In this paper, we will present a new 6-DOF parallel robot using a set of two Delta structures. An effective method is proposed to establish explicit relationships between the end effector co-ordinates and the active and passive joint variables. A simulation of the 2-Delta robot on a C.A.D. Robotics system will also be presented. This simulation will allow us to validate the cohesion of our calculations, and to show the workspace depending on the mechanical limits on passive joints variables. Finally, an approach is proposed to study the influence of small clearances of the passive joint on the precision of the position and rotation of the effector. This approach is based on a concept similar to that of Yoshikawa's manipulability.