Kinematics [electronic resource] : Theory and Applications /
Wittenburg, Jens.author.
The book deals with kinematics of mechanisms. It focuses on a solid theoretical foundation and on mathematical methods applicable to the solution of problems of very diverse nature. Applications are demonstrated in a large number of fully worked-out problems.  In kinematics a wide variety of mathematical tools is applicable. In this book, wherever possible vector equations are formulated instead of lengthy scalar coordinate equations. The principle of transference is applied to problems of very diverse nature. 15 chapters of the book are devoted to spatial kinematics and three chapters to planar kinematics. In Chapt. 19 nonlinear dynamics equations of motion are formulated for general spatial mechanisms. Nearly one half of the book is dealing with position theory and the other half with motion. The book is intended for use as reference book for researchers and as textbook in advanced courses on kinematics of mechanisms.
Description based upon print version of record.
Preface; Notation; Contents; Chapter 1 Rotation about a Fixed Point.Reflection in a Plane; 1.1 Direction Cosine Matrix; 1.2 Similarity Transformation; 1.3 Euler Angles; 1.4 Bryan Angles; 1.5 Rotation Tensor; 1.6 Euler-Rodrigues Parameters; 1.7 Relationships Between Euler-Rodrigues Parameters and Euler Angles; 1.8 Quaternions; 1.9 Relationships Between Three Positions of a Body; 1.10 Relationships Between four Positions; 1.11 Cayley-Klein Parameters; 1.12 Euler Vector. Exponential Form of the Direction Cosine Matrix; 1.13 Rodrigues Vector; 1.14 Wiener Vector; 1.15 Illustrative Problems
1.15.11 Decomposition of a Rotation into threeRotations1.15.12 Decomposition of a Rotation into three Rotations. Quaternion Formulation; 1.16 Reflection in a Plane; References; Chapter 2 Line Geometry; 2.1 Normal Vector of a Plane. Equation of a Plane; 2.2 Plücker Vectors. Plücker Coordinates of a Line; 2.3 Reflection in a Line; 2.4 Plücker Vectors of the Line of Intersection of two Planes; 2.5 Condition for two Lines to Intersect; 2.6 Plücker Vectors of the Common Perpendicular of two Lines; 2.7 Linear Complex; 2.7.1 Null Point. Null Plane; 2.7.2 Axis. Pitch
3.7 Resultant of two Screw Displacements. ScrewTriangle3.8 Dual Numbers; 3.9 Dual Vectors. Dual Angles; 3.10 Principle of Transference; 3.10.1 Dual Basis. Dual Direction Cosine Matrix; 3.10.2 Screw Axis, Screw Angle and Translation Determined from Dual Direction Cosines; 3.10.3 Dual Euler Angles. Dual Bryan Angles; 3.10.4 Dual Rodrigues Vector; 3.10.5 Dual Euler-Rodrigues Parameters. DualQuaternions; 3.11 Resultant of two Screw Displacements.Dual-Quaternion Formulation; 3.12 Equations for the Screw Triangle; 3.13 Resultant of two Infinitesimal Screw Displacements. Cylindroid
3.14 Screw Displacements Effecting a Prescribed Line Displacement
Includes bibliographical references and index.
The book deals with kinematics of mechanisms. It focuses on a solid theoretical foundation and on mathematical methods applicable to the solution of problems of very diverse nature. Applications are demonstrated in a large number of fully worked-out problems.  In kinematics a wide variety of mathematical tools is applicable. In this book, wherever possible vector equations are formulated instead of lengthy scalar coordinate equations. The principle of transference is applied to problems of very diverse nature. 15 chapters of the book are devoted to spatial kinematics and three chapters to planar kinematics. In Chapt. 19 nonlinear dynamics equations of motion are formulated for general spatial mechanisms. Nearly one half of the book is dealing with position theory and the other half with motion. The book is intended for use as reference book for researchers and as textbook in advanced courses on kinematics of mechanisms.
Vibration.
Dynamical systems.
Dynamics.
Mechanics.
Mechanics, Applied.
Vibration, Dynamical Systems, Control.
Solid Mechanics.
Classical Mechanics.