This paper addresses the instantaneous kinematics of robotic manipulators which have an in-parallel scheme of actuation. Hybrid geometries which require both serial and parallel actuation are also considered. Multifingered grippers, walking vehicles, and multiarm manipulation systems in addition to robot arms with a parallel structure can be included in this broad category. The direct and inverse kinematics (and statics) of these devices is discussed with particular attention to applications in control. An analytical method based on screw system theory for obtaining transformation equations between joint and end-effector coordinates is described. Special configurations in which the end-effector gains or loses a degree of freedom, which are also known as geometric singularities, are an important consideration in this study. This is because the number of special configurations or singularities in the workspace is far more for in-parallel manipulators than that for serial manipulators. The special configurations for a planar dual-arm manipulation system, which can be kinematically modeled as a 5-R linkage, are discussed in some detail as an example.

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