Screw Algebra and Geometric Kinematics

This open access book bridging a long-standing theoretical gap in kinematics, Screw Algebra and Geometric Kinematics delivers a comprehensive, modern algebraic framework that connects classical screw theory directly with Lie groups, Lie algebras and projective differential geometry. The 17-chapter monograph presents a rigorous, Lie-theoretic synthesis of classical spatial mechanics and modern differential geometry. Bridging nineteenth-century line geometry—from Mozzi, Chasles and Plücker to Ball, Klein and Clifford—with the intrinsic algebraic structures of SE(3) and its Lie algebra se(3), the book establishes a unified mathematical framework for Lie-group methods, adjoint representations and dual vector spaces in mechanism theory. The book’s text guides readers from the core Lie-algebraic structure of screws and dual numbers to adjoint transformations, multidimensional null spaces, reciprocity theorems and Lie-bracket formulations of kinematic constraints. It demonstrates how these advanced Lie-theoretic principles directly translate into practical mechanism design, providing closed-form mathematical tools for singularity analysis, posture-manifold characterization, workspace-boundary topology and the mobility analysis of metamorphic and origami-inspired reconfigurable mechanisms. Tailored for researchers, graduate students and mathematicians in robotics and theoretical kinematics, this volume serves as an authoritative reference on Lie-theoretic spatial motion. The monograph will serve as a benchmark for kinematics scholars, robotics researchers and design theorists for years to come.