Engineering Expert Witness Blog

      Last time we learned that the geometric shape specific to spur gear teeth is known as an involute profile.   Today we’ll look at the geometry behind this profile and the very specific place at which gear teeth meet, known as the point of contact.

      The transmission of mechanical energy between meshed gears may seem on its face to be straightforward, after all their gears are interlaced and interact with one another.   But their interaction involves some rather complex geometry, because forces are directed in a peculiar fashion between the teeth of the driving and driven gears.   Let’s consider the following illustration to get a better understanding.

Meshed Gear Tooth Geometry

      As we learned previously in this series, the pitch circle of a gear is an imaginary arc passing through each tooth between their top and bottom lands.   The pitch circles of the driving and driven gears are represented by heavy red dashed lines in the illustration.

      To ensure proper alignment and smooth action between gear teeth during rotation, the gears are spaced so that their pitch circles just meet but never intersect.   This specific point is known as the point of contact.   It is the only point at which gears will come into actual physical contact with one another, and it provides just enough contact so that when the driving gear turns in one direction, say clockwise, its teeth exert pressure upon the driven gear teeth, forcing it to move in the opposite direction, counterclockwise.

      The forces which come into play at the point of contact are represented in the illustration by a black dot with oppositional blue arrows extending from it.   These arrows represent the opposing mechanical forces, F₁ and F_{2 ,} which act upon the teeth when they make contact.

      We’ll learn more about the effect of those forces next time when we follow a locomotive from a stationary position into one of movement.

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