关键词: 弹性悬链线, 非线性分析, 刚度矩阵, 静力学, 索牵引机器人

Abstract: Because of the huge workspace of the cable-supporting system for the large radio telescope, sag of cables needs to be considered in the stiffness analysis. Therefore, the relationship between cable end tension and cable length is deduced by using elastic catenary equation. The static model of the cable-supporting system is constructed with this relationship. Based on the nonlinear relationship between the cable end tension and the cabin displacement, the incremental expression of the resultant force on the cabin exerted by cables is formulated in terms of the cabin displacement. Then the analytical expression of the static stiffness matrix is obtained. Numerical examples are presented to validate the method. Stiffness matrix is reported at a point and the stiffness distribution is depicted within the workspace. The results show that the rotational stiffness about the cabin central axis is relatively weak.

Key words: Cable-driven robot, Elastic catenary, Nonlinear analysis, Statics, Stiffness matrix