一种四自由度空间并联机构的奇异位形解析

Symbolic Approach for Singularity configuration Analysis of a 4dof Spatial Parallel Mechanism

通过建立一种四自由度空间并联机构位姿约束方程 ,导出了该并联机构具有二维移动和二维转动的运动性质。推导出了奇异位形判别的解析表达式 ,在推导过程中引入数值—符号处理技术 ,得到了多项式代数方程中每一系数元素的数值—符号形式的解析表达式 ,并得到了奇异曲面方程及奇异曲面的截面曲线图。

Constrain equations of position and orientation for a 4dof spatial parallel mechanism are established,kinematic characteristic of two dimension move and two dimension rotation for this parallel mechanism is derived.An analytical expression for determining of singularity configuration which is a polynomial equation is set,and the numeric symbolic manipulating technique is introduced.Analytical expressions of numeric symbolic form for each coefficient of the polynomial equation are derived.The equations of singularity surface are derived,and the section curve graph of a singularity surface is drawn.A numerical example of singularity configuration analysis is given for illustration.