The effects of cables' strain and specific stiffness on the stiffness of cable-driven parallel manipulators

A cable-driven parallel manipulator is driven by a set of cables instead of rigid links. Since cables usually have more flexibility than rigid links, the stiffness of a cable-driven parallel manipulator has been a concern for many applications that require controllable system stiffness. This paper studies how cables' strain and specific stiffness affect the stiffness of a cable-driven parallel manipulator that has p degrees of freedom and n(n≥p+1) cables. A decoupled stiffness model of a cable-driven parallel manipulator is derived mathematically. In the decoupled stiffness model, cables' specific stiffness is decoupled from the other factors that affect the stiffness of the cable-driven parallel manipulator, namely, cable strains, positions of anchor points on the end-effector, and extended lengths and orientations of cables. The concept of stiffness change ratio is proposed to reflect how significantly the stiffness of a cable-driven parallel manipulator can be regulated at a specific pose. The decoupled stiffness model shows that it is cable strains, rather than just cable tensions, that determine the stiffness change ratio of a cable-driven parallel manipulator at a specific pose. It is mathematically proved that, at a specific pose, the stiffness change ratio of a cable-driven parallel manipulator using cables with an extended strain range is larger than or equal to that of the cable-driven parallel manipulator using cables with the original strain range.