一种少自由度并联机构静刚度研究

Stiffness Analysis of One Limited-DOF Parallel Mechanism

并联机构,尤其是用于机加工的并联机床都需要很高的刚度要求,因此建立其刚度模型就显得尤为重要。现有的刚度建模方法多是基于集中刚度模型,但是该方法的物理意义不够明确。基于螺旋理论建立了一种少自由度并联机构的刚度模型,该方法将驱动刚度和约束刚度区别对待,物理意义明确。通过计算并联机构空间自由度,并利用螺旋方程的反螺旋解法,得出并联机构的运动雅可比矩阵和约束雅可比矩阵,经组合得到少自由度并联机构的完全雅可比矩阵,从而建立了其静刚度模型。建立的静刚度模型可以作为少自由度并联机构的性能评价指标,同时又可以为分析其他过约束的少自由度并联机构提供理论支持。

Stiffness is one of the most important performances of parallel mechanisms, particularly for those which are used as machine tools. Therefore, it is quite necessary to set up its stiffness modeling. By now, the stiffness analysis for some parallel manipulators are established in static condition by means of lumped stiffness model, but the physical meaning of this approach is not very clear. This paper presents an explicit approach for the static stiffness and degrees of freedom analysis of the Limited-DOF parallel manipulator based on the screw theory. The manipulator is divided into three branches for the convenience of analysis. The reciprocal screw system of each chain is derived from the twist equations. Then, the kinematic Jacobian sub-matrix and constraint Jacobian sub-matrix are derived based on the reciprocal product. According to these two sub-matrixes, the overall Jacobian matrix is obtained. The proposed stiffness model can be used as performance evaluation method for the Limited-DOF parallel manipulators.