GEARS
 
 
 
Welcome to the final section of the curriculum. This section deals with gear types, gear uses and most importantly how to draw a spur gear profile. The various sections of this course are shown below.
 
 
 
 Choose From Contents Menu 
 
GEARS - CONTENTS
 
Introduction to Rotary motion past to present
 
Gear types and their application
 
Involute spur gear terms
 
The involute and the gear tooth
 
The importance of clearance
 
Proportions and relations of standard involute 
 
spur gear terms
 
Drawing a spur gear profile

Finish

 
 
 
MAIN CONTENTS
 
 
 
 



 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Introduction to rotary motion
 
 
 

Introduction to flat pulleys:
 
Rotary motion is the most common type of motion for a shaft or an axle. One way in which an engineer uses rotary motion is by transmitting it from one shaft to another when the shafts are parallel. This can be done by using pulleys and belts. A pulley is a wheel which may or may not have a grooved rim.
The figure below shows a stacked vee pulleys and vee belts often used in car engines.
 
 
 

 
 
 
 

The main function of pulleys and belt systems are to transmit motion and torque from an engine to a machine. Various types of pulleys and belts are used on different machines. Machines used in the home, such as sewing machines, washing machines, spin dryers and vacuum cleaners. The picture below shows a flat belt and flat pulley used to transmit motion from an old heat engine.
 
 
 
 

 
 
 
 
 
 
 
 

 
 

 
 

From flat pulleys to toothed pulleys
 
 
 
In machines where a positive drive is essential and no slip between belt and pulleys can be accepted, a toothed belt and pulley is used. Toothed belts are mainly used for timing mechanisms, where quiet, positive (no slip) drive is required. The figure below shows a toothed belt and toothed pulleys used to drive a camshaft in a motor car engine.
 
 
 
 
                                                        Toothed belt and toothed pulleys
 
 
 
 
 
 
 
 
 
 

 
 
 
 
 
 
The gear wheel
 
 
 
The gear wheel is a basic mechanism. Its purpose is to transmit rotary motion and force. A gear is a wheel with accurately machined teeth round its edge. A shaft passes through its center and the gear may be geared to the shaft. Gears are used in groups of two or more. A group of gears is called a gear train. The gears in a train are arranged so that their teeth closely interlock or mesh. The teeth on meshing gears are the same size so that they are of equal strength. Also, the spacing of the teeth is the same on each gear. An example of a gear train is shown below.
 
 
 
                        Single gear                                     gear train
 
 
 
 
 
 
 
 
 

 
 
 
 
Rotation direction
 
 
When two spur gears of different sizes mesh together, the larger gear is called a wheel, and the smaller gear is called a pinion. In a simple gear train of two spur gears, the input motion and force are applied to the driver gear. The output motion and force are transmitted by the driven gear. The driver gear rotates the driven gear without slipping.
The wheel or the pinion can be the driver gear. It depends on the exact function the designer wishes the mechanism to fulfill. When two spur gears are meshed the gears rotate in opposite directions, as shown in the figure below.
 
 
 

 
                                                                   Wheel and pinion
 

 
 
 
 
 
 
 
 

 



 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 
 
 

Gear types

 
 

Bevel gears
 
 
These gears have teeth cut on a cone instead of a cylinder blank. They are used in pairs to transmit rotary motion and torque where the bevel gear shafts are at right angles (90 degrees) to each other. An example of two bevel gears are shown below.
 
 
 
 

 

       Bevel gears
 
 
 
 
 
 
 

 
 
 
 
Crossed helical gears
 
 
These gears also transmit rotary motion and torque through a right angle. The teeth of a helical gear are inclined at an angle to the axis of rotation of the gear.
The diagram below shows how the axis of rotation of two helical gears are crossed at right angles. Helical gears are smoother running than spur gears and are more suitable for rotation at high velocities. An example of two crossed helical gears are shown below.
 
 
 
 
Crossed helical gears
 
 
 
 
 
 
 
 

 
 
Worm and worm wheel
 
 
A gear which has one tooth is called a worm. The tooth is in the form of a screw thread. A worm wheel meshes with the worm. The worm wheel is a helical gear with teeth inclined so that they can engage with the thread like worm. Like the crossed helical gears, the worm and worm wheel transmit torque and rotary motion through a right angle. The worm always drives the worm wheel and never the other way round. The mechanism locks if the worm wheel tries to drive the worm. Worm mechanisms are very quiet running. An example of a worm and worm wheel is shown on the right hand side below. An application of the worm and worm wheel used to open lock gates is shown on the left hand side below.
 
 
 
 
 
 
   Worm and worm wheel
 
 
 
 
 
 
 

 
 
                                                                              application
 
 

 
 
 
 
 
 

 

 

The helical gear
 
This gear is used for applications that require very quiet and smooth running, at high rotational velocities.
Parallel helical gears have their teeth inclined at a small angle to their axis of rotation. Each tooth is part of a spiral or helix. The helical gears shown below have splines cut in their center holes. The gears can move along a splined (grooved) shaft, although they rotate with the shaft. An example of a helical gear is shown below.
Double helical gears give an efficient transfer of torque and smooth motion at very high rotational velocities. An example of a double helical gear is shown below.
 
 

 
 
                                                                                      Single helical gear
 

 

                                                Double helical gear
 
 

 



 
 

 

Spiral bevel gears
 
 
When it is necessary to transmit quietly and smoothly a large torque through a right angle at high velocities, spiral bevel gears can be used. Spiral bevel gears have teeth cut in a helix spiral form on the surface of a cone. They are quieter running than straight bevel gears and have a longer life. Spiral bevel gears are used in motorcar rear axle gearboxes. An example of spiral bevel gears are shown below.
 
 
 
 
 

                                                       Spiral bevel gears
 
 

 
 
 
 
 

 



 
 
 

 

Face cut gears
 
It is possible to cut gear teeth on the face of a gear wheel. Also, gear teeth can be cut on the inside of a gear ring an example of which is shown in the top figure below. Internal gears have better load carrying capacity than external spur gears. They are safer in use because the teeth are guarded. An example of an external face cut gear is shown below.
 
 
 
Internal face cut gear
 
 
 
 
 
 
 
 

 

External face cut gear
 
 
 
 
 
 

 



 
 
 

 
 

Rack and pinion
 
 
 
Converting rotary motion to linear motion.

 
A rack and pinion mechanism is used to transform rotary motion into linear motion and visa versa. A round spur gear, the pinion, meshes with a spur gear which has teeth set in a straight line, the rack. The rack and pinion can transform rotary motion into linear motion and visa versa in three ways:
 

a. Rotation of the pinion about a fixed center causes the rack to move in a straight line.
b. Movement of the rack in a straight line causes the pinion to rotate about a fixed center;
c. If the rack is fixed and the pinion rotates, then the pinion's center moves in a straight line taking the pinion with it.
 
 
 
 

 rack and pinion
 
 
 
 
 
 
 
 
 
 
application
 
 
 
 
 


 
 
 
Spur gears
 
The spur gear is the last gear we will look at and the most important as far as we are concerned. We will be looking at the gear terms and how to draw the gear teeth using Unwins construction. Firstly, we will discuss the spur gear itself.
 
A spur gear is one of the most important ways of transmitting a positive motion between two shafts lying parallel to each other. A gear of this class may be likened to a cylindrical blank which has a series of equally spaced grooves around its perimeter so that the projections on one blank may mesh in the grooves of the second. As the design should be such that the teeth in the respective gears are always in mesh the revolutions made by each is definite, regular and in the inverse ratio to the numbers of teeth in the respective gears. This ability of a pair of well made spur gears to give a smooth, regular, and positive drive is of the greatest importance in many engineering designs. An example of two spur gears in mesh are shown below.
 
 
 
 
Spur gears
 
 
 
 
 
 
 
 
Now that we have discussed the spur gear, we will look at the terms associated with spur gears.
 
 
 
 
 
 



 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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.
 
 
 
 
 
 
 
 
 



 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 

Involute gear teeth
 
 
 
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
 
 
 
 Two spur gears rotating in mesh
 
 
 
 
 Close up of rotating gears to show clearance
 
 
 
 
 
 
 
 

 



 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 

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.
 
 
 
 
 
 
 
 
 
  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 

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: click here to begin the drawing,
 
 
 
 Step 2: click here to continue the drawing,
 
 
 
Step 3: click here to complete the drawing.
 
 
 

 

 
 
 
 
 



 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 
 

Step 1 (animation)
 
 
 
 

 

 
 
 



 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 

Step 2 (animation)
 
 
 
 
 
 
 
 
 



 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 

Step 3 (animation)
 
 
 
 
 
 
 
 
 



 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   

You have now completed this last section on gears. This completes your visit to the site as you have now completed all the material on the curriculum. I hope you have enjoyed your visit and have learned all the material on the curriculum. Remember practice makes perfect, so visiting the site regularly will develop your knowledge of the curriculum content. 
 
 

Any comments you would like to make about this web site can be emailed to Kenneth Nolan at 9528091@student.ul.ie.  Feedback is appreciated as it will aid in improving and updating this web site.
 
 
 

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