Worm gearing . fore have to be selected. There is, however, another aspect tothis, and in it is involved the-question of reversibility. It must be remembered that the surface of the worm threadis constantly slipping over the faces of the wheel teeth, and the 22 PRESSURE ANGLE AND FORM OF THREAD 23 direction in which this slipping takes place is along a planemutually tangent to the face of the thread, and the face of thewheel teeth. It is evident that if this gliding angle be 45degrees, it will be immaterial whether the worm drives the wheelor the wheel the worm; with a square thread, however,
Worm gearing . fore have to be selected. There is, however, another aspect tothis, and in it is involved the-question of reversibility. It must be remembered that the surface of the worm threadis constantly slipping over the faces of the wheel teeth, and the 22 PRESSURE ANGLE AND FORM OF THREAD 23 direction in which this slipping takes place is along a planemutually tangent to the face of the thread, and the face of thewheel teeth. It is evident that if this gliding angle be 45degrees, it will be immaterial whether the worm drives the wheelor the wheel the worm; with a square thread, however, such agliding angle is only possible if the proportions of the worm aresuch that they are satisfied by the equation Td=L (18) The gear ratio and the dimensions of the worm and wheel may,and generally will, make this impossible. In Fig. 4, let a 6 c be a triangle where a c equals the lead and6 c is equal to the circumference of the pitch line of the the angle ab c equals the lead angle of the worm. The. working surface of the thread is shown in perspective by theplane a e db and, in a square-threaded worm, the angle a 6 c isthe gliding angle of the rubbing surfaces. As drawn, however,this angle is much less than 45 degrees and such a gear cannotbe reversible, except to a slight degree. Now suppose the planea e db partially rotated about the line a 6 as an axis until itassumes the position a g fb, the angle which the plane makeswith the horizontal plane dbch may become 45 degrees withoutany increment of the angle o 6 c, or in other words convertingthe square into a V thread, the gliding angle has been raised to45 degrees without increasing the lead angle. If then a glidingangle of 45 degrees were the one object to be attained, this would be satisfied by the equation a + ^ = 45 degrees where a 24 WORM GEARS equals lead angle and 6 equals the angle included between thefaces of the V thread as shown in Fig. 5, and any gear designed
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