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InternalInvoluteGear

CycloidGear

Gear

Description

The FCGear InvoluteRack command creates an involute gear rack with spur gearing by default that can also be transformed into a helical gearing or a double helical gearing.

Gear racks are used to convert a rotary motion into a linear motion or vice versa. The following examples show the different applications:

• A rack with gear on at a retaining weir.
• Various rack systems of rack-and-pinion railways.
• Rack and pinion steering in a vehicle.
• Rack and pinion winch as mechanical hoist (e.g. car jack).
• Pneumatic rack and pinion drives used to control valves in pipeline transport.

Involute racks from left to right: Spur gearing, helical gearing, double helical gearing

Usage

1. Switch to the Gear Workbench.
2. There are several ways to invoke the command:
   • Press the Involute Rack button in the toolbar.
   • Select the Gear → Involute Rack option from the menu.
3. Change the gear parameter to the required conditions (see Properties).

Properties

See also: Property View.

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

Data

base

• Dataadd_endings (Bool): If true (default), then the total length of the rack is teeth * pitch. If false, then the rack starts with a tooth-flank.
• Dataheight (Length): Default is 5 mm. Value of the rack width.
• Datamodule (Length): Default is 1 mm. The module multiplied by Pi equals the pitch, the distance between corresponding points on adjacent teeth (see Notes).
• Datanum_teeth (Integer): Default is 15. Number of teeth.
• Datarack (PythonObject): Python gear object.
• Datathickness (Length): Default is 5. Height from the tooth root to the lower side of the rod.

computed

• Datatransverse_pitch (Length): (read-only) Pitch in the transverse plane (see Notes).

fillets

• Datahead_fillet (Float): Default is 0 mm.
• Dataroot_fillet (Float): Default is 0 mm.

helical

• Datadouble_helix (Bool): Default is false, true creates a double helix rack (see Notes).
• Datahelix_angle (Angle): Default is 0°. With the helix angle β a helical rack is created – positive value → rotation direction right, negative value → rotation direction left.
• Dataproperties_from_tool (Bool): Default is false. If true and Datahelix_angle is not zero, gear parameters are recomputed internally for the rotated gear.

involute

• Datapressure_angle (Angle): Default is 20° (see Notes).

precision

• Datasimplified (Bool): Default is false, true generates a simplified display (without teeth).

tolerance

• Dataclearance (Float): Default is 0.25 (see Notes).
• Datahead (Float): Default is 0. This value is used to change the tooth height.

version

• Dataversion (String):

Notes

• Datahelix_angle (beta, ${\displaystyle \beta }$): Changing the helix angle does not change the pitch pitch, or more precise the transverse pitch (${\displaystyle p_t}$) since the Datamodule property represents the transverse module (${\displaystyle m_t}$) unless the Dataproperties_from_tool property is true. In that case it represents the normal module (${\displaystyle m_n}$), that has to be divided by ${\displaystyle cos(\beta )}$ and thus enlarged to give the transverse module (${\displaystyle m_t}$) needed to calculate the Datatransverse_pitch property (${\displaystyle p_t}$).
  • Spur rack: ${\displaystyle \beta =0^{\circ }}$, ${\displaystyle \cos (\beta )=1}$ and ${\displaystyle m_t=m_n}$
  • Helical rack: ${\displaystyle \beta >0^{\circ }}$, ${\displaystyle \cos (\beta )<1}$ and ${\displaystyle m_t=\frac{m_n}{\cos (\beta )}}$
  • ${\displaystyle p_t=m_t\cdot \pi =\frac{m_n}{\cos (\beta )}\cdot \pi }$
• Datatransverse_pitch (${\displaystyle p_t}$): The transverse pitch is the transverse module (${\displaystyle m_t}$) multiplied by pi: ${\displaystyle p_t=m_t\cdot \pi }$
  • The transverse pitch multiplied by the number of teeth (${\displaystyle z}$) gives the length (${\displaystyle l}$) of the rack: ${\displaystyle l=p_t\cdot z}$
• Dataclearance (${\displaystyle c}$): At a gear pair, clearance is the distance between the tooth tip of the first gear and the tooth root of the second gear.
• Datadouble_helix: Activates double helical gearing if the Datahelix_angle property is larger than 0 (${\displaystyle \beta >0^{\circ }}$).

• Datamodule (${\displaystyle m}$): Using ISO (International Organization for Standardization) guidelines, Module size is designated as the unit representing gear tooth-sizes.
  • The module multiplied by Pi (${\displaystyle \pi }$) defines the pitch (${\displaystyle p}$), the distance between corresponding points of adjacent teeth: ${\displaystyle p=m\cdot \pi }$
• Datapressure_angle (${\displaystyle \alpha }$): Only change the parameter, if sufficient knowledge of the gear geometry is available.

Useful formulas

See FCGear InvoluteGear.

Scripting

Use the power of python to automate your gear modeling:

import FreeCAD as App
import freecad.gears.commands
gear = freecad.gears.commands.CreateInvoluteRack.create()
gear.teeth = 20
gear.beta = 20
gear.height = 10
gear.double_helix = True
App.ActiveDocument.recompute()
Gui.SendMsgToActiveView("ViewFit")

InternalInvoluteGear

CycloidGear

Gear