Static Stiffness Analysis of Flexible-cable-driven Parallel Mechanism

The static stiffness of flexible-cable-driven parallel mechanism is studied and its theoretical formulation of the calculation model is deduced. The results show that the static stiffness matrix of flexible-cable-driven parallel mechanism can be decomposed into two parts. k1 results from the changes of position and orientation of the movable platform which correlates with cable tensions, while k2 is caused by the deformation and deflection of cables. The study further proves that the static stiffness of completely restrained positioning mechanism (CRPM) or redundantly restrained positioning mechanism (RRPM) mainly depends on k2. It is only affected by the elastic performances of all cables and the Jacobian matrix which represents the vectors of cable forces, and unrelated with the amplitudes of cable tensions. For the incompletely restrained positioning mechanism (IRPM), because of the existence of cable catenaries the static stiffness not only correlates with the elastic performances of all cables and the Jacobian matrix, but also the amplitudes of cable tensions. Two examples concerning the static stiffness estimation are given for RRPM and IRPM(the cable-driven cabin suspension of the five-hundred-meter aperture spherical telescope)respectively. The comparison between the analytical and simulation results proves the validity of the calculation model.