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现有索牵引并联机器人研究中,由于柔索长度较短大多将其处理成仅能受拉的直线索单元,没有考虑柔索垂度的影响,刚度分析过程与刚性支腿并联机器人相同。为考虑垂度影响,该文采用悬链线方程建立了大跨度柔索的静力学模型,推导出柔索的刚度矩阵。然后提出了一种刚度等效模型,将柔索等效为三根两两相互垂直的弹簧。于是便可将索牵引并联机器人等效为弹簧支撑并联机器人,从而利用现有的刚度分析结论即可完成大跨度索牵引机器人的刚度分析。最后,以大射电望远镜的索支撑系统为例研究了其刚度特性。
In the existing research on cable-pulling parallel robots, the stiffness analysis process is the same as the rigid leg parallel robots, because the length of the flexible cable is mostly shorter than the straight cable unit that can be pulled. In order to consider the influence of dip, a static model of long-span flexible cable is established by using catenary equation, and the stiffness matrix of flexible cable is deduced. Then, a stiffness equivalent model is proposed, which is equivalent to three springs with two perpendicular to each other. Therefore, the cable-pulling parallel robot can be equivalent to a spring-supported parallel robot so that the stiffness analysis of the long-span cable-pulling robot can be completed by using the existing stiffness analysis conclusion. Finally, taking the cable support system of a large radio telescope as an example, the stiffness characteristics are studied.