This library started as "Getriebe Bibliothek für OpenSCAD" by janssen86 on Thingiverse but has not been updated in some years.
Shortly after the publishing of the Janssen library Chris Pen did good work on it and published here in GitHub about 7 years ago, but has commited some fixes this year (2025).
I looked on Thingiverse for remixes and found this one by eleotlecram, OpenSCAD Gear Library with Customizer. This was expecially interesting because it added parameter definitions to enable the use of the Customizer panel. He also added a lot of internal documentation that explained the operation of the code in details. His work really helped my understanding of OpenSCAN, gear math, and coding it. As a side light he added a hub feature: some of the designs could be generated with a raised hub around the hole for the gear's axle.
k37z3r was working on his fork of that OG library up to about a year back. I have based my fork of the Gears-Library on his version.
My first goal was to document the code in k37z3r's version but when i found eleotlecram's superior documentation i shamelessly copied it into my own fork, which ment translating it from from the German. I have also incorporated the his idea to use the Customizer panel to drive the gear type example generation code, extending it with selector lists, range limits, and so on to limit the user to acceptable values for the input parameters. I also extended his addition of a raised hub at the center of some of the gear wheels to all of the gears that have the wheel form, even those making gear sets.
I have also moved a lot of the module documentation from this Readme to the repo's Wiki
| Single Gears | Double Helix versions | Gear Sets |
|---|---|---|
| rack | rack and pinion | |
| spur gear | herringbone gear | planetary gear set |
| ring gear | herringbone ring gear | |
| bevel gear | herringbone bevel gear | bevel gear set, bevel herringbone gear set |
| worm | worm gear set |
| Name | value | description |
|---|---|---|
| pi | 3.14159 | ratio between diameter and circumerence of a circle |
| rad | 57.29578 | degrees in a radian for conversions |
| clearance | 0.2 | arbitrary value for space to leave between mating gears |
convert an Angle in Radians to Degrees using formula:
(Angle in Radians) × 180°/π = Angle in Degrees
where 1 Radian = 180/π Degrees = 57.296 Degrees
was called grad(angle).
convert an Angle in Degrees to Radians using formula:
Angle in Degrees × π/180° = Angle in Radians
rho x π/180° = / 180°/π
QED degrees/57.29578 --> radians
was called radian( angle )
Convert a 2 dimensional position in polar coordinates into cartesian coordinates.
- The input vector must have form [radius,angle] were the angles are in degrees.
- It returns a vector of form [X,Y]
Adjust polar coords given by r (radius?) and rho to by a rotation ? or a translation ?
return a vector [x,y] ? where x will be radius/cosine(rho) and y = rad_to_deg(tan(rho) - deg_to_rad(rho)) i.e. polar_to_cartesian( ev(rb,rho_ra) )
The two angles, theta0 and theta, are used to calculate a mystery value.
convert a 3 dimensional position in polar coordinates into cartesian coordinates.\
where XYZCoords is a vector of form [radius,angle,angle] with the angles in degrees it returns a vector [X,Y,Z]
returns 1 when the given number is even and 0 when odd providing a value that, when multiplied by the modulus of a gear, either preserves it, or zeros it in the calculation.
Function to calculate a scalar value using a*phi + r0.
Gears have many forms and the parameters of their construction are the parameters for these modules. The following diagrams show the derivation and the relationship between them.
The Worm is the cylindrical spiral part of the set, and the Worm Gear is the circular wheel part.
This worm gear parameter is the distance measured along the pitch circle of the gear. It can be determined by measuring the distance between any two corresponding points of adjacent teeth as shown here.
In order to calculate this parameter, the axial module (m sub a) should be used, which can be calculated as the following relation.
where ( mn ) is the Normal Module of the gear.
The teeth of simple spur gears are parallel to the axis of the gear's rotation. Setting the teeth at an angle offers some mechanical advantages at the expense of making the cutting of the gear a bit more complex. This angle parameter is specified as a decimal number
With the helix_angle at the default value of zero the gear modules generate involute teeth that are parallel to the axis of the gear's rotation, for spur gears, or perpendicular to the axis of travel for racks. Alternatively a non-zero value specifies an angle to set the teeth causeing it to take its helical form, with the sign of the value indicating which way the teeth tilt.
This parameter is only used for modules that create a worm gear.
It is the angle between the tangent to the thread helix on the pitch cylinder and the plane normal to the axis of the worm. If one complete turn of a worm is imagined to be unwound from the body of the worm, it will form an inclined plane whose base is equal to the pitch circumference of the worm with altitude equal to lead of the worm, as shown below.
The lead ( 
) is the linear distance through which a point on a thread moves ahead in one revolution of the worm. For single start threads, lead is equal to the axial pitch. Therefore, lead can be calculated as the product of axial pitch and number of starts:
and we need this for the calculation of the Lead Angle:
where 
is the Axial Module, and 
is Pitch Diameter of the worm.
The lead angle is an important factor in determining the efficiency of a worm and worm gear set. Therefore, the efficiency increase as the lead angle increases.
The modulus of a gear is a dimensionless number that defines a great deal of its shape. This table gives the values allowed by the DIN 780 standard.
| a | b | c | d | e | f |
|---|---|---|---|---|---|
| 0.05 | 0.06 | 0.08 | 0.10 | 0.12 | 0.16 |
| 0.20 | 0.25 | 0.3 | 0.4 | 0.5 | 0.6 |
| 0.7 | 0.8 | 0.9 | 1 | 1.25 | 1.5 |
| 2 | 2.5 | 3 | 4 | 5 | 6 |
| 8 | 10 | 12 | 16 | 20 | 25 |
| 32 | 40 | 50 | 60 |
The original parameter name for this option was the misnomer "optimized". It is now an enumeration called "gear_web_fill" that controls the generation of the area inside the circle of the gear's rim. The values are
| enum | meaning |
|---|---|
| "none" | center area will be empty |
| "lighten" | a web thinner than the gear width will fill the center area. In addition, if the centre is large enough, holes will be made in the web to "lighten" it with the goal of the realized gear weighing less, and /or using less filament to print. |
| "full" | fill to the gear width |
Obviously this is not applied to the Rack Gear.
The relation of this pattern with the Normal Module (mn), the number of teeth (z)m and Lead Angle (γ) is given by
This parameter defaults to 20 degrees and represents the angle where the gear faces meet. It is the major factor in how force is transmitted from the driving to the driven gear.
A worm gear, or any other threaded item, may have more than one spiral, or screw thread. Each additional thread increases the pressure that transfers force at the mating faces of the gears.
This image shows thread starts as seen from the end of the worm gear.
This option, when false, places the gears of a set flat on the XY place placed to be 3D printed. Left at its default vlaue ot true the gear shapes will be placed so they mesh together.
The number of teeth that the gear will be created with. Modules making gear sets will have individual "_teeth" parameters for each member.
spur_gear(modul, tooth_number, width, bore, pressure_angle = 20, helix_angle = 0, optimized = true)
With helix_angle at its default value of zero this module creates a simple spur gear, otherwise a helical gear is created, like this one:
rack(modul, length, height, width, pressure_angle=20, helix_angle=0)
With helix_angle at its default value of zero this module creates a simple spur gear, otherwise a helical gear is created, like this one:
rack_and_pinion (modul, rack_length, gear_teeth, rack_height, gear_bore, width, pressure_angle=20, helix_angle=0, together_built=true, optimized=true)
This module uses the rack() and spur_gear() modules to make the desired set of gears.
worm(modul, thread_starts, length, bore, pressure_angle=20, lead_angle=10, together_built=true)
This module makes the cylindrical spiral gear part of a set of worm gears.
worm_gear(modul, tooth_number, thread_starts, width, length, worm_bore, gear_bore, pressure_angle=20, lead_angle=0, optimized=true, together_built=true)
Makes the Worm and the Worm gear as a set.
planetary_gear(modul, sun_teeth, planet_teeth, number_planets, width, rim_width, bore, pressure_angle=20, helix_angle=0, together_built=true, optimized=true)
The set includes the innermost sun, a number of "planets" greater than one, and the outer gear ring made using the herringbone_gear() and the herringbone_ring_gear() modules respectively.
The reason for using the herringbone modules is their helix_angle parameter.
Set to the default of zero the gears made will be simple spur gears.
For non-zero values it forms double helix gears, a deviation from the usual effect of this parameter simply tilting the gears teeth.
In planetary gears the self-centering effect of the double helix is nessessary to keep the gears aligned as they spin, thus the use of the herringbone modules.
herringbone_gear(modul, tooth_number, width, bore, pressure_angle=20, helix_angle=0, optimized=true)
bevel_herringbone_gear_pair(modul, gear_teeth, pinion_teeth, axis_angle=90, tooth_width, bore, pressure_angle = 20, helix_angle=0, together_built=true)
A crown and pinion set require different calculations for the meshing of gears that have their axes of rotation at an angle, namely the axis_angle parameter.
bevel_herringbone_gear(modul, tooth_number, partial_cone_angle, tooth_width, bore, pressure_angle=20, helix_angle=0)
Uses two instances of bevel_gear() to make a beveled, double helical gear.
herringbone_ring_gear(modul, tooth_number, width, rim_width, pressure_angle=20, helix_angle=0)
bevel_gear(modul, tooth_number, partial_cone_angle, tooth_width, bore, pressure_angle=20, helix_angle=0)
spiral_bevel_gear(modul, tooth_number, partial_cone_angle, tooth_width, bore, pressure_angle = 20, helix_angle=30)
Use 16 overlapping, bevel gear intances to make a spiral gear. The helix_angle parameter is ignored.
