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 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.

Professor Jian S. Dai is a pioneer and internationally recognized scholar in theoretical kinematics, Lie group methods, screw algebra, and reconfigurable mechanisms. He is a Fellow of the Royal Academy of Engineering (FREng), a Member of Academia Europaea (The Academy of Europe), and a Fellow of the IEEE, ASME, RSA and IMechE. 

Renowned for establishing the field of reconfigurable mechanisms and creating the sub-field of metamorphic mechanisms, Professor Dai has spearheaded three decades of groundbreaking mathematical research at the intersection of classical line geometry, dual vector spaces, and matrix Lie algebras. His theoretical discoveries have revolutionized the way researchers conceptualize variable-topology systems, origami-inspired mechanisms, and multi-fingered dexterous manipulation.

Professor Dai is the recipient of many of the highest honours in mechanical engineering and robotics, including the ASME Machine Design Award (58th recipient since 1958), the ASME Mechanisms and Robotics Award (27th recipient since 1974), the IFToMM Award of Merit (15th recipient since 2003), and the AT Yang Memorial Award in Theoretical Kinematics. He has authored over 700 peer-reviewed papers and numerous influential monographs, serves as Editor-in-Chief of Robotica, and educated generations of leading researchers worldwide.