This article analyzes three versions of a planar Compound Cable- Driven Parallel Robot (CCDPR), which consists of a tensegrity mechanism mounted on the moving-platform (MP) of a overconstrained planar cable-driven parallel robot (CDPR). The main objective of the proposed solution is twofold: (i) to allow reaching areas near and even beyond its frame and (ii) to provide stiffness modulation for safe human interaction. The tensegrity mechanism embedded on the MP is an anti-parallelogram joint (X-mechanism) antagonistically actuated by cables. Three different X-mechanism actuation schemes are proposed: (i) actuation by two actuated winches embedded in the MP, (ii) remote actuation via two cable loops that also contribute to the motion of the MP and (iii) remote actuation via two independent cables. The resulting three CCDPRs are analyzed and compared to a single CDPR based on their wrench feasible workspace and an equilibrium robustness index, named capacity margin. The comparison is carried out for a practical case study where the task is to inspect walls and ceiling. We show that the CCDPRs perform better than the single CDPR.