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对于渐开线圆柱齿轮而言，尼曼和温特尔的世界名著《机械零件》第2卷中对此有论述。
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对于啮合平面、啮合区域、接触线、作用线、啮合线、接触点的概念请参考DIN 3960 或 ISO 21771标准。
这里先复制ISO 21771标准中的5.4.2 和5.4.3 部分供你参考！
5.4.2 Plane of action, zone of action, contact line 啮合平面，啮合区域，接触线 The plane of action of a cylindrical gearpair is tangent to the base cylinders of the gear and mating gear. In the caseof an external gear pair, the plane of action passes between the basecylinders. The intersection of the two planes of action (one for each toothflank) is parallel to the gear axes, and is the pitch axis (see 5.2.5). Thezones of action are the parts of the planes of action which are limited by theusable tip cylinders of the gear and mating gear and by the facewidth and, inthe case of external gears, can be further limited by the start of theinvolute. A zone of action is linked to the flank that is normal to it. Hence,one of the planes of action is linked to the right flanks and the other to theleft flanks.
圆柱齿轮副的啮合平面是指两相啮齿轮的基圆柱面的公共切平面。对外齿轮副，啮合平面穿过两基圆柱面之间【译者注：对外齿轮，啮合平面是两基圆柱的内公切平面；对内齿轮副，啮合平面是两基圆柱的外公切平面】。两啮合平面（左右齿面各一个）的交线平行于齿轮轴线，即为节线轴（参见5.2.5）。啮合区域是啮合平面的一部分，其范围受可用齿顶圆柱面、配对齿轮、齿宽的限制；在外齿轮中，渐开线的起始点也是一个限制条件。啮合区域通常都是与齿面相关的。因此，如果一个啮合平面与右齿面相关，那么另一个啮合平面则与左齿面相关。
At any instant in time, the intersection ofthe zone of action with the corresponding tooth flanks of a gear pair is knownas the contact line. With the rotation of the gears around their axes, thecontact lines move through the zone of action. On tooth flanks, the contactlines are identical to the generators of flank and mating flank, see 4.3.1. 在任一瞬间，一对齿轮副相应齿面的接触区域的交线称为接触线。随着齿轮绕其轴线的转动，接触线逐步通过啮合区域。在齿面上，接触线是两相啮齿面的公共母线，参见4.3.1。
5.4.3 Line of action, path of contact, point of contact 作用线，啮合线，接触点 Lines of action are where the planes ofaction intersect transverse sections. According to 5.4.2, it is necessary todistinguish between the right flank line of action and the left flank line ofaction. A line of action is inclined to the common tangent to the pitch circlesat the pitch point (pitch circle tangent) by the working transverse pressureangle, file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtml1/04/clip_image002.gif (see Figures 15 and17), and it contacts the two base circles at the points file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtml1/04/clip_image004.gif and file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtml1/04/clip_image006.gif. 作用线是啮合平面与端截面的交线。根据5.4.2，作用线应划分为右侧齿面作用线和左侧齿面作用线。作用线与两节圆的公共切线在节点相交形成的夹角即为端面工作压力角file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtml1/04/clip_image002.gif（参见图15和17），其与两基圆相交于点file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtml1/04/clip_image004.gif和file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtml1/04/clip_image006.gif。 A path of contact is that part of the lineof action which is within the zone of action. The starting point, file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtml1/04/clip_image008.gif, of the path of contact is at or near the tip circle of thedriven gear. The finishing point, file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtml1/04/clip_image010.gif, of the path of contact is at or near the tip circle of thedriving gear. 啮合线是指位于啮合区域内的那一部分作用线。啮合线的起点A在或接近从动齿轮的齿顶圆；啮合线的终点E在或接近主动齿轮的齿顶圆。 NOTE In Figures 15 and 17, only the line of action of the working flanks isshown in each case. 注意：在图15和17中，只给出了一种情况下的工作齿面的作用线。 The lines of action intersect the centreline at pitch point file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtml1/04/clip_image012.gif (see 5.2.5). Pitchpoint file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtml1/04/clip_image012.gif is also the point atwhich the two lines of action intersect. 作用线与连心线的交点是节点C（参见5.2.5）。节点C同时也是两条作用线的交点。 A point of contact is a point where a pathof contact intersects the corresponding tooth flanks in a specific workingposition of the two gears. It is a point on the contact line. 接触点是两齿轮在工作位置上相应齿面的啮合线的交点。它是接触线上的一个点。 | 
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