ClassX Video Lessons Youtube Channel The Engineering Mindset Gears Explained – mechanical engineering
Have you ever noticed how hard it is to start pedaling a bike in a high gear? That’s because you need to start in a low gear to get moving. As you gain speed, your legs start spinning quickly, and you need to switch to a higher gear to go faster. The same principle applies when driving a car. You start in a low gear and shift to higher gears as you speed up, then shift back to a lower gear when going uphill.
Low gears provide low speed but high torque, while high gears offer high speed but low torque. Torque is the force that causes something to rotate around a point. Imagine trying to loosen a stuck nut with a wrench. A small wrench makes it difficult, but a longer wrench makes it easier because it provides more torque.
For example, if you use a 30 cm wrench and apply 90 Newtons of force, you get 27 Newton-meters of torque. But if you use a 60 cm wrench with the same force, you get 54 Newton-meters of torque. This shows that a longer wrench gives you more force to turn the nut.
When two gears are connected, turning one gear causes the other to rotate. The gear connected to the engine is the driver gear, and the other is the driven gear. If both gears are the same size, they have a 1:1 ratio, meaning they rotate at the same speed. If the driven gear is half the size of the driver gear, it rotates twice as fast, creating a 1:2 ratio.
If the driven gear is twice the size of the driver gear, it rotates half as fast, resulting in a 2:1 ratio. Notice that the driven gear rotates in the opposite direction. To make them rotate in the same direction, an extra gear called an idler gear is added, forming a gear train.
To save space, multiple gears can be mounted on the same axis, creating a compound gear train. This setup allows for changes in speed and direction without taking up much room.
To calculate the RPM and torque in gear systems, you can use these formulas:
For example, if gear A has 8 teeth and gear B has 10 teeth, the ratio is 1.25. If gear A rotates at 150 RPM, gear B rotates at 120 RPM. If gear A has a torque of 20 Nm, gear B has 25 Nm of torque.
Adding more gears, like gear C with 20 teeth, changes the ratio to 2, making gear C rotate at 60 RPM with 50 Nm of torque. Adding gear D with 8 teeth changes the ratio to 0.4, resulting in 150 RPM and 20 Nm of torque.
This setup helps you understand how gears change speed, torque, and direction. In a compound gear train, gears B and C share the same shaft, so they rotate at the same speed and torque. Gear D rotates faster but with less torque.
When designing a gearbox, consider how many gears are connected and the required torque and speed.
That’s a wrap on gears! To learn more about mechanical and automotive engineering, explore more resources and videos. Keep learning and exploring the fascinating world of engineering!
Gather some basic materials like cardboard, scissors, and pins to create your own simple gear system. Try making a driver and a driven gear, and experiment with different sizes to see how they affect speed and torque. Document your findings and share them with the class.
Using the formulas provided in the article, calculate the gear ratios, RPM, and torque for different gear setups. Create a table with your calculations and discuss how changing the number of teeth on each gear affects the overall system. Present your results to the class.
Use online simulation tools to design and test virtual gear trains. Experiment with different configurations, including compound gear trains, and observe how changes impact speed and torque. Take screenshots of your simulations and explain your observations in a short report.
Identify and analyze gear systems in everyday objects like bicycles, clocks, or hand drills. Take photos or draw diagrams of these systems, and explain how the gears work together to achieve their purpose. Share your findings in a class presentation.
Work in small groups to design a gearbox for a specific application, such as a toy car or a wind-up toy. Consider the required speed and torque, and choose appropriate gear sizes and arrangements. Present your design to the class, explaining your choices and how your gearbox meets the requirements.
Here’s a sanitized version of the provided YouTube transcript:
—
If you have ever ridden a bike, you know it’s very difficult to start pedaling in a high gear. So, we need to start in a low gear to get the bike moving. At a certain point, our legs are spinning very fast, but we can’t go any faster, so we need to change to a higher gear. When we reach a steep hill, we need to move to a lower gear. The same applies to a car; we start in our lowest gear and work our way up as the vehicle increases in speed, then change down when driving uphill.
A low gear provides low speed but high torque, while a high gear gives high speed but low torque. Torque is a measurement of the force that causes something to rotate around a point. Think of a wrench and a nut that has seized up. Using a small wrench is very hard to free the nut, but using a long wrench makes it much easier. This is due to torque.
For example, if we use a 30 cm wrench and apply 90 Newtons of force, we have 0.3 m multiplied by 90 Newtons, which gives us 27 Newton-meters of torque. However, if we apply the same 90 Newtons of force to a wrench that is 60 cm long, we get 0.6 m multiplied by 90 Newtons, resulting in 54 Newton-meters of torque. From this simple formula, you can see that we have more force acting on the nut by using a longer wrench. Essentially, we’re using a larger circle to turn a smaller circle; by changing the size, we change the speed and the torque.
If we connect two gears and rotate one of them, the other gear will also rotate. If we attach the engine to the first gear, this will be the driver gear, and the other gear is the driven gear. When the two gears are the same diameter, we have a 1:1 ratio, meaning every time the driver gear completes a full rotation, the driven gear also completes one rotation, so the output speed is the same as the input speed. If the driven gear is half the diameter of the driver gear, we have a 1:2 ratio, meaning for every full rotation of the driver gear, the driven gear completes two full rotations, rotating much faster.
Conversely, if the driven gear is twice the diameter of the driver gear, we have a 2:1 ratio, meaning for every one full rotation of the driver gear, the driven gear rotates only half a turn. Thus, the driver gear needs to rotate twice to complete a full rotation of the driven gear. Notice that the driven gear rotates in the opposite direction. To make the output rotate in the same direction as the input, we need to insert another gear, creating something known as a gear train. The middle gear is known as an idler gear.
We can add many gears side by side to change the speed and output direction, but this will take up a lot of room. Instead, we can mount gears on the same axis and create a compound gear train, which will do the same job but take up far less space.
Let’s look at how to calculate the RPM and torque of simple gear trains. You can download an Excel sheet for these calculations; links can be found in the video description. We will use the formulas:
– Ratio = teeth of the output gear divided by teeth of the input gear
– RPM output = RPM input divided by the ratio
– Torque output = ratio multiplied by the torque input
For example, if gear A has 8 teeth and gear B has 10 teeth, the ratio is 10 / 8, which is 1.25. If gear A rotates at 150 RPM, then 150 divided by 1.25 equals 120 RPM. If gear A has a torque of 20 Nm, then 1.25 multiplied by 20 gives us 25 Nm. This gear will rotate in the opposite direction to gear A; it will rotate slower because it is larger, but it will have more torque.
If we add gear C with 20 teeth, the ratio is 20 / 10, which gives us 2. The RPM output is 120 RPM from gear B divided by 2, which gives us 60 RPM. The torque will be 2 multiplied by 25 Nm from gear B, resulting in 50 Nm. This gear will rotate in the same direction as gear A but will rotate slower because it is larger, although it will have more torque.
If we were to add gear D with 8 teeth, then the ratio is 8 / 20, which gives us 0.4. The RPM is 60 RPM from gear C divided by the ratio of 0.4, which gives us 150 RPM. The torque is 0.4 multiplied by 50 Nm from gear C, resulting in 20 Nm. This gear will rotate in the opposite direction to gear A, but it is the same size, so it will rotate at the same speed and torque.
This setup allows you to visualize how gears manipulate speed, torque, and direction. What if we had a compound gear train with the same size gears, input torque, and rotational speed? Again, links in the video description for the Excel sheet calculator.
With this setup, we have four gears: A, B, C, and D, with B and C being compound. If gear A has 8 teeth and gear B has 10 teeth, the ratio is 10 / 8, which is 1.25. Gear A rotates at 150 RPM, so gear B is 150 RPM divided by 1.25, which gives us 120 RPM. Gear A has a torque of 20 Nm, so gear B is 1.25 multiplied by 20 Nm, which is 25 Nm. This gear rotates in the opposite direction to gear A; it will rotate slower because it is larger, but it has more torque.
If gear C has 20 teeth, the ratio is 20 / 10, which is 2. The RPM will be the same as B, which is 120 RPM, because these two gears are compound and share the same shaft. The torque will also be the same as B, so it’s 25 Nm. This gear also rotates in the opposite direction to gear A; it will rotate slower than gear A because of the size of gear B and will also have less torque than gear A, again because of gear B.
If gear D has 8 teeth, the ratio is 8 / 20, which is 0.4. The RPM is 120 RPM from gear C divided by 0.4, which is 300 RPM. The torque is 0.4 multiplied by 25 Nm from gear C, which equals 10 Nm. So, this gear rotates in the same direction as gear A; it rotates faster but with less torque.
We need to consider the application of the gearbox, how many gears are connected, and what torque and speed we require.
That’s it for this video! To continue learning about mechanical and automotive engineering, check out one of the videos on screen now, and I’ll catch you there for the next lesson. Don’t forget to follow us on social media and visit the engineering mindset website.
—
This version removes any informal language, typos, and unnecessary repetitions while retaining the core content and structure.
Gears – Gears are rotating machine parts with cut teeth that mesh with another toothed part to transmit torque. – In a bicycle, gears help change the speed and force needed to pedal.
Torque – Torque is a measure of the force that can cause an object to rotate about an axis. – The torque applied by the wrench was enough to loosen the bolt.
Speed – Speed is the rate at which an object covers distance. – The speed of the car increased as it moved downhill.
Ratio – Ratio is the quantitative relation between two amounts, showing the number of times one value is contained within the other. – The gear ratio determines how many times the output gear turns for each turn of the input gear.
RPM – RPM stands for revolutions per minute, a unit of rotational speed. – The engine was running at 3000 RPM during the test drive.
Force – Force is a push or pull upon an object resulting from its interaction with another object. – The force applied to the lever moved the heavy rock.
Rotation – Rotation is the action of rotating around an axis or center. – The rotation of the Earth causes day and night.
Engine – An engine is a machine designed to convert energy into useful mechanical motion. – The car’s engine was powerful enough to climb steep hills easily.
Geartrain – A geartrain is a mechanical system formed by mounting gears on a frame so that the teeth of the gears engage. – The geartrain in the clock ensures that the hands move at the correct speed.
Compound – In engineering, a compound refers to a system composed of two or more elements or parts. – The compound gear system in the machine allowed for more efficient power transmission.
