新型过约束2-UPS+2-RPU并联机构的刚度分析  

Stiffness Analysis of a Novel Over- constraint 2UPS+2-RPU Parallel Manipulator

作　　者：王书森 梅瑛[1] 李瑞琴[1] 

机构地区：[1]中北大学机械与动力工程学院,山西太原030051

出　　处：《机械传动》2016年第8期33-37,77,共6页Journal of Mechanical Transmission

基　　金：国家自然科学基金(51275486)

摘　　要：提出一种新型过约束2-UPS+2-RPU并联机构,该机构的2个RPU分支一共提供了4个约束,但由于机构运动副的特殊布置,其中的2个约束为过约束。首先,基于螺旋理论分析该机构中存在的约束反力,建立该机构的速度约束方程,并基于此分析该机构的自由度。其次,建立该机构的几何约束方程,利用解析矢量法求得机构位置逆解方程。随后,基于计算杆件变形方法及小变形叠加原理,分析各杆在支链约束力螺旋作用下产生的弹性变形,并定义了分支约束力螺旋系刚度矩阵。最后,建立机构的动平台位姿变化与外载荷关系,进而得到机构的整体柔度、刚度矩阵。得出约束力/矩对这类少自由过约束机构的刚度和变形影响很大且其弹性变形主要产生在约束力/矩轴线方向。A novel 2- UPS ＋ 2- RPU over- constraint parallel manipulator（ PM） is proposed. The two RPU legs of this PM provide four constraints whereas two of them are over- constraints due to the particular arrangement of the joints in RPU legs. Firstly,the constraint forces are analyzed on the basis of the screw theory and the velocity constraint equation of this PM is established,and based on this,the degree of freedom of this PM is analyzed. Secondly,the geometric constraint equations of this PM are established,and the inverse displacement analysis model is provided by using analytical methods. Then,the elastic deformation of the limb is analyzed with the limb constraint wrenches based on calculating deformation and superposition principle at small strain,and the stiffness matrix of the limb constraint wrenches is defined. Finally,the relationship between outer loads and both the line displacement and the angle displacement of the moving platform is set up,and then the matrices of flexibility and stiffness are obtained. It is found that the constrained force / torques have a major influence on the stiffness and elastic deformation of limited- DOF over- constraint PMs,and the elastic deformation are mainly in the axial direction of the constrained force / torques.

关 键 词：并联机构 刚度 过约束 约束力螺旋 弹性变形 

分 类 号：TH112[机械工程—机械设计及理论]