This paper presents a new approach to calculate the direct and inverse differential kinematics for serial manipulators. The approach is an extension of the Davies method for open kinematic chains based on a virtual kinematic chain concept introduced in this paper. It is a systematic method that unifies the kinematics of serial manipulators considering the type of kinematics and the coordinate system of the operational space and constitutes an alternative way to solve the differential kinematics for manipulators. The usefulness of the method is illustrated by applying it to an industrial robot.
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