
250(2)
5.5.6 Dynamic Analysis of the Stewart-Gough Platform
252(1)
5.5.6.1 Dynamic Formulation of the Limbs
253(5)
5.5.6.2 Dynamic Formulation of the Moving Platform
258(2)
5.5.6.3 Dynamic Formulation of the Whole Manipulator
260(1)
Problems
260(9)
6 Motion Control
269(122)
6.1 Introduction
269(1)
6.2 Controller Topology
270(4)
6.3 Motion Control in Task Space
274(8)
6.3.1 Decentralized PD Control
274(1)
6.3.2 Feed Forward Control
275(2)
6.3.3 Inverse Dynamics Control
277(2)
6.3.4 Partial Linearization IDC
279(3)
6.4 Robust and Adaptive Control
282(10)
6.4.1 Robust Inverse Dynamics Control
283(6)
6.4.2 Adaptive Inverse Dynamics Control
289(3)
6.5 Motion Control in Joint Space
292(7)
6.5.1 Dynamic Formulation in the Joint Space
293(1)
6.5.2 Decentralized PD Control
294(1)
6.5.3 Feed Forward Control
295(2)
6.5.4 Inverse Dynamics Control
297(2)
6.6 Summary of Motion Control Techniques
299(4)
6.6.1 Dynamic Formulations
300(1)
6.6.2 Decentralized PD Control
300(1)
6.6.3 Feed Forward Control
300(1)
6.6.4 Inverse Dynamics Control
301(1)
6.6.5 Partial Linearization IDC
301(1)
6.6.6 Robust Inverse Dynamics Control
301(1)
6.6.7 Adaptive Inverse Dynamics Control
302(1)
6.7 Redundancy Resolution
303(13)
6.7.1 Introduction
303(1)
6.7.2 Problem Formulation
304(3)
6.7.3 Lagrange and Karush-Kuhn-Tucker Multipliers
307(3)
6.7.4 Iterative Solutions
310(1)
6.7.4.1 Numerical Methods
310(2)
6.7.4.2 An Iterative-Analytical Method
312(4)
6.8 Motion Control of a Planar Manipulator
316(27)
6.8.1 Decentralized PD Control
316(7)
6.8.2 Feed Forward Control
323(4)
6.8.3 Inverse Dynamics Control
327(6)
6.8.4 Partial Linearization IDC
333(2)
6.8.5 Robust Inverse Dynamics Control
335(3)
6.3.6 Adaptive Inverse Dynamics Control
338(5)
6.8.7 Motion Control in Joint Space
343(1)
6.9 Motion Control of the Stewart-Gough Platform
343(39)
6.9.1 Decentralized PD Control
344(7)
6.9.2 Feed Forward Control
351(3)
6.9.3 Inverse Dynamics Control
354(4)
6.9.4 Partial Linearization IDC
358(2)
6.9.3 Robust Inverse Dynamics Control
360(5)
6.9.6 Motion Control in Joint Space
365(1)
6.9.6.1 Decentralized PD Control
365(8)
6.9.6.2 Feed Forward Control
373(3)
6.9.6.3 Inverse Dynamics Control
376(6)
Problems
382(9)
7 Force Control
391(86)
7.1 Introduction
391(1)
7.2 Controller Topology
392(8)
7.2.1 Cascade Control
394(1)
7.2.2 Force Feedback in Outer Loop
395(2)
7.2.3 Force Feedback in Inner Loop
397(3)
7.3 Stiffness Control
400(23)
7.3.1 Single-Degree-of-Freedom Stiffness Control
401(4)
7.3.2 General Stiffness Control
405(3)
7.3.3 Stiffness Control of a Planar Manipulator
408(8)
7.3.4 Stiffness Control of the Stewart-Gough Platform
416(7)
7.4 Direct Force Control
423(18)
7.4.1 Force Control of a Planar Manipulator
428(5)
7.4.2 Force Control of the Stewart-Gough Platform
433(8)
7.5 Impedance Control
441(23)
7.5.1 Impedance
443(2)
7.5.2 Impedance Control Concept
445(3)
7.5.3 Impedance Control Structure
448(3)
7.5.4 Impedance Control of a Planar Manipulator
451(5)
7.5.5 Impedance Control of the Stewart-Gough Platform
456(8)
Problems
464(13)
Appendix A Linear Algebra
477(10)
A.1 Vectors and Matrices
477(1)
A.2 Vector and Matrix Operations
478(2)
A.3 Eigenvalues and Singular Values
480(2)
A.4 Pseudo-Inverse
482(3)
A.4.1 Pseudo-Inverse Properties
483(1)
A.4.2 Linear Inverse Problems
484(1)
A.5 Kronecker Product
485(2)
Appendix B Trajectory Planning
487(6)
B.1 Point-to-Point Motion
487(4)
B.1.1 Cubic Polynomials
487(1)
B.1.2 Quintic Polynomials
488(1)
B.1.3 Linear Segments with Parabolic Blends
489(1)
B.1.4 Minimum Time Trajectory
490(1)
B.2 Specified Path with Via Points
491(2)
Appendix C Nonlinear Control Review
493(8)
C.1 Dynamical Systems
493(1)
C.2 Stability Definitions
494(1)
C.3 Lyapunov Stability
495(3)
C.4 Krasovskii-Lasalle Theorem
498(3)
References 501(10)
Index 511
Hamid D. Taghirad is currently a professor with the Faculty of Electrical and Computer Engineering, Department of Systems and Control, and the founder of the Advanced Robotics and Automated System (ARAS) at K.N. Toosi University of Technology, Tehran, Iran. He has been involved in numerous robotics industrial projects on the design and implementation of industrial robots, robotic cells, and currently on an industrial cable-driven parallel manipulator. He has also participated in joint international collaborations in the field of robotics. Dr. Taghirad was the founder and a member of the board of the Iranian Society of Mechatronics (ISM) and is currently a member of the board of the Iranian Robotics Society (IRS), editor in chief of Mechatronics Magazine, and a member of the editorial board of the International Journal of Robotics: Theory and Application. He also served as an organizing committee member of many international conferences, including the International Conference on Robotics and Mechatronics (ICRoM). His publications include five books and more than 190 papers in peer-reviewed international journals and conference proceedings.

For more information, see Professor Taghirads profile at K.N. Toosi University of Technology.
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