See: Add Gear-Pair


Mesh - two external gears can mesh (called External Mesh), or one external gear can mesh with one internal gear (called Internal Mesh). The default is External Mesh.

Driving-Gear - the input gear to the Gear-Pair.

Driven-Gear - the output gear from the Gear-Pair.

Edit the Gear-Pair


Edit the Gear-Pair:

1.Double-click a Gear-Pair in the graphic-area or Assembly-Tree.

- or -

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 

Mesh - see Terminology above


- or -


Centre Distance - (Read-Only)

see centre-distance calculation in Adjustments tab

Number-of-Teeth, z1 (Minimum =5)

The number of-teeth on the input-gear - called the Driving-Gear

Number-of-Teeth, z2 (Minimum = 5)

The number of-teeth on the Driven-Part - or the output from the Gear-Pair.



Gear Segment Parameters 


A Gear-Segment is not a complete gear.

Gear 1 or Gear 2 can be a Gear-Segment

Gear # Segmentation

Complete Gear - a normal gear
Gear Segment - to reduce the number of teeth.

To reduce the number-of-teeth of Gear 1 or Gear 2

1.Click ⊚ Gear-Segment
2.Edit the Start Angle : Minimum = 0, Maximum = 360
3.Edit the Segment Range : Minimum = 0; Maximum 360

Each Gear will have an integer number-of-teeth.

tog_minusAdjustments tab



Gear-Slip (degrees)

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

This parameter rotates the gear profile, not the Part.

Top-Tip: To keep the gears in mesh:

Gear-Slip 2 = –Z1

( Z2 × Gear-Slip 1)

Clearance (move gears apart), jr

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

It is intended to add a small amount of Backlash (Play) between the gears - and thus it should normally be a +ve value.

Although backlash may be introduced by increasing the Centre-Distance, it is more typical to thin the gear-teeth. The minimum value should be enough to accommodate a Lubricating Film.

Centre-Distance Calculation

If External Mesh = Clearance + (Module×(Number-of-Teeth Gear1+Number-of-Teeth Gear2)÷2)

If Internal Mesh = Clearance + (Module×(Number-of-Teeth Gear1+Number-of-Teeth Gear2)÷2)

Notes: Recommend Clearance - approximately.

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

An alternative way to get a small amount of clearance is to reduce the size of the gear teeth and not to change the centre-distance.

We do not offer this design parameter.

tog_minusParameters tab


Gear Tooth Parameters 

Edit these Gear Parameters to define the gear teeth.

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

In words, it the number of teeth for each Ømm.

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, ha - default = m.

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

Dedendum, hf - default = m * 1.25.

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, rf - 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

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

To display Gears more accurately, 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

Tooth Depth = Addendum + Dedendum

Default Values

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 all Read-Only

These parameters are for Gear Analysis only.


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 not be less than 1.1. Contact-Ratio should be a minimum of 1.2 for working gears.

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

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 = Pitch Circle Diameter.

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

Normal Backlash (mm)

This is the gap (backlash) between the gear-flanks  you can measure with a 'feeler gauge'.

Normal Backlash is a function of the Centre Distance Adjustment parameter ONLY.

Angular Backlash - Gear 1 (deg)

This parameter gives the maximum rotation of Gear 1 if you do not move Gear 2.

Angular Backlash is a function of the Centre Distance Adjustment parameter ONLY.

Angular Backlash - Gear 2 (deg)

This parameter gives the maximum rotation of Gear 2 if you do not move Gear 1.

Angular Backlash is a function of the Centre Distance Adjustment parameter ONLY.

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


Tutorials and Reference Help Files for MechDesigner and MotionDesigner 14.2 + © Machine, Cam, Mechanism, and Motion Design Software by PSMotion Ltd