The remote centre of motion (RCM) mechanisms are increasingly used to develop robotic surgical systems. Currently, parallelogram-based planar RCM mechanism are often combined with single revolute joint to deliver the two degrees of freedom (DOFs) required in the minimally-invasive surgical applications. However, parallelogram-based planar RCM mechanisms encounter issues associated with device footprint, which compromise optimal surgical functioning. The dual-triangular linkage (DT-linkage) with RCM is proposed in the attempt to replace the parallelogram-based linkage and resolve the footprint issue. This paper presents the work on the design and static analysis of cable-based auxiliary mechanism for DT-linkage. The aim is to achieve backlash-free and singularity-free mechanical constraint, such that the ROM of the original DT-linkage can be doubled without expanding the device footprint. A constraint approach is conducted to solve for the force within the cable sections. The analytical solution at singular configuration indicates tension in all cable sections hence proved the functioning of the cable constraint. By utilising the QR decomposition, the numerical solution of minimum required cable stiffness is also calculated from the constraint approach.