Yellow gear (tooth number Zy = 50) idly rotates on blue gear (tooth number Zb = 51). Both are in mesh with pink gear (tooth number Zp = 10).
1 rev. of blue gear corresponds (Zb/Zy) rev. of yellow gear.
In 1 rev. of blue gear, yellow gear rotates faster than blue gear an amount:
((Zb/Zy) – 1) = (Zb – Zy)/Zy = (51-50)/50 = 1/50 rev.
The video shows two rev. of blue gear.
The hand and the dial on yellow gear show revolutions of blue gear.
This mechanism shows that for a given center distance, a gear can meshes with two coaxial gears of different tooth numbers.
Backlash in mesh of yellow gear and pink pinion doesn’t much affect the counting result.
To eliminate the backlash, teeth of the yellow gear can be made thicker (corrected gears).