In this work the kinematics, including the acceleration analysis, of 3-RPS parallel manipulators has been successfully approached by means of screw theory. Firstly, the forward position analysis was carried out using recursively the Sylvester dialytic elimination method, such a procedure yields a 16-th polynomial expression in one unknown, and therefore all the possible solutions of this initial analysis are systematically calculated. Afterwards, the velocity and acceleration analyses are addressed using screw theory. To this end, the velocity and reduced acceleration states of the moving platform, with respect to the fixed platform are written in screw form through each one of the three limbs of the manipulator. Simple and compact expressions were derived in this contribution for solving the forward kinematics of the spatial mechanism by taking advantage of the concept of reciprocal screws via the Klein form of the Lie algebra e (3). The obtained expressions are simple, compact and can be easily translated into computer codes. Finally, in order to exemplify the versatility of the chosen methodology, a case study was included in this work.