Constructing directrix for conic curve 圓錐曲線準(zhǔn)線的幾何作圖
So far , the main frame of the conjugation of betrand are established , on the basis of which , it is given that the primary condition the directrix line must be satisfied , the relative curvature of the conjugating surfaces , the relations between non - interventional condition and curvature axle of the directrix line , and so on . the transmission of normal circular - arc gear is a typical bertrand conjugation . in order to promote the transformation from theory to technology , the general principle of this kind of transmission is studied 為了使研究更加貼近于工程,便于解析處理,提出準(zhǔn)面的概念,并確立由準(zhǔn)面到準(zhǔn)線的研究路線,給出了各種傳動形式下準(zhǔn)面與準(zhǔn)線的具體特征,證明了共軛準(zhǔn)面上兩準(zhǔn)線的誘導(dǎo)測地曲率等于零的這一不干涉條件,進(jìn)而指出,當(dāng)準(zhǔn)面為平行軸和相交軸傳動的節(jié)曲面時,不干涉條件自然滿足。
Based on the geometry characteristics of bertrand surfaces , the complicated surface conjugation issue can be discussed with their directrix line . according to the different generatrix line which can be divided into common plane curve , circular - arc curve and straight line , bertrand conjugation surfaces are parted into three typical types , and the basic equation and differential formula are established , then the conjugation conditions are found . aiming at the inclusive problem , the structure condition is given 論文將白川德共軛按母線為一般平面曲線、圓弧、直線分為三種典型類型,分別建立了共軛的基本方程與微分關(guān)系式,據(jù)此給出了各種類型的共軛基本條件,發(fā)現(xiàn)這是一類更強(qiáng)更嚴(yán)的條件,存在有相容問題,進(jìn)而研究了白川德共軛的結(jié)構(gòu)條件,至此確立了白川德共軛的基本框架。