运用螺旋理论分析了一种具有三维转动和一维移动(沿Z轴)的四自由度(4-SPS/CU)并联机构的自由度,得出该机构为无过约束机构.采用传统的拆杆法对该机构的每个活动构件进行了静力学分析,得出了该机构的静力学平衡方程组,判定该机构的静力学平衡方程组中方程个数大于未知量个数(属超定方程组).多余的方程个数就是该机构的局部自由度,并采取去掉局部自由度对应的静力学平衡方程来求解该超定方程组.通过求解该方程组,得出了该机构每个构件上的全部约束力/力矩,并分别得出了驱动力与主运动副以及恰约束从动支链的约束反力随该机构位姿变化的仿真曲线.证实了该机构比无恰约束从动支链的四自由度并联机构拥有更好的承载能力.研究结果可为该机构在工程中的应用与结构设计提供静力学理论分析的参考.%The degree of freedom of a 4-SPS/CU parallel mechanism which can perform three-dimensional rotations and translation along Z axis was analyzed based on the screw theory, and concluded that this parallel mechanism was a non-overconstrained mechanism. By the dismantle-bar method, the static equilibrium equations of the mechanism were set up. The equations' number are more than the unknown variables in the static equilibrium equations (belong to overdetermined equation), and the number of redundant equations were equal to the passive degrees of freedom. All of the forces/torques of each component of the mechanism was obtained by solving the static equilibrium equations which got rid of the redundant equilibrium equations corresponding to passive degree of freedom. The simulation curves of the driving force and constraint reactions were given with change of the mechanism's position and posture. It was confirmed that the mechanism had better carrying capacity than other 4-DOF parallel mechanism without the driven chain. The research results could provide the statics analysis method for the application of engineering and structure design.
展开▼
