In part 1 of How to on Gears tutorial I introduced you to the basics of the gear systems. Now we are going to examinate gear systems with more than two gears and take a look at cascade gear systems.

**#65**- 21 Dec 2014
- 7:20

In the first part of the tutorial I add a LEGO gear between the driver and the follower gear. After calculating the ratio we conclude, that it does not matter how many gears there are between the driver and the follower gear - the ratio is the ratio between the driver and the follower gear.

However, this does not mean that we are limited to ratios less than 5:1. If you want to achieve higher ratios you need to build cascade gear system - gear system where you have more than one gear per axle. In such cases the ratio between the gears multiply. To test this I use a gear system consisted of four gears. I attach one motor to the driver gear and one to the follower gear. Then set the first motor to move forward and using the Experiment tab in the LEGO EV3 Software I determine the number of rotations made by the second motor. By dividing this number by the number of rotations made by the first motor we reach the ratio of the gear system.

You could find the instructions for building the gear system together with the two LEGO EV3 Large Motors attached to it under the Materials tab.

### LEGO Gear Demonstration model

These are building instructions for a LEGO Mindstorms EV3 demonstration model. In the tutorial, we are using it to demonstrate the working and relations of LEGO Gears.

### The EV3 Project file with Experiment

### English

In episode 54 I introduced you to the basic concepts of gear systems. Today I will build on that knowledge. In part 1 we took a look at a gear system consisting of two gears only. But sometimes only two gears are not enough. Stay with me for the next several minutes when I'll answer the question what if we could not achieve what we need to with only two gears.

Do you remember this gear system? Now I wonder what would happen if I introduce one more gear between the driver and the follower gear. Let's calculate. So, for one rotation of the driver gear 40 teeth will go through the point of engage and that means that the grey gear will make 40 divided by 24 rotations. For each rotation of the grey gear that has 24 teeth the blue gear will make three rotations. So, for one rotation of the driver gear the follower gear will make 40 divided by 24, multiplied by 3, or 5 rotations. The same as the previous gear system. Actually, it does not matter if I put one or many gears in between. The ratio will be the same. But one thing will change. Each gear will change the direction of the rotation. So, for instance, if you need the driver and the follower gear to rotate in the same direction, you will need to put a gear in between. We will call the grey gear idler because it does not change the ratio. Now, let's see what the downside of using many gears is. I have five gears here that are attached to one another. I have blocked the big one using these two axles and, as you can see, it can't move. Still, the other big one, on the other end of the system, can move although it's attached to the first one. This is due to the gaps between the teeth of the gear wheels and this error occurs in every gear system. That's why it's better to use as few gears as possible. To illustrate that, I'll remove the gears in the middle and I'll move this gear next to the first one. Again, this one is blocked and can't move. As you can see, this one is moving way less than it did in the first construction. This error may cause you problems which is why you should try to use as few gears as possible. So far we've seen it does not matter how many gears we use. The ratio is the same as the ratio between the driver and the follower gear. Does this mean we could not achieve a ratio greater than 5? Actually, not. Let's take a look at this gear system. This time, instead of calculating the ratio, we'll use these two motors. One will drive the gear system and second one will be directly attached to the follower gear. We will find the ratio of the gear system by dividing the rotations of the driver motor by the rotations of the follower motor. Let's see how we'll do this. I have started the Lego Mindstorms EV3 software and opened a new project. But this time, instead of New Program, I'll open New Experiment. Here I have attached a brick with two motors - motors A and B. I will detect how many rotations each of the motors makes. The driver motor will be in green and the follower motor will be in red. I want motor B to move forward.

So, motor B will move forward at 100% power for 15 rotations. I will run the program on the brick.

Here you see the rotations each of the motor makes in real time. Now I'll use this tool - Analysis. I'll select point Analysis and I'll move the point till the end. As you see, motor B has made 15 rotations as it was programmed. And motor A has made minus 1 rotations. This is due to the fact that gears change the direction but the conclusion we could draw is that the gear system has a ratio of 15 to 1. So, let's get back to the gear system and see whether this is true and logical. We have three axles in this gear system. Let's calculate the number of rotations each of the axles makes. If this axle makes 1 rotation, the second one will make 5 rotations because the ratio between the red and the green gear is 1:5. If this axle makes 1 rotation, the third axle will make 3 rotations because the ratio between the yellow and the blue gear is 1:3. If the first axle makes 1 rotation, the second one will make 5 and for each rotation of the second axle the third one will make 3. Or, 5 multiplied by 3 is 15 rotations made by the third axle. It is true that the ratio of this gear system is 1:15. In conclusion, if you have gears attached to one another, without having two gears on one axle, the ratio is just the ratio between the driver and the follower gear. But if you have gears attached to one axle, the gear ratios multiply. I will stop here with the second part of the tutorials on gear systems. If you have any questions or suggestions that might be included in the next tutorial, post them as a comment below this video.