We present definitions of a robot manipulator, configuration space and kinematic map from a topological viewpoint. The classes of serial and parallel manipulators are studied to determine their kinematic mapping and its singular points. The kinematic mapping of serial manipulators and its singular points are computed using Denavit-Hartenberg parameters. We study the conditions under which singular points and singular values separate the configuration space of serial manipulators. For analysis of parallel manipulators the concepts of assembly modes and extended configuration space are presented. We determine the local kinematic mapping of parallel manipulators using the implicit function theorem.
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