Kinematics of general spatial mechanical systems. (2020)

• Record Type: Book
• Further Information: Note: M. Kemal Ozgoren.
• Authors: Özgören, M. Kemal, 1948-
• Contents: Preface xv Acknowledgments xix List of Commonly Used Symbols, Abbreviations, and Acronyms xxi About the Companion Website xxvii 1 Vectors and Their Matrix Representations in Selected Reference Frames 1 1.1 General Features of Notation 1 1.2 Vectors 2 1.2.1 Definition and Description of a Vector 2 1.2.2 Equality of Vectors 2 1.2.3 Opposite Vectors 3 1.3 Vector Products 3 1.3.1 Dot Product 3 1.3.2 Cross Product 3 1.4 Reference Frames 4 1.5 Representation of a Vector in a Selected Reference Frame 6 1.6 Matrix Operations Corresponding to Vector Operations 7 1.6.1 Dot Product 7 1.6.2 Cross Product and Skew Symmetric Cross Product Matrices 8 1.7 Mathematical Properties of the Skew Symmetric Matrices 9 1.8 Examples Involving Skew Symmetric Matrices 10 1.8.1 Example 1.1 10 1.8.2 Example 1.2 11 1.8.3 Example 1.3 11 2 Rotation of Vectors and Rotation Matrices 13 2.1 Vector Equation of Rotation and the Rodrigues Formula 13 2.2 Matrix Equation of Rotation and the Rotation Matrix 15 2.3 Exponentially Expressed Rotation Matrix 16 2.4 Basic Rotation Matrices 16 2.5 Successive Rotations 17 2.6 Orthonormality of the Rotation Matrices 18 2.7 Mathematical Properties of the Rotation Matrices 20 2.7.1 Mathematical Properties of General Rotation Matrices 20 2.7.2 Mathematical Properties of the Basic Rotation Matrices 22 2.8 Examples Involving Rotation Matrices 22 2.8.1 Example 2.1 22 2.8.2 Example 2.2 23 2.8.3 Example 2.3 24 2.8.4 Example 2.4 24 2.9 Determination of the Angle and Axis of a Specified Rotation Matrix 25 2.9.1 Scalar Equations of Rotation 25 2.9.2 Determination of the Angle of Rotation 26 2.9.3 Determination of the Axis of Rotation 26 2.9.4 Discussion About the Optional Sign Variables 29 2.10 Definition and Properties of the Double Argument Arctangent Function 29 3 Matrix Representations of Vectors in Different Reference Frames and the Component Transformation Matrices 31 3.1 Matrix Representations of a Vector in Different Reference Frames 31 3.2 Transformation Matrices Between Reference Frames 32 3.2.1 Definition and Usage of a Transformation Matrix 32 3.2.2 Basic Properties of a Transformation Matrix 33 3.3 Expression of a Transformation Matrix in Terms of Basis Vectors 34 3.3.1 Column-by-Column Expression 34 3.3.2 Row-by-Row Expression 34 3.3.3 Remark 3.1 35 3.3.4 Remark 3.2 35 3.3.5 Remark 3.3 36 3.3.6 Example 3.1 36 3.4 Expression of a Transformation Matrix as a Direction Cosine Matrix 37 3.4.1 Definitions of Direction Angles and Direction Cosines 37 3.4.2 Transformation Matrix Formed as a Direction Cosine Matrix 38 3.5 Expression of a Transformation Matrix as a Rotation Matrix 38 3.5.1 Correlation Between the Rotation and Transformation Matrices 38 3.5.2 Distinction Between the Rotation and Transformation Matrices 39 3.6 Relationship Between the Matrix Representations of a Rotation Operator in Different Reference Frames 40 3.7 Expression of a Transformation Matrix in a Case of Several Successive Rotations 40 3.7.1 Rotated Frame Based (RFB) Formulation 41 3.7.2 Initial Frame Based (IFB) Formulation 41 3.8 Expression of a Transformation Matrix in Terms of Euler Angles 42 3.8.1 General Definition of Euler Angles 42 3.8.2 IFB (Initial Frame Based) Euler Angle Sequences 42 3.8.3 RFB (Rotated Frame Based) Euler Angle Sequences 43 3.8.4 Remark 3.4 44 3.8.5 Remark 3.5 44 3.8.6 Remark 3.6: Preference Between IFB and RFB Sequences 45 3.8.7 Commonly Used Euler Angle Sequences 45 3.8.8 Extraction of Euler Angles from a Given Transformation Matrix 46 3.9 Position of a Point Expressed in Different Reference Frames and Homogeneous Transformation Matrices 51 3.9.1 Position of a Point Expressed in Different Reference Frames 51 3.9.2 Homogeneous, Nonhomogeneous, Linear, Nonlinear, and Affine Relationships 52 3.9.3 Affine Coordinate Transformation Between Two Reference Frames 53 3.9.4 Homogeneous Coordinate Transformation Between Two Reference Frames 54 3.9.5 Mathematical Properties of the Homogeneous Transformation Matrices 55 3.9.6 Example 3.2 58 4 Vector Differentiation Accompanied by Velocity and Acceleration Expressions 63 4.1 Derivatives of a Vector with Respect to Different Reference Frames 63 4.1.1 Differentiation and Resolution Frames 63 4.1.2 Components in Different Differentiation and Resolution Frames 64 4.1.3 Example 65 4.2 Vector Derivatives with Respect to Different Reference Frames and the Coriolis Transport Theorem 66 4.2.1 First Derivatives and the Relative Angular Velocity 66 4.2.2 Second Derivatives and the Relative Angular Acceleration 68 4.3 Combination of Relative Angular Velocities and Accelerations 70 4.3.1 Combination of Relative Angular Velocities 70 4.3.2 Combination of Relative Angular Accelerations 71 4.4 Angular Velocities and Accelerations Associated with Rotation Sequences 71 4.4.1 Relative Angular Velocities and Accelerations about Relatively Fixed Axes 71 4.4.2 Example 72 4.4.3 Angular Velocities Associated with the Euler Angle Sequences 74 4.5 Velocity and Acceleration of a Point with Respect to Different Reference Frames 77 4.5.1 Velocity of a Point with Respect to Different Reference Frames 77 4.5.2 Acceleration of a Point with Respect to Different Reference Frames 78 4.5.3 Velocity and Acceleration Expressions with Simplified Notations 79 5 Kinematics of Rigid Body Systems 81 5.1 Kinematic Description of a Rigid Body System 82 5.1.1 Body Frames and Joint Frames 82 5.1.2 Kinematic Chains, Kinematic Branches, and Kinematic Loops 83 5.1.3 Joints or Kinematic Pairs 83 5.2 Position Equations for a Kinematic Chain of Rigid Bodies 84 5.2.1 Relative Orientation Equation Between Successive Bodies 85 5.2.2 Relative Location Equation Between Successive Bodies 85 5.2.3 Orientation of a Body with Respect to the Base of the Kinematic Chain 85 5.2.4 Location of a Body with Respect to the Base of the Kinematic Chain 86 5.2.5 Loop Closure Equations for a Kinematic Loop 86 5.3 Velocity Equations for a Kinematic Chain of Rigid Bodies 87 5.3.1 Relative Angular Velocity between Successive Bodies 87 5.3.2 Relative Translational Velocity Between Successive Bodies 88 5.3.3 Angular Velocity of a Body with Respect to the Base 89 5.3.4 Translational Velocity of a Body with Respect to the Base 89 5.3.5 Velocity Equations for a Kinematic Loop 90 5.4 Acceleration Equations for a Kinematic Chain of Rigid Bodies 90 5.4.1 Relative Angular Acceleration Between Successive Bodies 91 5.4.2 Relative Translational Acceleration Between Successive Bodies 92 5.4.3 Angular Acceleration of a Body with Respect to the Base 92 5.4.4 Translational Acceleration of a Body with Respect to the Base 93 5.4.5 Acceleration Equations for a Kinematic Loop 93 5.5 Example 5.1 :A Serial Manipulator with an RRP Arm 94 5.5.1 Kinematic Description of the System 94 5.5.2 Position Analysis 95 5.5.3 Velocity Analysis 100 5.5.4 Acceleration Analysis 103 5.6 Example 5.2 :A Spatial Slider-Crank (RSSP) Mechanism 106 5.6.1 Kinematic Description of the Mechanism 106 5.6.2 Loop Closure Equations 108 5.6.3 Degree of Freedom or Mobility 109 5.6.4 Position Analysis 110 5.6.5 Velocity Analysis 119 5.6.6 Acceleration Analysis 122 6 Joints and Their Kinematic Characteristics 125 6.1 K
• Edition: 1st
• Publisher Details: Hoboken, New Jersey : John Wiley & Sons, Inc
• Publication Date: 2020
• Extent: 1 online resource
• Subjects: 621.815; Machinery, Kinematics of; Manipulators (Mechanism); Vector analysis; Matrices
• Languages: English
• ISBNs: 9781119195764; 9781119195757
• Related ISBNs: 9781119195733
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.