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On the stability for a cable-driven parallel robot while considering the cable sag effects

A stability measure approach with combination of force and position is proposed while considering the cable mass in this paper in order to assess the stability of a cable-driven parallel robot with long-span cables. The stability mentioned here implies the ability of the cable structure resisting the external disturbances to make the platform be in equilibrium. Firstly, the kinematic equation with highly nonlinear nature is set up regarding the large-span cables as catenaries. Secondly, an iterative optimization algorithm of the cable tension distributions is presented based on the kinematic equation, in which four factors having a significant effect on the stability of the robot at any pose are determined. Thirdly, the stability measure approach is described using the weighted method based on the four factors above. Finally, numerical examples are presented to demonstrate the significant effects of cable sags on both the cable tension distributions and the stability. In addition, the results show that it is necessary to take the cable sags into consideration for the large-span manipulators.