Ebook: Kinematics of general spatial mechanical systems

Vectors and their matrix representations in selected reference frames -- Rotation of vectors and rotation matrices -- Matrix representations of vectors in different reference frames and the component transformation matrices -- Vector differentiation accompanied by velocity and acceleration expressions -- Kinematics of rigid body systems -- Joints and their kinematic characteristics -- Kinematic features of serial manipulators -- Position and motion analyses of generic serial manipulators -- Kinematic analyses of typical serial manipulators -- Position and velocity analyses of parallel manipulators.;"This book is concerned primarily with the kinematic description and analysis of the spatial mechanical systems such as serial manipulators, parallel manipulators, and spatial mechanisms. However, a planar mechanical system is also considered whenever it helps to demonstrate and discuss a kinematic feature more neatly and clearly. Emphasis is placed on the analytical and semi-analytical methods in the treatment of the topics it covers, whilst purely numerical methods are kept beyond the scope of the book. Consideration is placed on four main elements: The necessary mathematics of spatial kinematics comprising the relevant theorems, formulas, and methods; the kinematic description of the links and joints, which are the basic constituents of mechanical systems; writing the kinematic chain equations for the systems to be analyzed; and solving the kinematic chain equations for the unspecified variables together with the multiplicity and singularity analyses. The book will have a wide coverage of topics ranging from rather elementary topics such as six-joint serial manipulators to more advanced topics such as non-holonomic spatial cam mechanisms. It presents an effective symbolic manipulation method that can be applied easily and straightforwardly. Thus, it will be possible to obtain neat and transparent (explicit in parameters) expressions to describe the systems kinematically. Such expressions will then conveniently lead to analytical or semi-analytical solutions. Owing to the analytical and semi-analytical solutions, the multiple solutions and the workspace restrictions can easily be detected and discussed. Moreover, the singularities can also be easily identified and their consequences can be discussed in detail. The coverage and the methodology of the book will attract the attention of those involved with robotics and spatial mechanisms, or interested simply in kinematics. It can serve as a supplementary text for graduate students, or as a reference book for researchers and professionals"--