Fig. 92.
In comparing the merits of involute with those of epicycloidal teeth, the direction of the line of pressure at each point of contact must always be the common perpendicular to the surfaces at the point of contact, and these perpendiculars or normals must pass through the pitch circles on the line of centres, as was shown in [Fig. 41], and it follows that a line drawn from c ([Fig. 91]) to any point of contact, is in the direction of the pressure on the surfaces at that point of contact. In involute teeth, the contact will always be on the line d e ([Fig. 92]), but in epicycloidal, on the line of the generating circle, when that circle is tangent at the line of centres; hence, the direction of pressure will be a chord of the circle drawn from the pitch circle at the line of centres to the position of contact considered. Comparing involute with radial flanked epicycloidal teeth, let c d a ([Fig. 91]) represent the rolling circle for the latter, and d c will be the direction of pressure for the contact at d; but for point of contact nearer c, the direction will be much nearer 90°, reaching that angle as the point of contact approaches c. Now, d is the most remote legitimate contact for involute teeth (and considering it so far as epicycloidal struck with a generating circle of infinite diameter), we find that the aggregate directions of the pressures of the teeth upon each other is much nearer perpendicular in epicycloidal, than in involute gearing; hence, the latter exert a greater pressure, tending to force the wheels apart. Hence, the former are, in this respect, preferable.
It is to be observed, however, that in some experiments made by Mr. Hawkins, he states that he found “no tendency to press the wheels apart, which tendency would exist if the angle of the line d e ([Fig. 92]) deviated more than 20° from the line of centres a b of the two wheels.”
A method commonly employed in practice to strike the curves of involute teeth, is as follows:—
Fig. 93.
In [Fig. 93] let c represent the centre of a wheel, d d the full diameter, p p the pitch circle, and e the circle of the roots of the teeth, while r is a radial line. Divide on r, the distance between the pitch circle and the wheel centre, into four equal parts, by 1, 2, 3, &c. From point or division 2, as a centre, describe the semicircle s, cutting the wheel centre and the pitch circle at its junction with r (as at a). From a, with compasses set to the length of one of the parts, as a 3, describe the arc b, cutting s at f, and f will be the centre from which one side of the tooth may be struck; hence from f as a centre, with the compasses set to the radius a b, mark the curve g. From the centre c strike, through f, a circle t t, and the centres wherefrom to strike all the teeth curves will fall on t t. Thus, to strike the other curve of the tooth, mark off from a the thickness of the tooth on the pitch circle p p, producing the point h. From h as a centre (with the same radius as before,) mark on t t the point i, and from i, as a centre, mark the curve j, forming the other side of the tooth.