Condition for Constant Velocity Ratio of Gears - Law of Gearing
1 Answer

In order to have a constant angular velocity ratio for all positions of the wheels, pitch point must be the fixed point for the two wheels. In other words, the common normal at the point of contact between a pair of teeth must always pass through the pitch point. This is a fundamental condition which must be satisfied while designing the profiles for the teeth of gear wheels. It is also known as the law of gearing.

The above condition is fulfilled by teeth of involute form, provided that the root circles from which the profiles are generated are tangential to the common normal.

Following are the two types of teeth commonly used.

  1. Cycloidal teeth
  2. Involute teeth

A cycloid is a curve traced by a point on the circumference of a circle which rolls without slipping on a fixed straight line. When a circle rolls without slipping on the outside of a fixed circle, the curve traced by a point on the circumference of a circle is known as epicycloid. On the other hand, if a circle rolls without slipping on the inside of a fixed circle, then the curve traced by a point on the circumference of a circle is called hypocycloid.

An involute of a circle is a plane curve generated by a point on a tangent, which rolls on the circle without slipping or by a point on a taut string which is unwrapped from a reel.

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Advantages of involute gears

  1. the centre distance for a pair of involute gears can be varied within limits without changing the velocity ratio. This is not true for cycloidal gears which require exact centre distance to be maintained.

  2. In involute gears, the pressure angle, from the start of the engagement of teeth to the end of the engagement, remains constant. It is necessary for smooth running and less wear of gears. But in cycloidal gears, the pressure angle is maximum at the beginning of the engagement, reduces to zero at pitch point, starts increasing and again becomes maximum at the end of the engagement. This results in the less smooth running of gears.

    The only disadvantage of the involute teeth is that the interference occurs with pinions having a smaller number of teeth. This may be avoided by altering the heights of addendum and dedendum of the mating teeth or the angle of obliquity of the teeth.

Advantages of cycloidal gears

  1. Since the cycloidal teeth have wider flanks, therefore the cycloidal gears are stronger than the involute gears for the same pitch. Due to this reason, the cycloidal teeth are preferred especially for cast teeth.

  2. In cycloidal gears, the contact takes place between a convex flank and concave surface, whereas in involute gears, the convex surfaces are in contact. This condition results in less wear in cycloidal gears as compared to involute gears. However, the difference in wear is negligible.

  3. In cycloidal gears, the interference does not occur at all. Though there are advantages of cycloidal gears they are outweighed by the greater simplicity and flexibility of the involute gears.

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