Gears and ratios

Try 24 teeth on the left and 48 on the right. After one blue revolution, the yellow gear has turned half a revolution. Give both gears the same number of teeth. What changes?

At the pitch point, the same length of each gear passes through the mesh. That is a larger fraction of the circumference on the smaller gear. Externally meshed gears turn in opposite directions.

Angles and gear ratio

θ₂ = −θ₁ × z₁ / z₂

θ is the signed rotation in radians and z is the tooth count. The minus sign indicates opposite rotation. With equal tooth pitch, the pitch radius is proportional to the tooth count.

The model draws ideal involute tooth flanks at a 20° pressure angle and simplifies the tooth root. The simulation shows the kinematic ratio and omits backlash, deformation, friction and contact sound.