FCGear CycloidGear

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 Properties).

Data
An FCGear CycloidGear object is derived from a Part Feature object and inherits all its properties. It also has the following additional properties:


 * : Default is . Change of the involute profile. Changing the value can lead to unexpected results.


 * : Default is . Value of the gear width.
 * : Default is . Module is the ratio of the reference diameter of the gear divided by the number of teeth (see Notes).
 * : Default is . Number of teeth.


 * : (read-only)
 * : (read-only) Working pitch diameter.


 * : (read-only) Diameter of the rolling circle of hypocycloid, normalized by the (see Notes).
 * : Default is . Diameter of the rolling circle of epicycloid, normalized by the (see Notes).


 * : Default is.
 * : Default is.


 * : Default is . With the helix angle β a helical gear is created – positive value → rotation direction right, negative value → rotation direction left.
 * : Default is, creates a double helix gear (see Notes).


 * : Default is . Backlash, also called lash or play, is the distance between the teeth at a gear pair.


 * : Default is (see Notes).
 * : Default is . Additional length of the tip of the teeth, normalized by the.



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
See FCGear InvoluteGear.