Forward Kinematics of the 3S-6S Spherical Stewart Platform by Means of Screw Theory


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Abstract


In this work the forward kinematics of a decoupled Gough-Stewart platform is approached by means of the theory of screws. The forward position analysis is carried out using recursive procedures based on simple analytic quadratic equations, thus this initial analysis is free of unwanted solutions. Afterwards, the forward acceleration analysis is simplified considerably by taking advantage of the properties of reciprocal screws. The expressions thus obtained for the computation of the angular acceleration of the moving platform, and the translational acceleration of a point fixed to it, do not require the values of the passive joint acceleration rates of the manipulator. Of course, this contribution also provides, as an intermediate step, the forward and inverse velocity analyses of the mechanism. Finally, a numerical example is provided and the results obtained via screw theory are compared with results generated with special software like ADAMS©.
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Keywords


Parallel Manipulator; Decoupled Motion; Klein Form; Screw Theory; Kinematics

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