Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms (Google eBook)

Front Cover
Jorge Angeles
Springer Science & Business Media, 2003 - Technology & Engineering - 521 pages
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Modern robotics dates from the late 1960s, when progress in the development of microprocessors made possible the computer control of a multiaxial manipulator. Since then, robotics has evolved to connect with many branches of science and engineering, and to encompass such diverse fields as computer vision, artificial intelligence, and speech recognition. This book deals with robots-such as remote manipulators, multifingered hands, walking machines, flight simulators, and machine tools-that rely on mechanical systems to perform their tasks. It aims to establish the foundations on which the design, control and implementation of the underlying mechanical systems are based. The treatment assumes familiarity with some calculus, linear algebra, and elementary mechanics; however, the elements of rigid-body mechanics and of linear transformations are reviewed in the first chapters, making the presentation self-contained. An extensive set of exercises is included. Topics covered include: kinematics and dynamics of serial manipulators with decoupled architectures; trajectory planning; determination of the angular velocity and angular acceleration of a rigid body from point data; inverse and direct kinematics manipulators; dynamics of general parallel manipulators of the platform type; and the kinematics and dynamics of rolling robots. Since the publication of the previous edition there have been numerous advances in both the applications of robotics (including in laprascopy, haptics, manufacturing, and most notably space exploration) as well as in the theoretical aspects (for example, the proof that Husty's 40th-degree polynomial is indeed minimal - mentioned as an open question in the previous edition). This new edition has been revised and updated throughout to include these new
  

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Contents

56 Synthesis of PPO Using Cubic Splines
201
Dynamics of Serial Robotic Manipulators
209
63 Fundamentals of Multibody System Dynamics
212
632 The EulerLagrange Equations of Serial Manipulators
213
633 Kanes Equations
222
Outward Recursions
223
Inward Recursions
229
65 The Natural Orthogonal Complement in Robot Dynamics
233

22 Linear Transformations
19
23 RigidBody Rotations
24
231 The CrossProduct Matrix
27
232 The Rotation Matrix
29
233 The Linear Invariants of a 3 x 3 Matrix
33
234 The Linear Invariants of a Rotation
34
235 Examples
36
236 The EulerRodrigues Parameters
42
24 Composition of Reflections and Rotations
46
25 Coordinate Transformations and Homogeneous Coordinates
47
251 Coordinate Transformations Between Frames with a Common Origin
48
252 Coordinate Transformation with Origin Shift
51
253 Homogeneous Coordinates
53
26 Similarity Transformations
57
27 Invariance Concepts
62
271 Applications to Redundant Sensing
65
Fundamentals of RigidBody Mechanics
70
32 General RigidBody Motion and Its Associated Screw
71
321 The Screw of a RigidBody Motion
73
322 The Plucker Coordinates of a Line
75
323 The Pose of a Rigid Body
79
33 Rotation of a Rigid Body About a Fixed Point
82
34 General Instantaneous Motion of a Rigid Body
83
341 The Instant Screw of a RigidBody Motion
84
342 The Twist of a Rigid Body
87
35 Acceleration Analysis of RigidBody Motions
90
36 RigidBody Motion Referred to Moving Coordinate Axes
92
37 Static Analysis of Rigid Bodies
94
38 Dynamics of Rigid Bodies
98
Kinetostatics of Simple Robotic Manipulators
103
42 The DenavitHartenberg Notation
104
43 The Kinematics of SixRevolute Manipulators
112
44 The IKP of Decoupled Manipulators
116
441 The Positioning Problem
117
442 The Orientation Problem
132
45 Velocity Analysis of Serial Manipulators
137
451 Jacobian Evaluation
144
452 Singularity Analysis of Decoupled Manipulators
149
453 Manipulator Workspace
151
46 Acceleration Analysis of Serial Manipulators
155
47 Static Analysis of Serial Manipulators
159
481 Displacement Analysis
162
482 Velocity Analysis
164
483 Acceleration Analysis
167
484 Static Analysis
169
49 Kinetostatic Performance Indices
170
491 Positioning Manipulators
175
492 Orienting Manipulators
178
493 Positioning and Orienting Manipulators
179
Trajectory Planning PickandPlace Operations
188
52 Background on PPO
189
53 Polynomial Interpolation
191
532 A 4567 Interpolating Polynomial
195
54 Cycloidal Motion
198
55 Trajectories with Via Poses
200
651 Derivation of Constraint Equations and TwistShape Relations
239
652 Noninertial Base Link
243
661 Planar Manipulators
247
662 Algorithm Complexity
260
663 Simulation
264
67 Incorporation of Gravity Into the Dynamics Equations
267
68 The Modeling of Dissipative Forces
268
Special Topics in RigidBody Kinematics
272
72 Computation of Angular Velocity from PointVelocity Data
273
73 Computation of Angular Acceleration from PointAcceleration Data
279
Kinematics of Complex Robotic Mechanical Systems
286
82 The IKP of General SixRevolute Manipulators
287
821 Preliminaries
288
822 The BivariateEquation Approach
301
823 The UnivariatePolynomial Approach
303
824 Numerical Conditioning of the Solutions
312
825 Computation of the Remaining Joint Angles
313
826 Examples
316
83 Kinematics of Parallel Manipulators
321
831 Velocity and Acceleration Analyses of Parallel Manipulators
336
84 Multifingered Hands
342
85 Walking Machines
347
86 Rolling Robots
351
862 Robots with Omnidirectional Wheels
357
Trajectory Planning ContinuousPath Operations
361
92 Curve Geometry
362
93 Parametric Path Representation
369
94 Parametric Splines in Trajectory Planning
382
95 ContinuousPath Tracking
388
Dynamics of Complex Robotic Mechanical Systems
400
102 Classification of Robotic Mechanical Systems with Regard to Dynamics
401
103 The Structure of the Dynamics Models of Holonomic Systems
402
104 Dynamics of Parallel Manipulators
405
105 Dynamics of Rolling Robots
416
1052 Robots with Omnidirectional Wheels
426
Kinematics of Rotations A Summary
436
The Numerical Solution of Linear Algebraic Systems
443
B1 The Overdetermined Case
445
B11 The Numerical Solution of an Overdetermined System of Linear Equations
446
B2 The Underdetermined Case
450
B21 The Numerical Solution of an Underdetermined System of Linear Equations
451
Exercises
453
2 Mathematical Background
456
3 Fundamentals of RigidBody Mechanics
464
4 Kinetostatics of Simple Robotic Manipulators
470
PickandPlace Operations
477
6 Dynamics of Serial Robotic Manipulators
480
7 Special Topics on RigidBody Kinematics
486
8 Kinematics of Complex Robotic Mechanical Systems
489
ContinuousPath Operations
493
10 Dynamics of Complex Robotic Mechanical Systems
497
References
500
Index
513
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