FCGear CycloidGear/en

Description
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.



Usage

 * 1) Switch to the [[Image:FCGear_workbench_icon.svg|16px]] FCGear Workbench.
 * 2) There are several ways to invoke the command:
 * 3) * Press the button in the toolbar.
 * 4) * Select the option from the menu.
 * 5) Change the gear parameter to the required conditions (see  below).

Data

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


 * : Default is 5,00. Diameter of the rolling circle of hypocycloid, normalized by the  (see also the information in ).
 * : Default is 5,00. Diameter of the rolling circle of epicycloid, normalized by the  (see also the information in ).


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

View
The parameter descriptions of the tab will be found in Property editor, further below at.

Straight line as hypocycloid
To obtain a straight line, directly towards the center, as hypocycloid, use the following expression for the :. Such a tooth form is often found in historical clockworks and thus called "clock toothing". A larger 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:

The reference diameter is d = m * z, with m being the and z being the. 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 ( 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 +. The dedendum, i.e. the tooth length below the reference circle, is 1 +. Both are normalized by the module, thus we need a head/clearance value of 1 - d_in. The additional and  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 Involute gear.