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.
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
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
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
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.
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.
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.
rack and pinion
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.
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.
Now that we have discussed
the spur gear, we will look at the terms associated with spur gears.
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
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.
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.
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.
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.
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.
tooth face is the surface of a tooth above the pitch circle,
parallel to the axis of the gear.
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
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.
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.
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
spur gears rotating in mesh
up of rotating gears to show clearance
spur gears in mesh animation
up of spur gears in mesh animation
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 = 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
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.
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.
view these three easy steps, simply click on the text below.
1: click here to begin the drawing,
2: click here to continue the drawing,
click here to complete the drawing.
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
Any comments you would like to
make about this web site can be emailed to Kenneth Nolan at firstname.lastname@example.org.
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