Stiffness analysis of cable-driven parallel mechanisms with cables having large sustainable strains

A cable-driven parallel mechanism is driven by a group of cables. Cable-driven parallel mechanisms can use various cables (e.g. steel cables, nylon cables, isoprene rubber cables, and extension springs) with different sustainable strains. This paper studies the stiffness of cable-driven parallel mechanisms with cables having large sustainable strains, aiming to achieve significantly adjustable overall stiffness. The overall stiffness of a cable-driven parallel mechanism can be decomposed into the constant base stiffness and the adjustable strain stiffness. This paper proposes and mathematically proves a theorem that guarantees that the overall stiffness of a cable-driven parallel mechanism at an arbitrary stable pose can be dominated by the adjustable strain stiffness when cable strains are larger than 100%. The theorem employs the minimum eigenvalues of stiffness matrices to characterize the stiffness of cable-driven parallel mechanism. The theorem provides a sufficient condition that guarantees that the overall stiffness of a cable-driven parallel mechanism at an arbitrary stable pose can be significantly adjusted (i.e. the adjustable strain stiffness contributes more than the constant base stiffness in determining the overall stiffness). The theorem is verified through the simulation of a cable-driven parallel mechanism with six degrees of freedom and seven cables.