Screw Algebra and Geometric Kinematics (el. knyga) (skaityta knyga) | knygos.lt

Aprašymas

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.