求解3-RPS并联机构刚度的新方法

对于少自由度机构来说,由于结构约束的存在,机构中出现了约束反力,约束反力会在机构中产生变形,影响整个机构的精度,在机构分析中必须加以考虑。基于此,以传统的3-RPS并联机构为例,给出考虑约束反力产生变形的刚度模型的建立方法。首先,用观察法分析该机构中存在的约束反力。其次,建立该机构的6×6形式雅可比矩阵,并运用虚功原理建立该机构的静力学模型。最后,分析机构在驱动力和约束力共同作用下产生的弹性变形。在约束反力产生的变形方向上虚设P副,将3-RPS机构的变形和刚度分析转化为一个等效的无约束反力的6自由度并联机构3-RPPS的变形和刚度分析。这种方法给少自由度机构的研究提供了一些新观点。

New Approach for Analyzing the Stiffness of 3-RPS Parallel Manipulator

For lower mobility parallel manipulators (PMs), the constrained forces/torques appear because the structure constraint exists. The constrained forces/torques must be considered in analyzing the stiffness for PMs because the constrained forces/torques can produce elastic deformation and affect the precision of PM. The stiffness of a traditional parallel manipulator 3-RPS is analyzed to illustrate this method. First, the constrained forces are analyzed on the basis of the observation method. Second, the 6×6 Jacobian matrix is established, and the statics model is established by applying the principle of virtual work. Finally, the deformation of the PM is analyzed with the active forces and the constrained forces considered. The stiffness of 3-RPS PM is analyzed by converting the 3-DOF PM into a 6-DOF PM free from constrained forces/torques by setting virtual P joints along the direction of constrained forces. This method provides some new points of view for lower mobility PMs.