DiseñoPiezas EngranajeEvolvente

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This page is a translated version of the page PartDesign InvoluteGear and the translation is 12% complete.
Outdated translations are marked like this.

PartDesign InvoluteGear.svg DiseñoPiezas EngranajeEvolvente

Ubicación en el Menú
DiseñoPiezas → Engranaje Evolvente...
Entornos de trabajo
Atajo de teclado por defecto
Introducido en versión
Ver también
Ambiente de trabajo FCEngranaje



Esta herramienta permite crear un perfil 2D de un engranaje evolvente. Este perfil 2D es totalmente paramétrico, y puede ser rellenado con la función DiseñoPiezas Pad.
Para una información más detallada ver las entradas de Wikipedia para: Gear y Involute Gear

For more detailed information see Wikipedia's entries for: Gear and Involute Gear

PartDesign Involute Gear 01.png


Create the profile


  1. Ir al menú DiseñoPiezas → PartDesign InternalExternalGear.svg Engranaje evolvente....
  2. Establezca los parámetros de evolvente.
  3. Haga clic en OK
  4. El engranaje evolvente se crea fuera del cuerpo activo. Arrastre y suéltelo en un cuerpo para la aplicación de otras características como el relleno.

Create a spur gear

  1. Select the gear profile in the Tree view.
  2. Press the PartDesign Pad.svg PartDesign Pad button.
  3. Set the pad's DatosLength to the desired face width of the gear.
  4. Click OK.

Create a helical gear

  1. Select the gear profile in the Tree view.
  2. Press the PartDesign AdditiveHelix.svg PartDesign AdditiveHelix button.
  3. Choose as Axis the normal of the gear profile, that is Normal sketch axis introduced in version 0.20. (In earlier versions the Base Z axis can be used as long as the profile's plane has not been altered.)
  4. Choose a Height-Turns mode.
  5. Set the DatosHeight to the desired face width of the gear.
  6. To set the desired helical angle an Expression for the DatosTurns is required.
    1. Click the blue Bound-expression.svg icon at the right of the input field.
    2. Enter the following formula: Height * tan(25°) / (InvoluteGear.NumberOfTeeth * InvoluteGear.Modules * pi), where 25° is an example for the desired helical angle (also known as beta-value) and InvoluteGear is the DatosName of the profile.
    3. Click OK to close the formula editor.
  7. Click OK to close the task panel.

Hint: To make the helical angle an accessible parameter, use a dynamic property:

  1. Select the profile.
  2. In the Property editor activate the Show all option in the context menu.
  3. Again in the context menu, select Add Property. Note: this entry is only available when Show all is active.
  4. In the Add Property dialog:
    1. Choose App::PropertyAngle as Type.
    2. Set Gear as Group.
    3. Set HelicalAngle as Name (without a space).
    4. Click OK.
  5. Now a new property DatosHelical Angle (space added automatically), with an initial value of 0.0°, becomes available.
  6. Assign the desired helical angle to the new property.
  7. In the formula of the DatosTurns property of the AdditiveHelix, you can now reference InvoluteGear.HelicalAngle instead of the hard coded value of e.g. 25°; again assuming InvoluteGear is the DatosName of the profile.

Cut a hub for an involute splined shaft

introduced in version 0.21

  1. Activate the correct body.
  2. Create an internal involute gear profile with the required number of grooves and adapt the values of pressure angle, addendum-, dedendum- and root fillet coefficient. See also the table in Notes below for feasible values. For example:
    • DatosExternal Gear: False
    • DatosNumber Of Teeth: 12
    • DatosPressure Angle: 37.5°
    • DatosAddendum Coefficient: 0.45
    • DatosDedendum Coefficient: 0.7
    • DatosRoot Fillet Coefficient: 0.3
  3. Select the gear profile in the Tree view.
  4. Press the PartDesign Pocket.svg Pocket button.
  5. Set the pocket's DatosType to Through All.
  6. Check the pocket's DatosSymmetric To Plane option.
  7. Click OK.


  • DatosAddendum Coefficient: The height of the tooth from the pitch circle up to its tip, normalized by the module. Default is 1.0 for the standard full-depth system. introduced in version 0.21
  • DatosDedendum Coefficient: The height of the tooth from the pitch circle down to its root, normalized by the module. Default is 1.25 for the standard full-depth system. introduced in version 0.21
  • Engranaje externo: Verdadero o falso
  • Alta precisión: Verdadero o falso
  • Módulos: Diámetro del paso dividido por el número de dientes.
  • Número de dientes: Establece el número de dientes.
  • Ángulo de presión: Ángulo agudo entre la línea de acción y una normal a la línea que une los centros de los engranajes. Por defecto es de 20 grados. (Más información)
  • DatosProfile Shift Coefficient: The distance by which the reference profile is shifted outwards, normalized by the module. Default is zero. Profile shift may be positive or negative. introduced in version 0.21
  • DatosRoot Fillet Coefficient: The radius of the fillet at the root of the tooth, normalized by the module. Default is 0.38 as defined by the ISO rack. introduced in version 0.21


  • In order for two gears to mesh they need to share the same module and pressure angle. Expressions may help to ensure consistency. Their center distance needs to be (NumberOfTeeth + OtherGear.NumberOfTeeth) * Modules / 2 (that is in case of the sum profile shift being zero). Subtract the number of teeth in case of an internal gear.
  • Profile shifting can be used to prevent undercut on gears with a small number of teeth. Another application is to adjust the center distance of two gears with a given number of teeth and module.
  • When visually checking for proper meshing or interferences a much lower value for VistaDeviation is helpful, e.g. 0.05 instead of the default 0.5. Otherwise the representation in the 3D view may be too coarse.
  • For standard gears the most common pressure angle is 20 °, followed by 14,5 °. Other applications, notably splines, use higher angles.
  • The standard full-depth system uses an addendum coefficient of 1.0 and a dedendum coefficient of 1.25, resulting in a clearance of 0.25 (the difference between the addendum of the one gear and the dedendum of the other). The actual tooth length is the sum of both coefficients, multiplied by the module.
  • Tooth length reduction may be required to prevent undercut or to strengthen the teeth (see stub teeth). For internal gears the addendum (here pointing inwards) may need shortening to avoid certain interferences or non-involute flanks; when indicated in combination with longer teeth of the pinion.
  • For splined shafts and hubs ISO 4156 defines the following parameters:
Pressure Angle 30 ° (flat root) 30 ° (fillet root) 37,5 ° 45 °
Addendum Coefficient 0.5 0.5 0.45 0.4
Dedendum Coefficient 0.75 0.9 0.7 0.6
Root Fillet Coefficient 0.2 0.4 0.3 0.25


  • It is currently not possible to adjust the tooth thickness. Tooth and tooth space are distributed equally on the pitch circle. Thus the only way to control backlash is to adjust the center distance in a gear paring.
  • There is currently no undercut in the generated gear profile. That means gears with a low number of teeth can interfere with the teeth of the mating gear. The lower limit depends on the DatosPressure Angle and is around 17 teeth for 20° and 32 for 14.5°. Most practical applications tolerate a missing undercut for gears a little smaller than this theoretical limit though.


Video: How to make gears in FreeCAD