**Gear-Tooth Action**

__Fundamental Law of Gear-Tooth Action__

Figure 5 shows two mating gear teeth, in which

Figure 5 Two gearing tooth

Tooth profile 1 drives tooth profile 2 by acting at the instantaneous contact point K.

N1N2 is the common normal of the two profiles.

N1 is the foot of the perpendicular from O1to N1N2

N2 is the foot of the perpendicular from O2to N1N2.

Although the two profiles have different velocities V1 and V2 at point K, their velocities along N1N2 are equal in both magnitude and direction. Otherwise the two tooth profiles

If the velocity ratio is to be constant, then P must be a fixed point. That is the the tangent

drawn at the pitch point must intersect the line of centres at a fixed point.

Point P is very important to the velocity ratio, and it is called the pitch point. Pitch point

divides the line between the line of centers and its position decides the velocity ratio of the

two teeth. The above expression is the fundamental law of gear-tooth action. ]

Path of contact:

Consider a pinion driving wheel as shown in figure. When the pinion rotates in clockwise, the contact between a pair of involute teeth begins at K (on the near the base circle of pinion or the outer end of the tooth face on the wheel) and ends at L (outer end of the tooth face on the pinion or on the flank near the base circle of wheel).

MN is the common normal at the point of contacts and the common tangent to the base circles. The point K is the intersection of the addendum circle of wheel and the common tangent. The point L is the intersection of the addendum circle of pinion and common tangent.

The length of path of contact is the length of common normal cut-off by the addendum circles of the wheel and the pinion. Thus the length of part of contact is KL which is the sum of the parts of path of contacts KP and PL. Contact length KP is called as path of approachand contact length PL is called as path of recess.

Arc of contact: Arc of contact is the path traced by a point on the pitch circle from the beginning to the end of engagement of a given pair of teeth. In Figure, the arc of contact is EPF or GPH.

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