# Filament Drive Gear Calculations

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

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

Variables:

• 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:

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