摘要
与传统的串联机构相比,纯并联机构在结构及运动特性上具有承载能力强、定位精度高、刚度重量比大、结构简单、动平台运动灵活等一系列优点。但并联机构同时也存在着工作空间小、控制复杂、运动学标定困难能缺点。相对于与以Stewart平台型并联机机构为代表的6自由度机构,少自由度并联机构由于具有结构简单、工作空间大、造价低等突出优点,近年来广受学术界和工业界的关注。本文提出一种四自由度并联机构新构型——2-TPR/2-TPS并联机构,对该机构进行了深入的分析研究,在此基础上通过在2-TPR/2-TPS并联机构机构上串联一个转动轴,提出了一种新型5轴并串联机床,对该机床机构进行了相关的运动学分析与结构参数设计的研究。
研究了新型2-TPR/2-TPS空间四自由度并联机构结构布局特点;应用螺旋理论分析了机构的运动性质,确定了机构的运动自由度;通过机构的结构约束关系推导了机构动平台位姿参数的解耦关系式;应用解析法推导了机构的位姿反解方程,应用数值方法给出了机构的位姿正解;在螺旋理论的基础上提出了一种分析并联机构奇异位形的新方法——瞬时坐标系法,并应用此方法得到了机构的三种奇异位形。
基于2-TPR/2-TPS并联机构,通过在其运动平台上串联一个回转轴,提出了一种新型5轴并串联机床。研究了该机床的结构特点,得出了该机床的位姿正反解;应用矢量几何法推导了机构一阶影响系数矩阵及二阶影响系数矩阵,并在此基础上进行了速度分析与加速度分析。
借助机床的位姿反解算法,采用空间三坐标交替搜索的数值方法生成了给定刀具最大加工倾角的机床刀头点的可达工作空间;分析了机床工作空间的特点,采用数值法计算了工作空间的体积;分析了刀具的加工倾角的变化对工作空间的影响;研究了机床工作空间的大小随机床结构参数变化的情况,为机床结构参数的设计提供了理论依据。
基于2-TPR/2-TPS空间四自由度并联机构的一阶影响系数矩阵,对机床的灵活度进行了解析;分析了机床的的位置灵活度和姿态灵活度指标在工作空间中的分布状况;研究了机床的灵活度指标随机床结构参数的变化情况,为机床的结构设计提供了必要的理论依据。
给出了机床工作空间的规则化表示,在此基础上进行了工作空间逆向分析,实现了基于给定工作空间的机床结构参数设计。在ADAMS软件环境下对机床进行了简化的三维实体建模,应用ADAMS仿真模块对机床进行了运动学仿真,通过仿真验证了机床的自由度数、虚约束数、位姿正反解算法及速度和加速度算法的正确性。
The pure parallel mechanisms have lots of the merits in structural configuration and kinematic characteristics compared with the traditional serial mechanisms, such as larger carrying capability, higher location accuracy, the great ratio of stiffness over weight, simple structure and agile mobile ability, etc. However, parallel mechanism has the following disadvantages, such as small workspace, complicated control system, difficulties in kinematic calibration, etc. Compared with six Degrees-Of-Freedom(DOFs) parallel mechanisms represented by Stewart platform, the research of the limit-DOF parallel mechanisms has been highly focused by academia and indutry, the outsdanding merits of the mechanism include the simple structure, the larger workspace and the lower cost, etc. A novel kind of 4-DOF parallel mechanism of 2-TPR/2-TPS is proposed in this thesis. The analysis of the concerned mechanism is investigated in details. Based on that mechanism a novel five axes serial-parallel machine tool is developed by combining a serial rotational axis. The kinamatic analysis and structural parameters design the concerned machine tool are investigated.
The structural layout features of 2-TPR/2-TPS parallel mechanism are discussed. Moving character of the concerned mechanism is analyzed by using the theory of screws, and then the movements of the mechanism are determined. The decoupling equation of position and posture parameters are formulated on the basis of structural constraint of the concerned mechanism. The inverse kinematic solution of this mechanism is deduced by analytical method and the forward kinematic solution of this mechanism is achieved by numerical method. A novel approach of analying singularity for parallel mechanism, instantaneous coordinate system method, is presented based on the theory of screws, and then three possible types of singular configuration of this mechanism are achieved by this method.
Based on the 2-TPR/2-TPS parallel mechanism, a novel five axes serial-parallel machine tool is proposed by combining a serial rotational axis on the moving platform of the mechanism. The structural characteristics of this machine tool is discussed. The inverse kinematic solution and forward kinematic solution of this machine tool are achieved. The first-order kinematic influence coefficient matrix and the sencond-order kinematic influence coefficient matrix can be obtained by using vector geometry approach, and then the ananlysis of the velocity and acceleration is carried out based on the influence coefficient matrixs.
On the basis of the inverse kinematic solution of this machine tool, the shape of the reachable workspace of the cutter of this machine tool with given the maximum cutter dip is described by numerical method of spatial three dimensions alternating search. The characteristics of workspace for this machine tool is discussed. The volume of the workspace for this machine tool is calculated by numerical method. The effect of the change on the cutter dip to the workspace of the machine tool is analyzed. The effects of the change on structural parameterts to the workspace are investigated, it povides a theoretical basis for the selecting design parameters of structure of this machine tool.
The dexterity of machine tool is resolved baesd on the first-order kinematic influence coefficient matrix of the 2-TPR/2-TPS parallel mechanism. The distribution in the workspace of position dexterity index and posture dexterity index for machine tool is discussed. The effects of the change on structural parameterts to the dexterity index of machine tool are investigated, it can serve as a theoretical basis for the selecting design parameters of structure of this machine tool .
The specified representation of working space for machine tool is represented, and then the inverse analysis of workspace is investigated. The structure design for this machine tool according to a given workspace is achieved. The three-dimensional solid model of the machine tool is established in ADAMS. The kinematic simulation of machine tool is carried out in the ADAMS simulation module. On the basis of the kinematic simulation of the machine tool, The results of the previous theoretical analysis are verified , including the number of degrees of freedom and redundant constraints, inverse kinematic solution and forward kinematic solution, the calculation of the velocity and acceleration.
引文
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