Cable Driven Parallel Robots (CDPRs) are parallel robots, in which the limbs are replaced by cables that are guided by pulleys. In many papers, the pulleys are considered as fixed points of passage and the cable elasticity is neglected. Those approximations simplify the robot modelling, but lead to some Moving-Platform (MP) pose errors. This paper deals with the modelling of suspended CDPRs considering the geometry and kinematics of the pulleys as well as the cable elasticity. Furthermore, a novel pulley architecture with an universal joint is designed. It is introduced to increase the accuracy of CDPRs and limit the bending moment in the pulleys. Then a sensitivity analysis conducted on these newly established models allows to precisely quantify the effect of design parameters on the MP pose and to exhibit the set of the most influentials elasto-geometric parameters. Both standard and extended direct elasto-geometric static models of the CDPRs are numerically solved to determine the MP pose for given cable lengths and external wrench. Then, an index is defined based on the MP pose difference, the latter being traced through the robot Cartesian workspace. This index is used to analyze and compare the pulleys effects on the MP pose errors. It turns out that the interaction between pulleys geometrical parameters are significant and should be considered in the elasto-geometric static models. Finally, it is shown that a CDPR equipped with the novel pulley architecture is more sensitive to cable elasticity, but this new architecture helps reducing the overall MP error.