FCGear CycloideGear

From FreeCAD Documentation
Jump to navigation Jump to search
Other languages:
Deutsch • ‎English • ‎français • ‎italiano • ‎polski
Arrow-left.svg Previous: FCGear InvoluteRack.svg InvoluteRack
Next: BevelGear FCGear BevelGear.svg Arrow-right.svg

FCGear CycloideGear.svg FCGear CycloideGear

Menu location
FCGear → Create a Cycloide gear
Default shortcut
Introduced in version
See also
FCGear InvoluteGear


Cycloidal gears are very sensitive to an inaccurate adjustment of the centre distance, which then leads to a change in the transmission ratio. For these reasons, cycloidal gears are hardly found in mechanical engineering but are only used in special cases such as in the watch industry, for roots type blowers or for the drive of gear racks.

Cycloid-Gear example 1.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).




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


  • Datainner_diameter: Default is 5,00. Diameter of the rolling circle of hypocycloid, normalized by the Datamodule (see also the information in Notes).
  • Dataouter_diameter: Default is 5,00. Diameter of the rolling circle of epicycloid, normalized by the Datamodule (see also the information in Notes).


  • Databackslash: Default is 0,00. Backlash, also called lash or play, is the distance between the teeths at a gear pair.
  • Databeta: With the helix angle β a helical gear is created (positive value → rotation direction right, negative value → rotation direction left).
  • Dataclearance: Default is 0,25 (see also the information in Notes).
  • Datadouble_helix: True creates a double helix gear (see also the information in Notes)
  • Datahead: Additional length of the tip of the teeth, normalized by the Datamodule. Default is 0.
  • Dataheight: Value of the gear width.
  • Datamodule: Module is the ratio of the reference diameter of the gear divided by the number of teeth (see also the information in Notes).
  • Datanumpoints: Default is 15, change of the involute profile. Changing the value can lead to unexpected results.
  • Datateeth: Number of teeth.


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


  • Cycloidal gears must always be specially matched to each other and can generally not be exchanged at will: In a gear pair, the value of inner_diameter on one gear must equal the outer_diameter on the other, and vice versa. See also the information in Properties cycloid parameter view below.
  • 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_helix: 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.

Special cases

Straight line as hypocycloid

To obtain a straight line, directly towards the center, as hypocycloid, use the following expression for the Datainner_diameter: teeth / 2. Such a tooth form is often found in historical clockworks and thus called "clock toothing". A larger Dataclearance makes the effect even more visible.

Full hypocycloid/epicycloid as tooth

To obtain a gear made of complete hypocycloid and epicycloid curves use the following expressions:

  • Datainner_diameter: 0.5 + 1e-6
  • Dataouter_diameter: inner_diameter
  • Dataclearance: (-1 + inner_diameter/1mm) * 2
  • Datahead: (-1 + outer_diameter/1mm) * 2

The reference diameter is d = m * z, with m being the Datamodule and z being the Datateeth. For a complete hypocycloid, the rolling diameter has to be d_i = d / (z*2) = m*z / (z*2). And if we now normalize this by the module, we get d_in = m*z / (z*2) / m = 1 / 2. The additional explicit tolerance value (1e-6 in the expression above) is required to overcome coincidence issues.

Now the cycloids' rolling circle diameters have to match the gear's addedum/dedendum. The addendum, i.e. the tooth length above the reference circle, is 1 + Datahead. The dedendum, i.e. the tooth length below the reference circle, is 1 + Dataclearance. Both are normalized by the module, thus we need a head/clearance value of 1 - d_in. The additional / 1mm and * 2 are required to overcome shortcomings already fixed in the development version of the FCGear Workbench, but porting those fixes back to the stable version may break existing models.

Such "gears" allow the the number of teeth to be as low as two and are used as rotary vanes in pumps or compressors (cf. Roots-type Supercharger).

Infinitely large epicycloid

If the radius of the epicycloid's rolling circle becomes infinitely large, it becomes a rolling straight line. Such a degenerated epicycloid is called involute. Gears with such a tooth form are handled by the involute gear command. It is by far the most common tooth form Today.

Useful formulas

For more information see FCGear InvoluteGear.svg Involute gear.

Properties cycloid parameter view

CycloidGear inner-outer-diameter 2.svg

Arrow-left.svg Previous: FCGear InvoluteRack.svg InvoluteRack
Next: BevelGear FCGear BevelGear.svg Arrow-right.svg