Involute spur gear terms 
The spur gear terms:
The pitch circle is the circle representing the original cylinder which transmitted motion by friction, and its diameter the pitch circle diameter.
The center distance of a pair of meshing spur gears is the sum of their pitch circle radii. One of the advantages of the involute system is that small variations in the center distance do not affect the correct the correct working of the gears.
The addendum is the radial height of a tooth above the pitch circle.
The dedendum is the radial depth below the pitch circle.
The clearance is the difference between the addendum and the dedendum.
The whole depth of a tooth is the sum of the addendum and the dedendum.
The working depth of a tooth is the maximum depth that the tooth extends into the tooth space of a mating gear. It is the sum of the addenda of the gear.
The addendum circle is that which contains the tops of the teeth and its diameter is the outside or blank diameter.
The dedendum or root circle is that which contains the bottoms of the tooth spaces and its diameter is the root diameter.
Circular tooth thickness is measured on the tooth around the pitch circle, that is, it is the length of an arc.
Circular pitch is the distance from a point on one tooth to the corresponding point on the next tooth, measured around the pitch circle.
The module is the pitch circle diameter divided by the number of teeth.
The Diametrical pitch is the number of teeth per inch of pitch circle diameter. This is a ratio.
The pitch point is the point of contact between the pitch circles of two gears in mesh.
The line of action. Contact between the teeth of meshing gears takes place along a line tangential to the two base circles. This line passes through the pitch point and is called the line of action.
The pressure angle. The angle between the line of action and the common tangent to the pitch circles at the pitch point is the pressure angle.
The tooth face is the surface of a tooth above the pitch circle, parallel to the axis of the gear.
The tooth flank is the tooth surface below the pitch circle, parallel to the axis of the gear. If any part of the flank extends inside the base circle it cannot have involute form. It may have ant other form, which does not interfere with mating teeth, and is usually a straight radial line.
For reasons of economy in production modern gear teeth are almost exclusively cut to an involute form. The involute is a curve, which is generated by rolling a straight line around a circle, where the end of the line will trace an involute. The figure below shows the construction of an involute. To use this method to draw a gear profile would be very time consuming, so we will use an approximation called Unwins construction.
Involute
If two meshing gear were manufactured with square teeth instead of being cut to an involute form, the gears would not be able to rotate in mesh. The diagram below shows two such gears. note how the gears are locked together.
square teeth 
The importance of clearance
Clearance is the distance from the tip of a tooth to the circle passing through the bottom of the tooth space with the gears in mesh and measuring radially.
The correct clearance is vital to the motion of gears. To view two spur gears rotating in mesh and the necessity for clearance, simply click on the text below.
Rotating spur gears in mesh animation
close up of spur gears in mesh animation
Proportions and relations of standard involute spur gear teeth
The following formulas are required to calculate the dimensions needed to draw a tooth of a spur gear.
Addendum = module,
Dedendum = addendum + clearance,
Clearance = 0.25 x module,
Module (m) = pitch circle diameter (PCD) / number of teeth,
So, PCD = m x T,
Circular pitch (P) = pi (3.14) x m,
Circular tooth thickness = pi / 2,
Base circle diameter (BCD) = (PCD) x cos. Y ,
Pressure angle ( Y ) = 14.5 degrees or 20 degrees , the British standard recommendation is 20 degrees.
This value reduces the possibility of interference and gives the tooth a wider root.
Now that we know what spur gears are used for, what they look like, and how to calculate the information required to draw them, we can turn to the next page to see how each step is drawn. 
The pitch circle is the circle representing the original cylinder which transmitted motion by friction, and its diameter the pitch circle diameter.
The center distance of a pair of meshing spur gears is the sum of their pitch circle radii. One of the advantages of the involute system is that small variations in the center distance do not affect the correct the correct working of the gears.
The addendum is the radial height of a tooth above the pitch circle.
The dedendum is the radial depth below the pitch circle.
The clearance is the difference between the addendum and the dedendum.
The whole depth of a tooth is the sum of the addendum and the dedendum.
The working depth of a tooth is the maximum depth that the tooth extends into the tooth space of a mating gear. It is the sum of the addenda of the gear.
The addendum circle is that which contains the tops of the teeth and its diameter is the outside or blank diameter.
The dedendum or root circle is that which contains the bottoms of the tooth spaces and its diameter is the root diameter.
Circular tooth thickness is measured on the tooth around the pitch circle, that is, it is the length of an arc.
Circular pitch is the distance from a point on one tooth to the corresponding point on the next tooth, measured around the pitch circle.
The module is the pitch circle diameter divided by the number of teeth.
The Diametrical pitch is the number of teeth per inch of pitch circle diameter. This is a ratio.
The pitch point is the point of contact between the pitch circles of two gears in mesh.
The line of action. Contact between the teeth of meshing gears takes place along a line tangential to the two base circles. This line passes through the pitch point and is called the line of action.
The pressure angle. The angle between the line of action and the common tangent to the pitch circles at the pitch point is the pressure angle.
The tooth face is the surface of a tooth above the pitch circle, parallel to the axis of the gear.
The tooth flank is the tooth surface below the pitch circle, parallel to the axis of the gear. If any part of the flank extends inside the base circle it cannot have involute form. It may have ant other form, which does not interfere with mating teeth, and is usually a straight radial line.
For reasons of economy in production modern gear teeth are almost exclusively cut to an involute form. The involute is a curve, which is generated by rolling a straight line around a circle, where the end of the line will trace an involute. The figure below shows the construction of an involute. To use this method to draw a gear profile would be very time consuming, so we will use an approximation called Unwins construction.
Involute
If two meshing gear were manufactured with square teeth instead of being cut to an involute form, the gears would not be able to rotate in mesh. The diagram below shows two such gears. note how the gears are locked together.
The importance of clearance
To construct a gear profile using Unwins construction
Because the drawing contains a large amount of construction lines, the gear profile is drawn in three steps. Before you begin to draw the gear profile, you must obtain all the information needed using the given data and above formulas.
To view these three easy steps, simply click on the text below.
Step 1 (animation)
Step 2 (animation)
Step 3 (animation)
Because the drawing contains a large amount of construction lines, the gear profile is drawn in three steps. Before you begin to draw the gear profile, you must obtain all the information needed using the given data and above formulas.
To view these three easy steps, simply click on the text below.
Step 1 (animation)
Step 2 (animation)
Step 3 (animation)
Clearance is the distance from the tip of a tooth to the circle passing through the bottom of the tooth space with the gears in mesh and measuring radially.
The correct clearance is vital to the motion of gears. To view two spur gears rotating in mesh and the necessity for clearance, simply click on the text below.
Proportions and relations of standard involute spur gear teeth
The following formulas are required to calculate the dimensions needed to draw a tooth of a spur gear.
Addendum = module,
Dedendum = addendum + clearance,
Clearance = 0.25 x module,
Module (m) = pitch circle diameter (PCD) / number of teeth,
So, PCD = m x T,
Circular pitch (P) = pi (3.14) x m,
Circular tooth thickness = pi / 2,
Base circle diameter (BCD) = (PCD) x cos. Y ,
Pressure angle ( Y ) = 14.5 degrees or 20 degrees , the British standard recommendation is 20 degrees.
This value reduces the possibility of interference and gives the tooth a wider root.
Now that we know what spur gears are used for, what they look like, and how to calculate the information required to draw them, we can turn to the next page to see how each step is drawn.
Distributed by Abu-Iyad
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