Variable-stiffness decoupling of redundant planar rotational parallel mechanisms with crossed legs

For redundant planar rotational parallel mechanisms (RPRPM), stiffness consists of active stiffness resulting from internal forces and passive stiffness caused by compliances of flexible elements, and the active stiffness is coupled with the passive stiffness. The stiffness variations with stretching internal force and compressing internal force of flexible elements are analyzed. By combining the leg-crossed RPRPM and leg-uncrossed RPRPM of different leg arrangements, the active stiffness is decoupled from the passive stiffness. The stiffness is modulated by changing the internal force and hence the spring stretching length independently to avoid being influenced by the passive stiffness. The stiffness variation multiple with given spring stretching length is maximized by decoupling the active stiffness from the passive stiffness. The variation of natural frequency of RPRPM is maximized by maximizing the stiffness variation, and the RPRPM can employ vibration of resonance to improve the working performance in a large range of driving frequency.