# Non-circular Gear

Special-shaped gears, also known as non-circular gears, are those whose indexing surface is not a rotating surface.

When paired with another gear, the instantaneous angular velocity ratio of the gear pair changes according to a certain motion law during the meshing process.

## 1) The characteristics of non-circular gears

Non-circular gears have the ability to achieve unique motion and function calculations, which can greatly benefit the motion characteristics of a mechanism. This can lead to improved performance of the mechanism and better movement conditions overall.

## 2) The application

Non-circular gears find widespread use in automatic machine instrumentation and solving devices.

## 3) Non-circular gear transmission

Non-circular gear transmission refers to a type of gear transmission in which the cross-sectional surface of at least one of the gears is not a rotating curved surface.

At least one of the gears in the transmission does not have a geared surface that is a rotating curved surface.

When a pair of non-circular gears are engaged in the transmission, the instantaneous transmission ratio changes periodically according to a certain regular pattern.

The section curves of the two non-circular gears 1 and 2 shown in Fig. 1 are J1 and J2, respectively. When the two wheels mesh, J1 and J2 undergo a pure roll without slipping. The instantaneous transmission ratio is given by i12 = ω1 / ω2 = r2 / r1, where ω1 and ω2 are the instantaneous angular velocities of the two gears and r1 and r2 are their instantaneous vector radii.

To achieve non-circular gear transmission and ensure that the two-wheel instantaneous trajectory is a pure rolling contact, the following two conditions must be met:

• The sum of any two instantaneous vector radii should be equal to the center distance a of the two gears, i.e., r1 + r2 = a.
• The length of the section curve J2 must be an integral multiple of J1.