Cable-Driven Parallel Robots (CDPRs) are composed of a base frame and a moving-platform. A set of cables actuated by winches and guided by pulleys on the base frame are attached to the moving-platform. Those cables are used to generate motions or to apply forces to the moving-platform throughout its workspace. CDPRs are being increasingly used in industry due to several advantages provided by the cables such as a large translational workspace, a high payload-to-weight ratio and high velocities and accelerations. However since the cables can only pull the moving-platform, the latter cannot go out of the robot base frame bounded by the pulleys. An example is the treatment of large structures by using a CDPR. The structure itself can be used to hold the pulleys of the CDPR and the moving-platform would therefore need to go out of the robot volume to reach it. To overcome this issue a grasping device is mounted onto the moving-platform to grab the structure. It should be noted that when the structure is grabbed, the model of the overall system changes as the motions of the moving-platform is not only controlled by cables anymore, but the contact between the grasping device and the structure should be considered. This paper deals with the conceptual design of a grasping device for CDPRs and the definition of two workspaces. The first workspace characterize the area covered by the moving-platform when the latter is free of contact with the environment. The second workspace is the region that the gripper can follow during gripping phase. It turns out that the robot workspace increases while considering the structure grasping into the system modeling