一类含复合驱动及约束分支少自由度并联机构理论研究

发布时间：2018-06-16 04:17

本文选题：并联机构 + 运动学　；参考：《燕山大学》2016年博士论文

【摘要】：少自由度并联机构具有相对较高的刚度、较少的驱动分支、较大的工作空间、较强的承载能力、结构简单和容易控制等优点。与传统的6自由度并联机构不同,少自由度并联机构中存在结构上的约束,导致机构分支中产生了约束力旋量,即约束力/力矩。为确定机构的应力、精度和选择适合的执行器,必须解出机构中的驱动-约束力旋量。通过构建复合驱动分支来减少驱动分支数量,合理布置分支和分配误差,提高少自由度并联机构的运动精度。刚度是并联机构重要的性能指标之一,因此分析刚度和变形对揭示少自由度并联机构特性是非常重要的。文中为确定少自由度并联机构的约束力旋量的位置并进一步分析静力学问题,提出一种静力学矢量分析方法。总结21种含有线性或转动驱动器的驱动分支,通过静力学矢量分析来确定施加在各分支上的约束力旋量的位置。对可调式少自由度并联机构驱动分支进行设计,通过3种运动副间的转换实现少自由度并联机构样式的变换。通过推导和使用6×6的Jacobian矩阵和静力学方程求解驱动-约束力旋量。使用静力学矢量分析法求解3自由度的3-RRPRR并联机构和4自由度的2-SPS+2-SPR并联机构的驱动-约束力旋量。提出一种运用CAD变量几何求解含有SPR驱动分支少自由度并联机构的驱动-约束力的方法。以含有SPR驱动分支的3-5自由度的3-SPR,2-SPS+2-SPR和4-SPS+SPR并联机构为例,首先构建它们的运动模拟机构,再进一步构建力学模拟机构,使用CAD变量几何方法求解其驱动-约束力矩阵和驱动-约束力。从而验证使用CAD变量几何方法在求解含有SPR驱动分支的并联机构的驱动-约束力问题上的可行性。提出并构建一种含有UPU复合驱动分支的3分支5自由度2-SPS+UPU并联机构和一种含有PUP复合驱动分支的3分支4自由度2-SPS+PUP并联机构,系统地分析复合驱动分支对运动学和静力学的影响。通过构建UPU和PUP复合驱动分支来提高少自由度并联机构的运动精度。考虑约束力旋量推导66?Jacobian矩阵和6阶66?Hessian矩阵,建立位移、速度、加速度模型并进行了静力学分析。对这两种并联机构进行运动仿真分析,比较解析结果和运动仿真结果。以驱动-约束力旋量为基础,求解3-SPS+UP和3-UPS+RRPR少自由度并联机构中驱动/约束分支的弹性变形,并推导驱动/约束分支的伴随矩阵。以驱动/约束分支的6×6的Jacobian矩阵和伴随矩阵为基础,求解这两种并联机构的总刚度和弹性变形。建立两种并联机构的有限元仿真模型,分析并比较机构动平台中心的弹性变形的解析结果与有限元仿真结果。分析约束力旋量对少自由度并联机构的刚度和弹性变形的影响。
[Abstract]:The small degree of freedom parallel mechanism has the advantages of relatively high stiffness, less driving branches, large workspace, strong bearing capacity, simple structure and easy control. Different from the traditional 6-DOF parallel mechanism, there are structural constraints in the low-degree-of-freedom parallel mechanism, which leads to the formation of binding force spinor, that is, the binding force / torque, in the branch of the mechanism. In order to determine the stress and precision of the mechanism and select a suitable actuator, the driving-binding spinor must be worked out. In order to reduce the number of driving branches, reasonably arrange the branches and allocate errors, the kinematic accuracy of the parallel mechanism with less degrees of freedom can be improved by constructing compound driving branches. Stiffness is one of the important performance indexes of parallel mechanism, so it is very important to analyze stiffness and deformation to reveal the characteristics of small degree of freedom parallel mechanism. In this paper, a static vector analysis method is proposed to determine the position of the binding spinor of a small degree of freedom parallel mechanism and to further analyze the statics problem. 21 kinds of driving branches with linear or rotational actuators are summarized, and the position of binding spinor applied on each branch is determined by static vector analysis. The driving branch of the adjustable parallel mechanism with less degrees of freedom is designed and the style of the mechanism is changed through the conversion of three kinds of kinematic pairs. A 6 脳 6 Jacobian matrix and statics equation are used to solve the drive-binding spinor. The driving-binding spinor of 3-RRPRR parallel mechanism with 3 degrees of freedom and 2-SPS 2-SPR parallel mechanism with 4 degrees of freedom is solved by static vector analysis. A method for solving the driving-binding force of a parallel mechanism with SPR driving branches with less degrees of freedom by using CAD variable geometry is proposed. Taking 3-SPR-2-SPS 2-SPR and 4-SPS SPR parallel mechanisms with 3-5 degrees of freedom as examples, their motion simulation mechanisms are first constructed, and then mechanical simulation mechanisms are further constructed. CAD variable geometry method is used to solve the driving-binding matrix and drive-binding matrix. The feasibility of using CAD variable geometry method to solve the driving-binding problem of parallel mechanism with SPR driving branch is verified. A 3-branch 5-DOF 2-SPS UPU parallel mechanism with UPU compound driving branch and a 3-branch 4-DOF 2-SPS PUP parallel mechanism with pup compound driving branch are proposed and constructed. The effects of compound driving branches on kinematics and statics are systematically analyzed. The kinematic accuracy of the parallel mechanism with less degrees of freedom is improved by constructing the UPU and PUP compound driving branches. In this paper, the displacement, velocity and acceleration models are established and statically analyzed considering the binding spinor derivation of the 66U Jacobian matrix and the 66th Hessian matrix of order 6. The kinematic simulation results of the two parallel mechanisms are compared and compared. Based on the driving-binding spinor, the elastic deformation of driving / constrained branches in 3-SPS up and 3-UPS RRPR parallel mechanisms with less degrees of freedom is solved, and the adjoint matrix of driving / constrained bifurcation is derived. Based on the Jacobian matrix and adjoint matrix of 6 脳 6 driving / constrained branches, the total stiffness and elastic deformation of these two parallel mechanisms are solved. The finite element simulation models of two parallel mechanisms are established, and the analytical results of elastic deformation of the center of the moving platform are analyzed and compared with the results of finite element simulation. The influence of the binding force on the stiffness and elastic deformation of a small degree of freedom parallel mechanism is analyzed.
【学位授予单位】：燕山大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TH112

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