机构离散运动几何学研究

发布时间：2018-01-07 12:15

本文关键词：机构离散运动几何学研究　出处：《大连理工大学》2016年博士论文　论文类型：学位论文

【摘要】：本论文在国家自然科学基金(No.51275067)的资助下,依据基于瞬心线和瞬轴面的刚体连续运动几何学理论,将经典的有限分离位置几何学发展到极大极小度量下的刚体离散运动几何学理论,为机构多位置运动综合奠定了理论基础,也为机器精度分析与设计提供了理论支撑。简要阐述通过瞬心线和瞬轴面的运动不变量来描述点和直线运动轨迹的曲率不变量及高阶特性。利用不动/准不动直线和平面条件,并借助于包络条件式得到直线族包络曲线的特征点和平面族包络直纹面的特征直线相对于瞬心和瞬轴的矢量关系。以瞬心线和瞬轴面的运动不变量表示包络线和包络直纹面的曲率不变量,通过高阶曲率特性分析包络图形的几何性质并进而揭示直线族和平面族的几何特征。以具体机构说明如何通过瞬心线和瞬轴面的运动不变量得到连杆上几何元素运动轨迹和包络图形的曲率性质。将极大极小度量引入离散轨迹整体几何性质的评价,首先定义平面离散运动刚体上点的离散轨迹的鞍线和鞍圆,它们分别由曲线上的三个和四个特征点完全确定并对应着刚体的相应特征位置。通过特征点的分布方式确定离散轨迹分布直线和分布圆的方位和大小并推导相应误差的代数方程,离散运动刚体上点的多位置鞍线和鞍圆误差函数本质上分别由三位置分布直线误差和四位置分布圆误差子函数构成,从而由少特征位置的极点多边形出发分析鞍线和鞍圆误差的代数性质,以及误差曲面上各面片的边界特征以及极小值点——鞍滑点和鞍圆点的几何特性,通过相应的鞍滑点误差和鞍圆点误差描述刚体点的离散轨迹与直线和圆曲线的最接近程度,揭示刚体的平面离散运动特性。接着以极大极小度量定义球面离散轨迹的鞍球面圆,并由鞍球面圆误差评价离散轨迹和球面圆曲线的整体逼近程度。依据球面离散轨迹上的四个特征点的分布方式确定其分布球面圆的位置、大小及其误差的代数方程。无论给定刚体多少球面离散位置,均由四位置分布球面圆误差表示刚体上点的鞍球面圆误差,从而建立少刚体位置和球面离散轨迹的整体几何性质的联系,为基于转动极的球面离散运动特性研究奠定基础。最后定义了空间离散轨迹的鞍球面和鞍圆柱面,并由轨迹上的特征点的分布方式确定分布球面和圆柱面的位置、大小与离散运动参数的关系。非退化情形下,分别以五位置分布球面误差和六位置分布圆柱面误差表示多位置鞍球面和鞍圆柱面误差,并分析了误差曲面随着刚体给定位置数增加情形下的演变。从空间离散曲线与空间机构约束曲线的极大极小度量角度出发,揭示了空间离散曲线的整体几何性质。
[Abstract]:In this paper, the National Natural Science Foundation (No.51275067) funding, according to instantaneous line based on axode rigid continuous motion geometry theory, discrete geometry of motion theory classical geometry to finitely separated positions of minimax metric, the multi position movement as the machine has laid a theoretical foundation, but also provides the theoretical support for the analysis and design of the machine precision. Curvature invariant and high-order characteristic briefly by centrodes and axode invariants to describe the motion of point and line trajectory. Using real / quasi real peace line surface condition and envelope condition obtained feature points of linear enveloping curve and plane family the envelope of the ruled surface feature line relative to the vector relation of instantaneous center and instantaneous axis. With the help of to centrode and axode motion invariants of envelope line and ruled surface curvature The variable, high-order curvature characteristic analysis of geometric properties of envelope graphics and reveals the geometric characteristics of straight lines and planes. To illustrate the specific mechanism centrodes and axode invariant properties of geometric elements to obtain curvature trajectories and envelope graphic linkages. The minimax evaluation metric into discrete trajectory integral geometry in nature, first define the discrete saddle line trajectory plane motion of rigid body discrete points on the saddle and circle, respectively by three and four feature points on the curve is completely determined and corresponding corresponding feature position. To determine the discrete algebraic equations of rigid body trajectory distribution lines and distribution circle and the orientation and size of the corresponding error the distribution of feature points, multi position saddle line discrete motion of a rigid body and saddle circle error function essentially respectively by three and four bit error distribution line The distribution of circular error functions, algebraic properties to analyze the circular error and saddle saddle line starting from the pole position of the small polygon feature, and the boundary features of each patch on the error surface and minimum geometric properties, saddle point and saddle point slide, the closest degree through the corresponding sliding saddle and saddle point error dot point error description of rigid body trajectory and discrete linear and circular curve, discrete plane motion characteristics reveal a rigid body. Then with the minimax saddle spherical metric definition spherical discrete trajectory circle, and the roundness error evaluation of spherical saddle discrete trajectory and spherical circular curve approximation. The overall distribution of spherical circular position are determined based on the distribution of four feature points on the trajectory of the discrete algebraic equation of spherical surface, size and error. No matter how much a given rigid spherical discrete position, by the four position distribution of the spherical error table The spherical error in saddle point on the rigid body, so as to establish the overall geometric properties of less rigid spherical discrete position and trajectory of the contact, to lay the foundation for the study of discrete motion characteristics of spherical polar rotation. Based on the definition of the spherical and saddle saddle cylindrical space discrete trajectory, and the distribution of feature points on the trajectory of the distribution of spherical and cylindrical surface, the relation between the size and the discrete motion parameters. The non degenerate case, respectively in the five position and the six position distribution of spherical error distribution of cylindrical error representation multiposition spherical and saddle saddle cylindrical error, and analyzes the error surface with the evolution of a given position to increase the number of rigid case. From space discrete curve and space curve constraint mechanism of minimax measuresfurther reveals the overall geometric properties of discrete space curves.

【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TH113

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