This book presents recent advances in robot kinematics and computational geometry in kinematics. More than fifty contributions report the most effective mathematical forms for mapping between various types of coordinate systems, methods to minimise the numerical complexity of algorithms for real-time control schemes, and discover analytical tools for understanding and evaluating motion properties of various mechanisms used in a robotic system. The book is divided into twelve sections, identified as the prevalent areas of contemporary research in kinematics and computational geometry as applied to robots and mechanisms. They include the following topics: workspace and trajectory analysis, computational geometry in kinematics, kinematic errors and calibration, kinematics of mobile robots, kinematic performance, kinematics in control, force and elasticity analysis, inverse kinematics, kinematic design, kinematic analysis, parallel manipulators, as well as task and motion planning. The book is of interest to researchers, graduate students, mathematicians and engineers specialising in kinematics of robots and mechanisms in the area of mathematical modelling, design, control, and simulation.