Cable-driven parallel robots (CDPRs) have larger workspace, simple design, are easy to transport, assemble and disassemble, and hence, possess a great potential in on-site 3D printing of large structures. However, they are prone to collision of cables with the preceding layers of structures being 3D printed. Therefore, this work proposes an analytical approach to determine the boundary of the collision-free workspace of planar over-constrained cable robots. This workspace is composed of poses that can be reached while avoiding the collision of lower cables with the structure being printed. The analytical expressions of the collision-free workspace have been obtained for both cases, i.e., considering zero platform orientation and variable platform orientation. These analytical expressions have been utilized for rapid computation of collision-free workspace. Simulation results have been obtained for both cases, and the effect of orientation on the collision-free workspace is analyzed. Additionally, the optimal design problem of CDPR is presented to achieve the desired collision-free workspace while minimizing the installation space of the robot. The results show a significant reduction in installation space by considering the variable orientation of the platform.