Gear-Pair dialog-box

See: Add Gear-Pair

A Gear-Pair is a kinematic joint.

Before you add the Gear-Pair:

The input to the Gear-Pair is a rotating-Part, with a known motion - it is a Green, kinematically-defined Part.
The output is a rotating-Part that is not kinematically-defined,

After you add the Gear-Pair, the elements are:

The output Part becomes kinematically-defined.
The motion of the output Part is a function of the ratio of the gear-teeth and the motion of the rotating-Part at the input.

To edit the Gear-Pair

To edit the parameters of the Gear-Pair, open the Gear-Pair dialog-box:

1.Click the Gear-Pair element in the Assembly-Tree or the graphic-area.

The Gear-Pair element should show in the Selection-Window.

2.Right-click the Gear-Pair in the Selection-Window to show a contextual-menu.
3.Click 'Edit element' in the contextual-menu

The Gear-Pair dialog-box


There are three tabs in the Gear-Pair dialog-box.

Define tab

Adjustments tab

Parameters tab

tog_minusDefine tab


Gear Mesh and # Teeth 


Gears can have an internal or external mesh (also called 'tooth form').


- or -


Centre Distance - [Read-Only (see also Clearance in the Adjustments tab)]

If External Mesh: Centre-Distance = Clearance + [Module × (Number-of-Teeth Gear1 + Number-of-Teeth Gear2) ∕ 2]

If Internal Mesh  : Centre-Distance = Clearance + [Module × (Number-of-Teeth Gear1 - Number-of-Teeth Gear2) ∕ 2]

Number-of-Teeth, z1 [Minimum =5]

This is the Gear on the DriveR Part that has a Green Part-Outline before you do Add Gear-Pair.

Number-of-Teeth, z2 [Minimum = 5]

This is the Gear on the DriveN Part that has a Blue Part-Outline before you do Add Gear-Pair. The Part becomes Green after you add the Gear-Pair.


Gear Segment Parameters 

Gear N Segmentation

Complete Gear
Gear Segment

Gear-Segments are incomplete gears.

If you want to reduce the number-of-teeth of Gear 1 or Gear 2 so that the Gear is 'incomplete', click Gear-Segment

Gear 1 is the 'input gear'

Gear 2 is the 'output gear'

Start Angle : 'Start Angle' of the Gear Segment for the Gear [0 – 360].

0º is at the point between the gears when the Master Machine Angle = 0.

Segment Range : How much of the Gear you want as a Gear Segment

To see one Gear-Tooth

Segment Rangemin =  Round-Down[No-of-Teeth[total] ÷ 360 ]

They have an integer number-of-teeth.

tog_minus        Adjustments tab



Gear-Slip [degrees]

These two parameters move Gear 1 and Gear 2 around the rotating centre of each Part at the Pin-Joint.

This parameter does not rotate the Part, only the Gear.

To adjust Gear-Slip, and keep the gears in mesh, you must adjust the gears by vegear ratio.

Top-Tip: To keep the gears in mesh:

Gear-Slip 2 = – Z1 ∕ (Z2 × Gear-Slip 1)

Clearance [to move gears apart]

This parameter increases or decrease the centre-distance between the two gears.

It is intended to add a Backlash [Play] between the Gears - and thus it should normally be a +ve value

Notes: Recommend Backlash:

Minimum: 0.006 × (Centre-Distance)0.5
Maximum: 0.024 × (Centre-Distance)0.5

An alternative way to get a small amount of backlash is to cut the gears more.

The gear teeth become slightly smaller but the centre distance remains the same.

We do not offer this design parameter.

tog_minus        Parameters tab


Gear Tooth Parameters 

Edit the Standard Gear Parameters to define the gear teeth.

Module [m] = P.C.D (in mm)  ∕  Number-of-Teeth.

[Fewer teeth for a P.C.D., means each tooth is bigger]. The default module is calculated from Number-of-Teeth, Centre-Distance and External Mesh.

Pressure Angle [α] [Default = 20º].

Standard gears are typically 20º. Other 'standards' are: 14º (weaker, quieter), 17.5º, 22.5º and 25º (stronger, noisier).

Addendum [Default = m].

The radial height of the gear tooth from the pitch circle to the tip of the tooth.

Dedendum [Default Value = m * 1.25 (when m > 1)].

The radial depth of the Gear tooth below the Pitch Circle to the root of the tooth. It is usually larger than the Addendum so there is clearance for the Gear Teeth to mesh without binding.

If 0.25<m<1, Dedendum is typically = m *.1.4

If  m>1, Dedendum is typically = m *.1.25

Root Radius, or 'Flank Radius' [Default is 0.3 * m]

The small fillet between the Flank and the Root of the Gear Tooth.

Note: In reality, if the gear is manufactured from a Hob/Rack Cutter, then the root of the gear is a Trochoid.

# Points along Profile' [and # Points Root Radius*2]

The number of 'facets' along the gear tooth flank [and around the two Root Radii].

To display Gears more accurately, then increase the number of points. Otherwise, 4 is adequate, 10 is good.

There is a CPU overhead when drawing Gear-Pairs, do not increase the number of facets without a good reason.

Gear Terminology: Working Depth, Addendum, Dedendum, Whole Depth, Pitch Circle

For information:

Working Clearance = Dedendum - Addendum

Working Depth = Addendum * 2

Whole or Tooth Depth = Addendum + Dedendum

Pitch Circle Diameters: d1= z1*m ;  d2=z2*m,

Addendum = 1.0*m;  Dedendum = 1.25*m ; Root Radius =~0.3*m

Tip Diameter = d + 2*m

Root diameter = d - 2.5*m

Centre Distance = (d1 + d2) / 2


Gear Parameters 

There are a number of parameters that are available for Gear Analysis.


Each gear tooth is in contact with another gear tooth as it moves through the meshing position.

The 'Contact-Ratio' gives the number-of-teeth that are in contact with another, on average, as they pass through the meshing point. A contact ratio between 1 and 2 means that contact alternates between two and one pairs of teeth in contact at any one time. Gears that have a 'high' Contact-Ratio are smoother and quieter. The Contact-Ratio of an Internal Gear-Pair is higher than that of a similar External Gear-air, even greater than 2. Contact-Ratio should never be less than 1.1. Contact-Ratio should nearly always 1.2 or greater.

If the Contact-Ratio is too low, then consider:

Decrease the pressure angle
Increase the number-of-teeth
Increase the working depth.

Working Clearance = Dedendum - Addendum

The distance between the top land of a gear tooth and the bottom land of the gear with which is meshed.

Gear 1 PCD & Gear 2 PCD

PCD is Pitch Circle Diameter of each Gear.

PCD = Module * Number-of-Teeth, m*z

Normal Backlash [mm]

If you move the Gears apart, with the Centre Distance Adjustment Parameter, then there is backlash between the Gears at the mesh point.

This is the gap between the gear-flanks with a 'feeler gauge'.

Angular Backlash - Gear 1 [deg]

This parameter gives the maximum rotation of Gear 1 without moving Gear 2, as a consequence of moving the gears apart with the Centre Distance Adjustment Parameter.

Angular Backlash - Gear 2 [deg]

This parameter gives the maximum rotation of Gear 2 without moving Gear 1, as a consequence of moving the gears apart with the Centre Distance Adjustment Parameter.

Useful Gearing Calculations and Equations

Image Courtesy of the Internet - an image available from so many sources it is difficult to know which is the original source.

Image Courtesy of the Internet - an image available from so many sources it is difficult to know which is the original source.




Pitch Diameter

Module, m, number-of-teeth, N

D = mN

Circular Pitch


pc = m.π = D.π  ∕  N


Diametrical Pitch, Pd

m = 25.4  ∕  Pd


Module, m, Pitch Diameter, D

N = D  ∕  m


Module, m

a = m


Module, m

b = 1.25m

Outside Diameter

Module, m, Pitch Diameter, D, or number-of-teeth, N

Do = D + 2m = m (N + 2)

Root Diameter

Pitch Diameter, D, Module, m

DR = D – 2.5m

Base Circle Diameter

Pitch Diameter & Pressure Angle

Db = D cos μ

Base Pitch

Module, m, & Pressure Angle, μ

pb = m π cos μ

Tooth Thickness at

Standard Pitch Diameter

Module, m

Tstd = π. m  ∕ 2

Center Distance

Module, m, number-of-teeth, N

C = m . (N1 + N2) ∕ 2

Contact Ratio for Spur Gears

( 1 < CR < 2 )

Outside Radii, Base Circle Radii, Centre Distance, Pressure Angle

CR = (√R012 – Rb12 + √R022 – Rb22 – C sin μ)  ∕  m π cos μ

Backlash (linear)

Change in Centre Distance, ΔC

B = 2( ΔC )tan μ

Backlash (linear)

Change in Tooth Thickness, ΔT

B = ΔT

Backlash (linear) along


Linear Backlash along Pitch Circle, B

BLA = B cos μ


Backlash, Angular

Linear Backlash, D

Ba = 6880 B ∕ D (arc minutes)

Min. No. of Teeth

for No Undercutting

Pressure Angle, μ

Nc = 2 ∕ sin2 μ

Nc (20º) = ~17 Teeth

Useful Gearing Definitions




the height of the gear tooth above the pitch circle diameter


the angle the output shaft of the gearbox can move without the input shaft moving

Base Circle:

an imaginary circle used in involute gearing to generate the involutes that form the tooth profiles

Bevel Gears:

used for right-angle applications. There are two types of bevel gears which are straight and spiral

Center distance:

distance between the axes of two meshed gears - Length of the Line-of Centres

Circular Thickness:

the thickness of the tooth on the pitch circle.


the depth of the tooth below the diameter of the pitch circle.

Diametrical Pitch:

the teeth per inch of the diameter of the pitch circle

Differential Gear:

a bevel gear which allows two shafts to rotate at a different speed.


a wheel with teeth that meshes with another wheel with teeth to translate motion.

Gear Center:

the center of the pitch circle.

Gear Train:

two or more gears meshed by their teeth. A gear train generates power speed through the meshed gears rotating

Gear Ratio:

the ratio between the numbers of teeth of meshing gears.

Helical Gear:

gear with the gear teeth cut at angles

Line of Contact:

the line or curve along which two tooth surfaces are tangent to each other


the curve which describes a line which is unwound from the circumference of the gear


a small cogwheel which fits into a larger gear or track.

Pitch Circle:

the curve of intersection of a pitch surface of revolution and a plane of rotation

Pitch Diameter:

the diameter of the pitch circle

Pitch Radius:

the radius of the pitch circle

Planetary Gears:

a system that consists of three components: the sun gear, ring gear, and two or more planet gears. The sun gear is in the center, the ring gear is the outermost gear, and the planet gears are the gears surrounding the sun gear inside the ring gear.

Pressure Angle:

the angle between the line-of-action and the normal [90º, perpendicular] to the surface of the tooth

Spiral Bevel Gears:

shafts whose axes are perpendicular [90º] to each other and are used in right-angle applications

Spur Gear:

connect parallel shafts which have involute teeth that are parallel to the shaft

Sun Gear:

a gearwheel that rotates around its own axis and has other gears (planet gears) that rotate around it

Torsional Strength:

the measure of the amount of torque that a radial shaft can sustain during its rotation in a mechanical system

Working Depth:

the max depth a tooth of one gear extends into the tooth gear of a mating gear

Worm Gear:

a gear with one or more teeth with screwed threads

Gear Modifications








Topping and Semi-Topping


End Radius and Edge Radius/End Relief

Top Round/Semi-topping



Definition of Circular Pitch, p

Circular Pitch  = pitch circle circumference[pi.d] / number of teeth[z] ; p = Π.d / z

Module = Pitch Diameter[d] / Number of Teeth[z] ; m = d/z

Circular Pitch[p] / Module[m] = pi ; p/m = Π

Pitch Diameter[d] = module[m]*number of teeth[z] ; d = m.z


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