Abstract

GALLARDO-ALVARADO, J; RICO-MARTINEZ, J.M.  and  OROZCO-MENDOZA, H. An Algorithm to Solve Forward Kinematics Gough Stewart 6-3 Platforms. Comp. y Sist. [online]. 2004, vol.8, n.2, pp.132-149. ISSN 2007-9737.

An algorithm for solving the forward kinematics, up to the acceleration analysis, of a Gough Stewart platform with a special topology, namely type 6-3, is introduced in this work. The forward position analysis is carried out by applying simple geometric procedures that leads to a non-linear system of three equations with three unknowns, which is solved by means of the Newton-Raphson method. Afterwards, the properties of the Klein form, a bilinear symmetric form or inner product of the Lie algebra e(3), allow to obtain simple and compact expressions for the computation of the angular velocity and the angular acceleration of the moving platform with respect to the fixed platform. To this end, the velocity state, or the twist about a screw (Ball 1900), and the reduced acceleration state of the moving platform are expressed in screw form through each one of the six limbs of the parallel manipulator. With the aid of special software like Maple a numerical example is solved, and the numerical results so obtained are validated with the software of analysis ADAMS ©.

Keywords : Parallel platform; Acceleration Analysis; Klein form; Screw Theory; Kinematics.

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