Robots interact with the world through curves and surfaces — the subjects of study in differential geometry. This book applies the moving-frame method, developed extensively by Élie Cartan, and the adjoint approach, conceived by Ernesto Cesàro, to study the kinematics of two surfaces subject to rolling contact and sliding–rolling contact to demonstrate the applications in robotic in-hand manipulation. Firstly, it explores two surfaces, and the geometry of both surfaces comes into play. Secondly, the book focuses on the geometry of the two surfaces within the encompassing space (extrinsic) rather than within the surfaces (intrinsic) because the book is concerned with the kinematics of one surface in three-dimensional Euclidean space — the real world. The book then concludes by applying this approach in robotic in-hand manipulation in the last chapter. Sample Chapter(s) Preface Chapter 1 : Introduction Contents: Preface About the Authors Introduction The Moving-Frame Method and Adjoint Approach: Curvatures of Curves and Surfaces via the Moving-Frame Method The Adjoint Approach to Curves and Surfaces Forward Kinematics of Rolling–Sliding Contact: From Trajectories to Velocity: Forward Kinematics of Rigid Surfaces with Rolling Contact From Trajectories to Velocity: Forward Kinematics of Rigid Surfaces with Rolling–Sliding Contact Inverse Kinematics of Rolling–Sliding Contact: From Velocity to Trajectories: Inverse Kinematics of Rigid Surfaces with Rolling Contact From Velocity to Trajectories: Inverse Kinematics of Rigid Surfaces with Rolling–Sliding Contact Kinematics of In-Hand Manipulation: Kinematic Analysis of the Metahand with Fixed-Point Contact Workspace and Posture Analysis of the Metahand Rolling Contact in Kinematics of In-Hand Manipulation Appendix Bibliography Index Readership: Undergraduate students, graduate students, engineers, and researchers in the field of biorobotics.