Filament Drive Gear Calculations

Some equations relevant to indentations produced by a filament drive gear:

Filament Drive Gear Indentations
Filament Drive Gear Indentations

For reference, the smaller indentations are 0.25 mm deep and 1.3 mm across the bottom.


  • d = filament (a.k.a. circle) diameter
  • r = filament radius
  • m = chord depth (inward from circle)
  • c = chord length
  • Θ = angle across chord from circle center, degrees
  • A = chord area (a.k.a. indentation face area)

The length of the chord at the bottom of the indentation, perpendicular to the filament axis:

c = 2 sqrt(2mr - m2)

The chord angle:

Θ = 2 arcsin(c/2r)

The chord area, which would be the indentation face if it were perpendicular, which it isn’t:

A = (r2 / 2) x ((πΘ / 180) - sin(Θ))

If you measured Θ in radians, the π/180 factor would Go Away.

Some doodles showing that reducing the indentation from 0.25 to 0.15 reduces the chord area by a factor of two:

Filament Drive Gear - indentation doodles
Filament Drive Gear – indentation doodles

The implication being that you must maintain fairly constant force on the drive bearing against the filament to prevent stripping the indentations.