Drawing gear systems
In this chapter, you will learn how to draw gear systems. First you will do some orthographic or two-dimensional (2D) drawings that show the exact sizes and numbers of teeth on the gears. For these types of drawings, you do not have to draw the teeth, so it is much easier.
Then you will write a design brief for some gear systems of your own and produce specifications for the systems. You will learn to use drawing instruments and an isometric grid to draw your gear systems in three dimensions (3D).
Draw gears in two dimensions (2d)
When you draw a gear wheel, you show a number of different circle sizes, but you do not show the gear teeth. The specification for the gear wheels and teeth is shown using notes and tables.
Figure 3 shows all the important information for a gear wheel:
- The pitch is the space for each tooth.
- The pitch diameter is the size of the circle that can fit all the teeth, up to where they mesh with the teeth of another gear.
- The outside diameter shows the size of the circle that surrounds the teeth.
- The inside diameter shows where the teeth are joined to the inner wheel.
- The depth of the teeth is the difference between the outside and inside diameters.
The pitch circle diameter on this gear is 35,8 mm. The distance around the pitch circle of this gear is the pitch circle circumference, which is:
Circumference = π × D = 3,1428 × 35,8 mm = 112,5 cm.
So the pitch, or the space for each tooth = 112,5 ÷ 15 = 7,5 mm.
Look at Figure 4. This figure shows how to draw a gear wheel.
Now draw this gear wheel on the grid by following these steps:
- Step 1: Draw two crossing centrelines to mark the centre of the gear wheel.
- Step 2: Draw the pitch circle using a compass. In this case, you will need to set the compass radius to ½ of 3,5 cm (35 mm), which is 17,5 mm.
- Step 3: Draw the outside diameter using a compass. You will need to set the compass radius to ½ of 4,25 cm (42,5 mm), which is a little more than 21 mm.
- Step 4: Draw the inside diameter. You will need to set the compass radius to ½ of 2,75 cm (27,5 mm), which is just under 14 mm.
Drawing meshing gears
Look at the drawing of the meshing gears in Figure 6. A small driver gear is shown on the left. It is driving a larger driven gear on the right.
Two spur gears will only mesh properly if:
- the size and shape of their teeth are the same, in other words the pitch and the depth of gear teeth on both gears are the same, and
- the pitch circle circumferences of the two gears are touching each other.
The line connecting the centres of the two gears is called the centre line. Centre lines are drawn as chain lines, with long and short dashes.
The distance between the gear centres is shown on this drawing as the centre distance. The exact centre distance for two meshing gears is the pitch circle radius of the driver gear plus the pitch circle radius of the driven gear.
Remember: The radius is ½ of the diameter.
If, for example, this driven gear had 15 teeth and a pitch circle diameter of 35 mm, and the driven gear had 30 teeth and a pitch circle diameter of 70 mm, then the centre distance would be:
Centre distance = ½ × 35 mm + ½ × 70 mm = 17,5 mm + 35 mm = 52,5 mm.
How to draw meshing gear systems
Look at the meshing gears in Figure 6 on the previous page. Figure 7 below shows how to draw a diagram of this gear system, which has a 15-tooth driver gear and a 30-tooth driven gear.
- Step 1: Start by drawing a horizontal centre line for both gears.
- Step 2: Draw a vertical centre line for the driver gear on the left. This marks the centre of the driver gear wheel.
- Step 3: Calculate the pitch centre distance. In this case, it would be: ½ of 36 mm + ½ of 72 mm = 54 mm.
- Step 4: Measure the centre of the driven gear from the centre of the driver gear.
- Step 5: Use a compass to draw the two pitch circles so that they just touch each other. In this case, the pitch circle of the driver gear will be 36 mm, so you will need to set the compass to a radius of 18 mm. The radius setting for the larger driven gear will be 36 mm, twice as big.
- Step 6: Use your compass to draw in the inside diameter (ID) and outside diameter (OD) circles.
- Step 7: Now add the information that tells people about the teeth. This is written underneath each gear wheel or on a table next to the drawing.
Draw gear systems with the driven gear rotating in the opposite direction of the driver gear
1. Use the steps on the previous page to draw a gear system with 15 teeth on a driver gear with a 36 mm diameter and 30 teeth on a driven gear with a 72 mm diameter. Use the grid paper in Figure 8. The driver gear drawing has been started for you.
2. When you have finished your drawing, use arrows to show the direction of rotation of the driven gear if the driver is turning clockwise.
3. Will the driven gear be rotating faster or slower than the driver?
Draw gear systems with the driven gear rotating in the same direction as the driver gear
Do you remember what an idler gear does? It meshes between the driver and the driven gear. The idler does not change the gear ratio. All it does is change the direction of the driven gear. A gear system with an idler can have the driven and the driver gear turning in the same direction.
To draw a gear system with an idler, you will need to draw three gears instead of two. But the principle stays the same.
1. Draw the gear system in Figure 9 on the grid paper on the next page.
2. Draw arrows to show which way each gear will turn.
3. Do the driver and driven gears rotate in the same or in opposite directions?
4. If the driver gear rotates at 1 500 rpm, how fast will the driven gear rotate?
Homework: draw gear systems with the driven gear rotating faster than the driver gear
Part A: Rotating in opposite directions
1. Draw the gear system shown in Figure 11. The driver gear has 45 teeth and a pitch circle diameter of 107 mm. The driven gear has 15 teeth and a pitch circle diameter of 36 mm. Use the grid paper in Figure 12.
2. What can you say about the speed of the driven gear compared to the driver gear?
3. Does this system change the direction of rotation?
Part B: Rotating in the same direction
1. Add an idler to this gear system as shown in Figure 13. Now draw this new system on the grid paper in Figure 14.
2. Draw arrows on the drawing to show the direction of rotation of each gear.
3. What does the idler do?
Write a design brief with specifications for gears
Gear systems have two important uses:
- A gear system can give a mechanical advantage. In this case, a small driver gear is used to turn a larger driven gear. The output of the system turns more slowly, but with greater turning force.
- Gears can also give a speed advantage. In this case, a large driver gear will turn a smaller driven gear. The driven gear turns faster than the driver gear, but with less turning force.
In this lesson, you will design gear systems that use both these advantages.
A design brief for a gear that gives a mechanical advantage
Look at Figure 15. It shows a winch for a tow truck. Winches are used to pull broken-down cars onto the back of a tow truck.
A problem with this winch
The company using this winch has found that is not powerful enough to pull large vehicles.
The company asked you to improve the winch. They want the winch to pull large vehicles that are three times as heavy as ordinary cars.
The word tow means to pull a car behind a moving truck for a certain distance. Tow trucks can tow cars, but they can also pull cars onto the back of the truck to carry them to the repair shop.
Write a design brief
1. Write a few short, clear sentences that summarise the problem that needs to be solved, as well as the purpose of the proposed solution. Begin your first sentence with the words:
I am going to design ...
2. Write a list of specifications for the new winch solution.
Remember: Specifications are lists of things that your solution must do, and some things that it must not do.
A design for the improved winch
3. Describe how you are going to improve this winch.
4. How will you know that the winch can pull vehicles that are up to three times heavier than an ordinary car?
5. Complete the drawing in Figure 16 to show how you will improve the winch. Draw the driver gear on top of the motor. Then show where you will place the winder, and draw the winder gear. Use a pitch of 7,5 mm and a depth of 5,0 mm for the gear teeth. Label your drawing with the pitch and number of teeth on each of the gear wheels.
Write a design brief for a gear that gives a speed advantage
Look at the system shown below. It shows the inside of a wind turbine. The wind turns the propeller and the propeller turns an electric generator to make electricity.
The problem with wind turbines
The blades of wind turbines turn slowly, at about 9 to 19 rpm. But the electric generator that is driven by a wind turbine needs to turn faster. A turbine manufacturer needs a gear system that will make the generator turn at least four times faster than the wind turbine. Can you help?
1. Write a design brief. You need to write a few short, clear sentences that summarise the problem that needs to be solved, and the purpose of the proposed solution. Begin your first sentence with the words:
I am going to design ...
2. Specifications for your solution. Write a list of specifications for the gear system solution.
A design for the improved wind turbine
1. Draw your design on the grid in Figure 18. Your design should show how you will make the driven generator of the wind turbine move four times faster than the driver. Use a pitch of 0,75 cm and a height of 0,50 cm for the gear teeth.
2. Label your drawing with the pitch and number of teeth on each of the gear wheels.
Draw gears in three dimensions (3d)
Drawing gears in 3D is mostly about drawing circles in 3D. In this activity, you will draw 3D gears on isometric grid paper.
If you follow the instructions step by step, your drawing will be correct.
How to draw an isometric circle
Look at the pictures in Figure 19. They show how to draw a circle on isometric grid paper. This circle has a diameter of 2, so it is nearly the size of a small gear wheel. Below is an outline of how it can be done.
- Step 1: Make a dot where you want the centre of the circle to be.
- Step 2: Draw a horizontal chain line going from left to right up the sloping lines of the grid.
- Step 3: Draw a vertical chain line going through your centre point up the page.
- Step 4: Draw a guide box that will surround your circle. This box is shown in red on picture A.
- Step 5: Mark four dots at the centre points of the square. These dots are shown in red in Figure 19B. These dots mark the outside points of your circle.
- Step 6: Now sketch a curve joining these four dots. This shape is not a true circle. Its actual shape is an ellipse slanting at 30°.
- Step 7: Now see if you can draw one for yourself. Copy the diagram in Figure 20 A onto the isometric grid in Figure 20 B.
Draw the gear system that you designed for the winch
Look at the picture in Figure 21. Two gears have been drawn in 3D using isometric grid paper. The teeth of the gear are not shown.
1. Use the grid on the next page to help you draw the system you designed for the winch. Draw the gears to the same size as you specified for the winch in section 3.2.
2. Add a table of information to your drawing that gives all the information necessary for someone to make these gears.
Draw your gear system for the winch onto the grid in Figure 22:
Next week
Next week, you will investigate a type of gear called bevel gears. You will look at the gears on a bicycle and learn about chain and belt drives. Then you will learn how to analyse gear systems using the systems approach.