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 Elie Cartan, and the
adjoint approach, conceived by Ernesto Cesaro, 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.
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