Kinematics of General Spatial Mechanical Systems. M. Kemal Ozgoren

      Table of Contents

      1  Cover

      2  Preface

      3  Acknowledgments

      4  List of Commonly Used Symbols, Abbreviations, and Acronyms

      5  About the Companion Website

      6  1 Vectors and Their Matrix Representations in Selected Reference Frames Synopsis 1.1 General Features of Notation 1.2 Vectors 1.3 Vector Products 1.4 Reference Frames 1.5 Representation of a Vector in a Selected Reference Frame 1.6 Matrix Operations Corresponding to Vector Operations 1.7 Mathematical Properties of the Skew Symmetric Matrices 1.8 Examples Involving Skew Symmetric Matrices

      7  2 Rotation of Vectors and Rotation Matrices Synopsis 2.1 Vector Equation of Rotation and the Rodrigues Formula 2.2 Matrix Equation of Rotation and the Rotation Matrix 2.3 Exponentially Expressed Rotation Matrix 2.4 Basic Rotation Matrices 2.5 Successive Rotations 2.6 Orthonormality of the Rotation Matrices 2.7 Mathematical Properties of the Rotation Matrices 2.8 Examples Involving Rotation Matrices 2.9 Determination of the Angle and Axis of a Specified Rotation Matrix 2.10 Definition and Properties of the Double Argument Arctangent Function

      8  3 Matrix Representations of Vectors in Different Reference Frames and the Component Transformation Matrices Synopsis 3.1 Matrix Representations of a Vector in Different Reference Frames 3.2 Transformation Matrices Between Reference Frames 3.3 Expression of a Transformation Matrix in Terms of Basis Vectors 3.4 Expression of a Transformation Matrix as a Direction Cosine Matrix 3.5 Expression of a Transformation Matrix as a Rotation Matrix 3.6 Relationship Between the Matrix Representations of a Rotation Operator in Different Reference Frames 3.7 Expression of a Transformation Matrix in a Case of Several Successive Rotations 3.8 Expression of a Transformation Matrix in Terms of Euler Angles 3.9 Position of a Point Expressed in Different Reference Frames and Homogeneous Transformation Matrices

      9  4 Vector Differentiation Accompanied by Velocity and Acceleration Expressions Synopsis 4.1 Derivatives of a Vector with Respect to Different Reference Frames 4.2 Vector Derivatives with Respect to Different Reference Frames and the Coriolis Transport Theorem 4.3 Combination of Relative Angular Velocities and Accelerations 4.4 Angular Velocities and Accelerations Associated with Rotation Sequences 4.5 Velocity and Acceleration of a Point with Respect to Different Reference Frames

      10  5 Kinematics of Rigid Body Systems Synopsis 5.1 Kinematic Description of a Rigid Body System 5.2 Position Equations for a Kinematic Chain of Rigid Bodies 5.3 Velocity Equations for a Kinematic Chain of Rigid Bodies 5.4 Acceleration Equations for a Kinematic Chain of Rigid Bodies 5.5 Example 5.1 : A Serial Manipulator with an RRP Arm 5.6 Example 5.2 : A Spatial Slider‐Crank (RSSP) Mechanism

      11  6 Joints and Their Kinematic Characteristics Synopsis 6.1 Kinematic Details of the Joints 6.2 Typical Lower Order Joints 6.3 Higher Order Joints with Simple Contacts 6.4 Typical Multi‐Joint Connections 6.5 Rolling Contact Joints with Point Contacts 6.6 Rolling Contact Joints with Line Contacts 6.7 Examples

      12  7 Kinematic Features of Serial Manipulators Synopsis 7.1 Kinematic Description of a General Serial Manipulator 7.2