發(fā)布時(shí)間：2018-01-07 12:15

  本文關(guān)鍵詞：機(jī)構(gòu)離散運(yùn)動(dòng)幾何學(xué)研究　出處：《大連理工大學(xué)》2016年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 運(yùn)動(dòng)幾何學(xué) 離散運(yùn)動(dòng) 包絡(luò) 極大極小 運(yùn)動(dòng)不變量

【摘要】：本論文在國(guó)家自然科學(xué)基金(No.51275067)的資助下,依據(jù)基于瞬心線和瞬軸面的剛體連續(xù)運(yùn)動(dòng)幾何學(xué)理論,將經(jīng)典的有限分離位置幾何學(xué)發(fā)展到極大極小度量下的剛體離散運(yùn)動(dòng)幾何學(xué)理論,為機(jī)構(gòu)多位置運(yùn)動(dòng)綜合奠定了理論基礎(chǔ),也為機(jī)器精度分析與設(shè)計(jì)提供了理論支撐。簡(jiǎn)要闡述通過(guò)瞬心線和瞬軸面的運(yùn)動(dòng)不變量來(lái)描述點(diǎn)和直線運(yùn)動(dòng)軌跡的曲率不變量及高階特性。利用不動(dòng)/準(zhǔn)不動(dòng)直線和平面條件,并借助于包絡(luò)條件式得到直線族包絡(luò)曲線的特征點(diǎn)和平面族包絡(luò)直紋面的特征直線相對(duì)于瞬心和瞬軸的矢量關(guān)系。以瞬心線和瞬軸面的運(yùn)動(dòng)不變量表示包絡(luò)線和包絡(luò)直紋面的曲率不變量,通過(guò)高階曲率特性分析包絡(luò)圖形的幾何性質(zhì)并進(jìn)而揭示直線族和平面族的幾何特征。以具體機(jī)構(gòu)說(shuō)明如何通過(guò)瞬心線和瞬軸面的運(yùn)動(dòng)不變量得到連桿上幾何元素運(yùn)動(dòng)軌跡和包絡(luò)圖形的曲率性質(zhì)。將極大極小度量引入離散軌跡整體幾何性質(zhì)的評(píng)價(jià),首先定義平面離散運(yùn)動(dòng)剛體上點(diǎn)的離散軌跡的鞍線和鞍圓,它們分別由曲線上的三個(gè)和四個(gè)特征點(diǎn)完全確定并對(duì)應(yīng)著剛體的相應(yīng)特征位置。通過(guò)特征點(diǎn)的分布方式確定離散軌跡分布直線和分布圓的方位和大小并推導(dǎo)相應(yīng)誤差的代數(shù)方程,離散運(yùn)動(dòng)剛體上點(diǎn)的多位置鞍線和鞍圓誤差函數(shù)本質(zhì)上分別由三位置分布直線誤差和四位置分布圓誤差子函數(shù)構(gòu)成,從而由少特征位置的極點(diǎn)多邊形出發(fā)分析鞍線和鞍圓誤差的代數(shù)性質(zhì),以及誤差曲面上各面片的邊界特征以及極小值點(diǎn)——鞍滑點(diǎn)和鞍圓點(diǎn)的幾何特性,通過(guò)相應(yīng)的鞍滑點(diǎn)誤差和鞍圓點(diǎn)誤差描述剛體點(diǎn)的離散軌跡與直線和圓曲線的最接近程度,揭示剛體的平面離散運(yùn)動(dòng)特性。接著以極大極小度量定義球面離散軌跡的鞍球面圓,并由鞍球面圓誤差評(píng)價(jià)離散軌跡和球面圓曲線的整體逼近程度。依據(jù)球面離散軌跡上的四個(gè)特征點(diǎn)的分布方式確定其分布球面圓的位置、大小及其誤差的代數(shù)方程。無(wú)論給定剛體多少球面離散位置,均由四位置分布球面圓誤差表示剛體上點(diǎn)的鞍球面圓誤差,從而建立少剛體位置和球面離散軌跡的整體幾何性質(zhì)的聯(lián)系,為基于轉(zhuǎn)動(dòng)極的球面離散運(yùn)動(dòng)特性研究奠定基礎(chǔ)。最后定義了空間離散軌跡的鞍球面和鞍圓柱面,并由軌跡上的特征點(diǎn)的分布方式確定分布球面和圓柱面的位置、大小與離散運(yùn)動(dòng)參數(shù)的關(guān)系。非退化情形下,分別以五位置分布球面誤差和六位置分布圓柱面誤差表示多位置鞍球面和鞍圓柱面誤差,并分析了誤差曲面隨著剛體給定位置數(shù)增加情形下的演變。從空間離散曲線與空間機(jī)構(gòu)約束曲線的極大極小度量角度出發(fā),揭示了空間離散曲線的整體幾何性質(zhì)。
[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.

【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：TH113

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