连杆曲线的形态学分类及演化

发布时间：2018-05-23 21:09

本文选题：连杆曲线 + 分类与度量　；参考：《西南科技大学》2017年硕士论文

【摘要】：连杆机构连杆平面上的点可再现复杂代数曲线这一特性,在实际工程中有重要的应用价值,平面机构连杆曲线是指平面连杆机构中连杆做平面运动时,连杆上的点在机架固定坐标系下的轨迹曲线。连杆曲线的性质与分布规律体现了连杆平面运动的几何学性质,也是机构综合的重要理论基础。平面四杆机构的连杆曲线可分为鹅蛋形、鸭梨形、雨滴形、香蕉形、“8”字形和双“8”字形,然而上述对连杆曲线定性的认识,缺乏定量的数学度量指标或者不完善,很难将机构的运动特性与曲线的形态特征联系起来。伴随数值图谱法的发展,机构学者根据数值图谱法中连杆轨迹匹配参数提取的需要,从计算存储和检索速度的角度出发提出了数值识别方法,即采用特定的偏差公式计算全部生成曲线与样本曲线之间的综合偏差值,然后根据相应的综合偏差值对轨迹曲线进行分类识别,该方法旨在利用曲线之间的综合偏差值对轨迹曲线进行识别分类,有一定的优点,但它很难直接通过曲线的特征参数去认识曲线的形态特征,或者不能将连杆曲线的突变和渐变规律与机构尺度的变化联系起来。20世纪以来,Muller等人对平面运动几何学的曲率理论的建立和完善,Savary曲率理论中的Euler-Savary公式,Cauchy的刚体平面运动瞬心线对滚,Bobillier定理,Ball点,Burmester点等相关理论趋于成熟,平面连杆曲线局部几何特性的分布规律被逐步揭示,而连杆曲线形态的改变通常依赖于其局部几何特征的突变,这为基于机构运动特性的连杆曲线形态学分析提供了条件。本文把奇点的位置信息与机构尺度变化信息结合起来,利用现代几何学曲线曲率理论,构建了尖点、二重点和自切点的数学方程,依据平面四杆机构运动的几何约束关系,解算奇点存在的约束方程,分析了尖点、二重点和自切点的渐变特性,实现了对连杆曲线奇点间相对拓扑关系和位置信息的数学描述,获得了连杆曲线的奇点拓扑环,利用奇点间的拓扑结构去描述连杆曲线的形态特征,这对于分析连杆曲线形态特征的尺度变化规律具有一定的优势。
[Abstract]:The point on the plane of the connecting rod mechanism can reproduce the complex algebraic curve, which has important application value in the practical engineering. The connecting rod curve of the plane mechanism means that the connecting rod in the plane linkage mechanism is moving in the plane. The trace curve of a point on a connecting rod in a fixed frame coordinate system. The properties and distribution of the connecting rod curve reflect the geometric properties of the planar motion of the connecting rod, and are also the important theoretical basis of mechanism synthesis. The connecting rod curve of planar four-bar linkage can be divided into goose egg shape, pear shape, raindrop shape, banana shape, "8" shape and double "8" shape. It is difficult to relate the kinematics of the mechanism to the shape of the curve. With the development of numerical map method, according to the need of extracting the matching parameters of linkage trajectory in the numerical map method, a numerical recognition method is proposed from the point of view of computing storage and retrieval speed. That is to calculate the synthetic deviation value between the generated curve and the sample curve by using the specific deviation formula, and then classify and identify the trajectory curve according to the corresponding comprehensive deviation value. This method is aimed at identifying and classifying the trajectory curve by using the synthetic deviation value between curves, which has some advantages, but it is difficult to recognize the shape characteristics of the curve directly through the characteristic parameters of the curve. Or we can't relate the sudden change and gradual change of connecting rod curve to the change of mechanism scale. Since the 20th century, the author and others have established the curvature theory of plane motion geometry and perfected the Euler-Savary formula in Savary's curvature theory and the rigid body of Cauchy. The theory of the instantaneous centroid of plane motion, such as Ball point and Burmester point, tends to be mature. The distribution of the local geometric characteristics of planar connecting rod curves is revealed step by step, and the change of the shape of connecting rod curves usually depends on the abrupt changes of their local geometric characteristics, which provides a condition for morphological analysis of connecting rod curves based on the kinematic characteristics of mechanisms. In this paper, the position information of singularity is combined with the information of mechanism scale change, and the mathematical equations of tip point, two focal point and self-tangent point are constructed by using the theory of curve curvature of modern geometry, according to the geometric constraint relation of the motion of planar four-bar mechanism. The constraint equations of singularities are solved, and the gradient characteristics of tip, two-point and self-shear points are analyzed. The relative topological relation and position information between singularities of connecting rod curves are described mathematically, and the topological loops of singularities of connecting rod curves are obtained. The topological structure between singularities can be used to describe the morphological characteristics of the connecting rod curve, which has a certain advantage in analyzing the scale variation law of the shape characteristic of the connecting rod curve.
【学位授予单位】：西南科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH112

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