本文選題：連桿曲線 + 分類與度量��； 參考：《西南科技大學(xué)》2017年碩士論文

【摘要】：連桿機(jī)構(gòu)連桿平面上的點(diǎn)可再現(xiàn)復(fù)雜代數(shù)曲線這一特性,在實(shí)際工程中有重要的應(yīng)用價(jià)值,平面機(jī)構(gòu)連桿曲線是指平面連桿機(jī)構(gòu)中連桿做平面運(yùn)動(dòng)時(shí),連桿上的點(diǎn)在機(jī)架固定坐標(biāo)系下的軌跡曲線。連桿曲線的性質(zhì)與分布規(guī)律體現(xiàn)了連桿平面運(yùn)動(dòng)的幾何學(xué)性質(zhì),也是機(jī)構(gòu)綜合的重要理論基礎(chǔ)。平面四桿機(jī)構(gòu)的連桿曲線可分為鵝蛋形、鴨梨形、雨滴形、香蕉形、“8”字形和雙“8”字形,然而上述對(duì)連桿曲線定性的認(rèn)識(shí),缺乏定量的數(shù)學(xué)度量指標(biāo)或者不完善,很難將機(jī)構(gòu)的運(yùn)動(dòng)特性與曲線的形態(tài)特征聯(lián)系起來(lái)。伴隨數(shù)值圖譜法的發(fā)展,機(jī)構(gòu)學(xué)者根據(jù)數(shù)值圖譜法中連桿軌跡匹配參數(shù)提取的需要,從計(jì)算存儲(chǔ)和檢索速度的角度出發(fā)提出了數(shù)值識(shí)別方法,即采用特定的偏差公式計(jì)算全部生成曲線與樣本曲線之間的綜合偏差值,然后根據(jù)相應(yīng)的綜合偏差值對(duì)軌跡曲線進(jìn)行分類識(shí)別,該方法旨在利用曲線之間的綜合偏差值對(duì)軌跡曲線進(jìn)行識(shí)別分類,有一定的優(yōu)點(diǎn),但它很難直接通過(guò)曲線的特征參數(shù)去認(rèn)識(shí)曲線的形態(tài)特征,或者不能將連桿曲線的突變和漸變規(guī)律與機(jī)構(gòu)尺度的變化聯(lián)系起來(lái)。20世紀(jì)以來(lái),Muller等人對(duì)平面運(yùn)動(dòng)幾何學(xué)的曲率理論的建立和完善,Savary曲率理論中的Euler-Savary公式,Cauchy的剛體平面運(yùn)動(dòng)瞬心線對(duì)滾,Bobillier定理,Ball點(diǎn),Burmester點(diǎn)等相關(guān)理論趨于成熟,平面連桿曲線局部幾何特性的分布規(guī)律被逐步揭示,而連桿曲線形態(tài)的改變通常依賴于其局部幾何特征的突變,這為基于機(jī)構(gòu)運(yùn)動(dòng)特性的連桿曲線形態(tài)學(xué)分析提供了條件。本文把奇點(diǎn)的位置信息與機(jī)構(gòu)尺度變化信息結(jié)合起來(lái),利用現(xiàn)代幾何學(xué)曲線曲率理論,構(gòu)建了尖點(diǎn)、二重點(diǎn)和自切點(diǎn)的數(shù)學(xué)方程,依據(jù)平面四桿機(jī)構(gòu)運(yùn)動(dòng)的幾何約束關(guān)系,解算奇點(diǎn)存在的約束方程,分析了尖點(diǎn)、二重點(diǎn)和自切點(diǎn)的漸變特性,實(shí)現(xiàn)了對(duì)連桿曲線奇點(diǎn)間相對(duì)拓?fù)潢P(guān)系和位置信息的數(shù)學(xué)描述,獲得了連桿曲線的奇點(diǎn)拓?fù)洵h(huán),利用奇點(diǎn)間的拓?fù)浣Y(jié)構(gòu)去描述連桿曲線的形態(tài)特征,這對(duì)于分析連桿曲線形態(tài)特征的尺度變化規(guī)律具有一定的優(yōu)勢(shì)。
[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.
【學(xué)位授予單位】：西南科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TH112

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