Thus we may suppose tooth d to be another position of tooth a, the contact being at f, and as motion was continued the contact would pass along the thickened curve until it arrived at the line of centres x. Now since the teeth have during this path of contact approached the line of centres, this part of the whole arc of action or of the path of contact is termed the arc of approach. After the two teeth have passed the line of centres x, the path of contact of the teeth will be along the dotted arc from x to l, and as the teeth are during this period of motion receding from x this part of the contact path is termed the arc of recess.
That contact of the teeth would not occur earlier than at c nor later than at l, is shown by the dotted teeth sides; thus a and b would not touch when in the position denoted by the dotted teeth, nor would teeth i and k if in the position denoted by their dotted lines.
If we examine further into this path of contact we find that throughout its whole path the face of the tooth of one wheel has contact with the flank only of the tooth of the other wheel, and also that the flank only of the driving-wheel tooth has contact before the tooth reaches the line of centres, while the face of only the driving tooth has contact after the tooth has passed the line of centres.
Thus the flanks of tooth a and of tooth d are in driving contact with the faces of teeth b and e, while the face of tooth h is in contact with the flank of tooth i.
These conditions will always exist, whatever be the diameters of the wheels, their number of teeth or the diameter of the generating circle. That is to say, in fully developed epicycloidal teeth, no matter which of two wheels is the driver or which the driven wheel, contact on the teeth of the driver will always be on the tooth flank during the arc of approach and on the tooth face during the arc of recess; while on the driven wheel contact during the arc of approach will be on the tooth face only, and during the arc of recess on the tooth flank only, it being borne in mind that the arcs of approach and recess are reversed in location if the direction of revolution be reversed. Thus if the direction of wheel motion was opposite to that denoted by the arrows in [Fig. 33] then the arc of approach would be from m to x, and the arc of recess from x to n.
Fig. 34.
It is laid down by Professor Willis that the motion of a pair of gear-wheels is smoother in cases where the path of contact begins at the line of centres, or, in other words, when there is no arc of approach; and this action may be secured by giving to the driven wheel flanks only, as in [Fig. 34], in which the driver has fully developed teeth, while the teeth on the driven have no faces.
In this case, supposing the wheels to revolve in the direction of arrow p, the contact will begin at the line of centres x, move or pass along the thickened arc and end at b, and there will be contact during the arc of recess only. Similarly, if the direction of motion be reversed as denoted by arrow q, the driver will begin contact at x, and cease contact at h, having, as before, contact during the arc of recess only.