Sometimes the answer that you get by calculating seems not to be right. Is it the calculation that is wrong. Probably it is not the calculation, but something is happening with the robot.
- 09 Apr 2017
- LEGO MINDSTORMS
- EV3, Attachments, FLL 2016, Gears, Math, Construction, FLL, Classes with students
- K.Mitov, D.Staykov
Losses in a system
In every mechanical system, there are losses, because of friction, because of wrong alignments, because of the resistance of different elements, torsion, sagging and others. In our case, we have an answer from the previous tasks that 18.75 rotation should result in the last gear wheel rotation to 90 degrees. That is what the mathematical model behind our attachment tells us about the way it should work.
Torsion and other losses
It is possible for me to rotate the driving axle with this affecting the final driven wheels. Check it out in the video to see how this happens.
Gaps between the LEGO Mindstorms Gear Wheels
There is always some gap between the teeth of the gear wheels. This gap is not large but in a system of gear wheels, the overall "gap" in the system is a product of the gaps and ratios between each pair of wheels.
Are the losses the answer?
No, they do contribute to the overall difference between the experimental value and the calculated value, but there is more general problem with the calculation that we've done.
For the FIRST LEGO League 2016-2017 Animal Allies we prepared an attachment for lifting the robot. The idea of the attachment is to show how you could lift the whole robot with a system of gear wheels, levers, and scissors constructions.
Built mainly from LEGO Mindstorms EV3 parts but could probably be constructed from NXT sets.
Previously we calculated that if we rotate this gear wheel on the driving axle to 18.75 rotations, it will result in the last gear wheel to rotate to 90 degrees. And that's the mathematical model behind our attachment. But it is not working. It is only rotating the gear wheel to about 30 degrees. Something of that sort. In this video we'll discuss the losses in every gear system and in every mechanical system. There are 3 main reasons for the whole construction not behaving as we have calculated. And these 3 things are torsion, sagging and the gap between the gear wheels. And let's look at them one by one. The end result of these 3 effects is that I can actually rotate this driving axle without the final driven wheel being rotated. I'll fix with one hand the large wheel so that it does not move and then I'll start rotating the small gear wheel. And you see that I've made a couple of rotations before it even tries to move my hand. It's very slowly trying to move my hand but it can't because I fixed it. And I can rotate even more and more and I've probably done like 5 or 10 rotations here and if I release, it will return. So, it is possible to rotate this driving axle without the final wheel being rotated and that's for 3 reasons: torsion, sagging and the gap between the gears. First, I'll start with the gap.
If we have two Lego gear wheels, the way they are constructed there is a certain gap between the gears when they are working. I'll fix this gear wheel on my left side and then you see that we can move the right gear wheel and there is a small gap. And when we have a gear system with 10 different gears this small gap accumulates. Its effect is not that large, not as torsion and sagging but it's very important part of the whole calculation. We have a small gap between the gears. We also have a small gap right here in the axles. You see that the axles I can fix the beam and I can move the axle. This small gap also adds to the final effect and when we have like 6 or 7 different axles it again accumulates. So, this is the first reason for this end result where we have the driving wheel not actually transferring the power to the driven wheel. If we have other gears, for example, built by metal or if we have them in a serious machine, then the gap here will still be there but it will be very very small. It will be like small parts of the centimeter or of the millimeter and even smaller part of the inch. There are always gaps in the Lego sets because they are built with plastic there are very large gaps. The effect of torsion is also there. And just as a reminder when you have an axle and you have 2 gear wheels on both ends I'll fix one of the gear wheels and I'll rotate the other. And you see that the axle twists. There's the effect of torsion. The other effect is the effect of sagging where we have again the two gear wheels and because of the force that's applied to the whole attachment the axle will bend. Like this. Now, these effects are difficult to calculate and to add in our calculation. And the easiest way is actually to experiment. And to see how these effects contribute to the whole behavior of our robot. We know that mathematically we would have to do 18.75 rotation but we have to do a few rotations more to achieve our result. And now we must experiment with something above 18.75 and this will be number of rotations that are actually because of the gap between the gears, of the torsion and of the sagging.
Courses and lessons with this Tutorial
This Tutorial is used in the following courses and lessons