Abstract
In this work the kinematics of a parallel manipulator performing Schönflies motion is investigated by means of the theory of screws. As an intermediate step, the displacement analysis is reported in semi-closed form solution based on the coordinates of two points embedded in the moving platform. This strategy allows to employ only one reference frame avoiding the computation of the rotation matrix. The input-output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. To this aim, the robot is treated as a six-degrees-of-freedom parallel manipulator incorporating pseudo kinematic pairs connecting the limbs to the fixed platform and one virtual kinematic chain in order to apply without restrictions the Lie algebra se(3) of the Euclidean group SE(3). The singularity analysis is investigated based on the input-output equation of velocity. Numerical examples are included in order to show the application of the method.
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