FCGear: Koło zębate ewolwentowe

From FreeCAD Documentation
Jump to navigation Jump to search
This page is a translated version of the page FCGear InvoluteGear and the translation is 3% complete.
Other languages:
Deutsch • ‎English • ‎français • ‎italiano • ‎polski

FCGear InvoluteGear.svg FCGear InvoluteGear

Menu location
FCGear → Create an Involute gear
Default shortcut
Introduced in version
See also
FCGear CycloideGear


Due to the favourable meshing ratio and the relatively simple production, involute gearing is the most common tooth form in mechanical engineering. Gear wheels can be found wherever movement and force are to be transferred from one part to another. For example, they can be found in machines, cars, watches or household appliances. The movement is often transferred directly from one gear wheel to the other, but sometimes also via a chain. In addition, the direction of rotation can be changed. It is also possible to change a radial movement into a linear one via Involute Rack (FCGear InvoluteRack.svg Create an Involute rack).

Involute-Gear example.png

From left to right: Spur gearing, helical gearing, double helical gearing


  1. Switch to the FCGear workbench icon.svg FCGear Workbench.
  2. Invoke the command several way:
  3. Change the gear parameter to the required conditions (see Properties → Data below).




  • DANEPlacement: Placement is the location and orientation of an object in space.
  • DANELabel: User name of the object in the Tree view.

computed (All properties in this group are calculated automatically and thus read only)

  • DANEda: Outside diameter, measured at the addendum (the tip of the teeth).
  • DANEdf: Root diameter, measured at the foot of the teeth.
  • DANEdw: Working pitch diameter.
  • DANEtransverse_pitch: Pitch in the plane of rotation.


  • DANEbeta: With the helix angle β a helical gear is created – positive value → rotation direction right, negative value → rotation direction left (see also the information in Notes).
  • DANEclearance: Default is 0,25 (see also the information in Notes).
  • DANEdouble_gear: True creates a double helix gear (see also the information in Notes)
  • DANEhead: Default is 0,00. This value is used to change the tooth height.
  • DANEheight: Value of the gear width.
  • DANEmodule: Module is the ratio of the reference diameter of the gear divided by the number of teeth (see also the information in Notes).
  • DANEproperties_from_tool: If helix angle β is given and properties_from-tool is enabled, gear parameters are internally recomputed for the rotated gear.
  • DANEshift: Default is 0,00, generates a positive and negative profile shift (see also the information in Notes).
  • DANEteeth: Number of teeth (see also the information in Notes)
  • DANEundercut: True changes the profil of the tooth root (see also the information in Notes).


  • DANEpressure_angle: Default is 20° (see also the information in Notes).


  • DANEnumpoints: Default is 6, change of the involute profile. Changing the value can lead to unexpected results.
  • DANEsimple: True generates a simplified display (without teeth and only a cylinder in pitch diameter).


  • DANEbackslash: Default is 0,00. Backlash, also called lash or play, is the distance between the teeths at a gear pair.
  • DANEreversed_backslash: True backlash decrease or False backlash increase (see also the information in Notes).


The parameter descriptions of the View tab will be found in Property editor, further below at Example of the properties of a PartDesign object.


  • beta: When beta is changed, pitch diameter also changes. The following formula illustrates how the parameters interact: d = m * Z / cos beta (Z = number of teeth, d = pitch diameter, m = module). This means for the spur gear: cos beta = 0 and for the helical gear: cos beta > 0. However, a helix angle of less than 10° has hardly any advantages over straight teeth.
  • clearance: At a gear pair, clearance is the distance between the tooth tip of the first gear and the tooth root of the second gear.
  • double_gear: To use the double helical gearing the helix angle β (beta) for the helical gearing must first be entered.
  • module: Using ISO (International Organization for Standardization) guidelines, Module size is designated as the unit representing gear tooth-sizes. Module (m): m = 1 (p = 3.1416), m = 2 (p = 6.2832), m = 4 (p = 12.566). If you multiply Module by Pi, you can obtain Pitch (p). Pitch is the distance between corresponding points on adjacent teeth.
  • shift: Profile shift is not merely used to prevent undercut. It can be used to adjust center distance between two gears. If a positive correction is applied, such as to prevent undercut in a pinion, the tooth thickness at top is thinner.
  • teeth: If the number of teeth is changed, the pitch diameter also changes (dw).
  • undercut: Undercut is used when the number of teeth of a gear is too small. Otherwise the mating gear will cut into the tooth root. The undercut not only weakens the tooth with a wasp-like waist, but also removes some of the useful involute adjacent to the base circle.
  • pressure_angle: 20° is a standard value here. The pressure angle is defined as the angle between the line-of-action (common tangent to the base circles) and a perpendicular to the line-of-centers. Thus, for standard gears, 14.5° pressure angle gears have base circles much nearer to the roots of teeth than 20° gears. It is for this reason that 14.5° gears encounter greater undercutting problems than 20° gears. Important. the pressure angle changes with a profile shift. Only change the parameter, if sufficient knowledge of the gear geometry is available.
  • reversed_backslash: If there are several gears, pay attention to which gear the parameter is set for.


A 2D tooth profile, obtained by setting the DANEheight to zero, cannot be used with features requiring a 2D shape. For example PartDesign Pad and PartDesign AdditiveHelix features do not accept such a profile as base. For technical details, please refer to the related issue on GitHub.

Useful formulas

Standard Spur Gears

Here “standard” refers to those spur gears with no profile shift coefficient ().

Basic formulas common to internal and external standard spur gears
Symbol Term Formula FCGear Parameter
Module -
Number of Teeth -
Pressure Angle -
d Reference Diameter or Pitch Diameter -
Addendum Coefficient -
Dedendum Coefficient -
Addendum -
Dedendum -
Tooth Height or Tooth Depth
Profile Shift Coefficient -
For standard gears,
Basic formulas specific to external standard spur gears
Symbol Term Formula
Tip Diameter


Root Diameter


Basic formulas specific to internal standard spur gears
Symbol Term Formula
Tip Diameter


Root Diameter


Basic formulas specific for a pair of external standard spur gears
Symbol Term Formula
Center Distance
Tip and Root Clearance


  • Helical and double helical gearing
    • pitch diameter (dw) = module * teeth : cos beta
    • axle base = (pitch diameter (dw) 1 + 2) : 2
    • addendum diameter = pitch diameter (dw) + 2 * module
    • module = pitch diameter (dw) * cos beta : teeth


Use the power of python to automate your gear modeling:

import FreeCAD as App
import freecad.gears.commands
gear = freecad.gears.commands.CreateInvoluteGear.create()
gear.teeth = 20
gear.beta = 20
gear.height = 10
gear.double_helix = True