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In this work the kinematics of a three-legged parallel manipulator with asymmetrical limbs and decoupled motions over its moving platform is investigated by means of the theory of screws. The solution of the forward displacement analysis (FDA) is presented in echelon-form solution using a novel procedure based on simple geometric constraints, thus all the feasible locations of the moving platform, with respect to the fixed platform, are computed given a set of generalized coordinates. After, the velocity and acceleration analyses are carried out using the theory of screws. Finally, a numerical example is included and the results obtained via the screw theory are verified with the aid of special commercially available software like MSC.Adams©.