This paper presents a geometrical model of a constrained robot of three degrees of freedom (d.o.f) added to a PPP passive central segment. This structure provides a pure translation motion. We will also determine the relations between generalized and articular velocities by using the inverse Jacobian matrix. Further, we determine the reciprocal relations between cartesian and angular velocities of the end-effector via articular velocities by simple derivation of the direct geometrical model expressions. A determination of the workspace based on the geometrical model analysis is derived followed by a numerical calculation of all the atteignables points enabling a graphical visualisation of such a workspace. Moreover, the analysis of the Jacobian matrix has permitted to ensure that there are no singularities of type 1 and 2 in such a structure. A prototype of a parallel robot has been built up in our laboratory in order to validate the proposed models.