Introduction To Gear Ratios

[Music] hi so i've been asked to talk a little bit about um gears in particular gear ratios and other ways of making them in particular packing cage gears so i thought i'd start off by talking about gear ratios because it seems to confuse people a lot now cogs are very little more than circles with teeth in them so if we look at the circles we'll be able to get hold of those basic concepts and so get to what the gear ratio is now this circle obviously has two interesting bits about it one is the center and two is the edge that might seem fatuous it isn't it'll come clear later now if i put a spindle on that center and revolve that spindle up once every second the edge will revolve once every second too now in a wheel on a car if i do that that will move like that and travel a distance and it does that because the distance around the edge is the same as the distance is going to be traveled in a straight line map measurers do exactly the same thing so i put a little mark on this circle and if i roll it across my paper till i get to the other mark what i'll do is i'll get a straight line that straight line there is the distance that it has traveled around that edge so that edge distance and this distance on a straight line they're the same distance for the same amount it has to travel and we know that just by getting into a car turn the wheel that wheel will move you a distance based on the distance it's moved around the circumference now as we get a larger circle and we still turn this at one meter per second this edge will also turn at one meter per second and it'll move a greater distance and the same with even larger one it'll move an even larger distance so these distances are getting progressively longer as we draw them because the circles are getting bigger now they are all turning at the same rate and i can put those all together like that and if i turn that at one meter per second all of those edges will cover that distance in one second what does that mean well if you're going a greater distance faster you're traveling at more speed we all know this if you um want to drive and get somewhere quicker you've got to put your foot on the throttle and travel faster equally should tell you there's no free lunch because if you do that you're going to burn more petrol and it's exactly the same thing as you travel faster you need more power in there to make it travel you can feel it when you actually try to do that it takes more effort to turn a larger circle than it does to turn a smaller circle because you're traveling further in the same time now it gets confusing when we wrap it around in a circle but when you lay it out as a straight line you can see that the distances are getting larger the time to travel that is the same and so the speed must be quicker just because we're traveling a greater distance now there is a relationship obviously between those and that relationship actually is really something we have we understand we just understand it can intuitively so if i take this thing and i set it apart at a distance like that i'll draw a circle if i make that distance bigger i'll draw a bigger circle and bigger i'll draw an even bigger circle so there's a clear relationship between the point here and the point there and the size of the circle that i draw now the size of a circle that i draw gets bigger and bigger as those points move apart and that points move apart is called the radius the the relationship of the size of the radius is fixed the bigger the radius the bigger the circle the bigger the circle the bigger this line around the edge the circumference and so the bigger the circumference the longer the distance it moves in the same time all those relationships are the same relationship they're being expressed in different ways but they're identical relationships so if i want to use two gears because it's really unusual to use one you hardly ever do that you see them in relation to each other we go back to those distances traveled so if i'm turning this at once every second it will turn with those two distances moving against each other if this turns a full rotation in one second this will have turned more times why it's a smaller distance it has to travel what's the relationship between this and this it's a direct relationship between the distances traveled so let's have a look at this and we will say that this is twice the distance of this just for example so we're saying that this is twice the distance of this so every time that turns once that will turn twice so that relationship is a two to one sorry um two to one one turn of this two turns of this why twice the distance it's also going to be twice the radius because it's twice the circumference so all of those relationships are going to hold true whatever the form it's in whether it's in a circle circumference or it's in a straight line then going to be the same relationship now we can govern the size we make our circles by setting our compass to the size we want drawing them out and cutting them out we can make them the size that we want them to be and so we can govern those relationships again remember there isn't a free lunch here it does take more energy to do that but that is basically what you're doing you're basically creating two circles you've got one that you're moving the other one is going to move in relation to the ratio of the circumference to the circumference which is the same ratio as the radius to the radius now it's not the same exactly but it is the same ratio exactly so this is two centimeters in its radius and this is one centimeter in its radius this will turn once this will turn twice so you don't need to know this bit but mathematically then that holds up because remember the circumference is pi times diameter diameter is two times the radius so the circumference is equal to two pi r now pi and two are constants and so don't play a part in ratios so the ratio of the circumference which is the ratio which is the distance it travels remember is the same as the ratio of the two radii and that's all you need to remember really so there's a mathematical proof for it there in terms of ratios but all you really need to remember is that this distance from the center to the edge has the same ratio as the distance from center to that edge so if that distance is twice that distance the ratio is two to one that's all you need to remember and you can create those gears yourself if you want a two to one ratio just by doubling the amount you open that by and the reason for it is the distances will have that relationship so all of these things have fixed relationships just from the shape of it you determine the shape because you use that to draw it so it's that simple to get a grasp of what those ratios are what it means is that if that's turning once a second that will turn twice a second because it's got half the distance to travel or that distance every time it travels half a distance this one will travel a full distance so all of that stuff you can just work out just from common sense because you fix it by using that to draw your circle now it holds very true for circles but circles and cogs look different because they've got teeth and circles don't but they're essentially the same kind of thing remember i mean this circle pulley cog chain and sprocket that all the same kind of thing now the simplest thing we can do is just butt the two up against each other if we do that we in fact have a gear that works by friction it's just rubbing on the surface and that rubbing will force that one to move of course it's prone to slip and it's got an awful lot of friction that's been wasted there so it's not a particularly efficient way of doing it but it will work if we separate them out a little bit and put a belt on like a rubber belt that will grip the surface a bit more well we've got this pulleys but the pulley will do exactly the same thing if i turn that once that will turn twice just fastening it up with a bit a belt doesn't change that ratio it works by friction just the pulley belt has more friction that it can grip the surface of the wheel and transfer the energy more efficiently because i put a lot of teeth on there and put a chain between the two it's exactly what a pulley system is only it's more efficient because there's more grip if you like now one of the things um about pulleys and chains is that they are prone to slippage they're prone to where they're not that that efficient putting two things together and having a friction rub against each other isn't that efficient either so what some bright spark came up with and this was a very long time ago was to put teeth on the edge if you put little teeth on the edge then the teeth will knock and push that around just by using the teeth to do it and then we get our cogs and gears that we recognize as being cogs and gears but all of those things that i've mentioned the pulley the chain and the sprocket and the friction are all valuable ways of transferring from one rotation to another in a ratio and we can use all of those structures now we have used those we've used friction we've used v-belts we've used pulleys we've used chains and lately we've been working with those gears that are actually relatively simple to make so let's have a think about those gears so mostly because of grain mills actually as people were pondering this and they were looking at these this transfer of power and the slip that that may sometimes have rather than being able to do that and it will slip if that's too much to turn and that one's got trying to turn it you'll get a lot of slip but anyway they were pondering and some bright spark noticed that if you did something like this and this was trying to turn and this was turning and you had a peg in there and it knocked it then it wouldn't slip anymore because there's something knocking it preventing that slip that was happening when it was just two bare circles now of course what you should be noticing almost immediately is this is beginning to look like a gear these things here actually are just pegs and if we keep putting pegs around here we put another one in and another one in and another one in and another one in and so on and so on and so on then as they return they turn they will keep on knocking against each other and that taking the circle and driving pegs into it was the beginning of the peg gear peg gears are actually great things to make and we'll be making some peg gears but that was the beginning of it the next thing they did was create little flaps on it which is what we've got here i've got these little plastic ones to make it easier for me but you'll notice that those flaps do exactly the same thing that the pegs were doing so you've got peg gears and then flap gears and then you've got this engagement here and of course we are looking then at something like that which is a gear that we recognize now all of these gears are the same thing the kind of an evolution of gears if you like from our circles to our pegs to our flaps and to our teeth where we get the toothed gear that we actually know and love there we go we can see the little progression of it all going through that now they're all very valuable ways of transferring power from one shaft to the next shaft at the ratio that we've just been discussing and depending on the availability of the equipment depends on how easy it is for you to make them now we've been making this one we've been using this one we've been making this one we are going to make this one but we haven't made this one now this one needs a degree of um effort to make it this one we know is relatively easy and this one is even easier now if we look at this one then there's a thing to notice about it that is it's got this flap and then it's got this little hollow that the flap can fit into and that flap and little hollow that distance there is fixed it will always be the same size as we go around there because if it doesn't they won't engage so they must be the same size the other thing to notice is they take up space so if i've got my circle and i want to put a flap and a hollow on it and i have some size there's my flap there's my hollow that distance there takes up a part of the circumference so depending on how big that is will depend on how many of those i can get around the edge obviously it's a finite distance so i've got to put a whole number of these things flaps and hollows all the way around the edge and i can work out what those number of flaps and hollows are to go around the edge of that circle the other thing i can do is work out how many flaps and hollows i want of a fixed size and then how many i have to put together to make a circle either those will work really really well but you have to remember that there is a fixed distance between flap and hollow and it's the same thing on the gear there's a fixed difference between the tooth and the little engagement that a tooth goes into and it has a distance that distance must travel around the circumference so the size of the circumference and the size of the flap and the hollow are clearly related to each other you can't get more teeth on there than there is distance to put them on that should be really obvious you can't do that so there will be a fixed number of teeth and that fixed number will be a relationship between the size between the flap and the hollow and the distance around your circumference now you can work that out using a little bit of mass or you can actually just measure it you could put a line on here like i've done roll it on a bit of paper and you will get a straight line when you know what the distance between your flap and hollow is from there to there we can work out how many flaps and hollows will actually go on there because that distance little distance and big distance i have a relationship there are only so many of these little distances i can get in this big distance and that'll tell you the number of teeth that you're going to be able to put on to your gear and when you can calculate the number of teeth you put on your gear you're on a winner now earlier we did something where we created the flap and the hollow using a fixed drill bit size our drill bit size created the hollow so we took this to be one which would be for example 15 millimeters and this one to be a little bit bigger and you can see that actually if you look at that that's smaller than that because we need a little bit of leeway so we take the next one of the hollow to be 16 millimeters and we add those together we get 31 millimeters and that is the distance between here and here or if you like the distance between here and here now if this one is 310 millimeters clearly i can get 10 little d's all the way around that and i would put 10 teeth all the way around that so the same relationships hold true whether it's a straight line and you're just dividing one by the other or it's around the edge of a circle nothing changes and that's all you really need to know about these things when you do that then you'll be able to calculate work out cut the number of teeth that you actually want onto your gear now obviously these teeth have to fit each other so if that tooth is going to engage in that it needs to be the same size if it's bigger it won't fit if it's smaller it won't fit it needs to be the same size just so it fits this isn't a mystery if you get a nut and a bolt and your nut is smaller than your bolt it's not going on if your nut is bigger than your bolt is going to rattle around it's the same stuff the gap and the hollow on the two different wheels need to be the same size now it's not a problem when they're both identical like that it's easy to see how you do that you just cut the same number of teeth but what about if you want a larger gear so that you get a gear ratio well the distance it travels has to be further so let's say this distance is 620 so it's twice the distance so we'll have a two to one gear ratio now we know we got 10 teeth on here how many teeth we're going to get on there it's not really a challenge is it it's going to be 20 teeth of the same size we'll go on this so if we're looking at this one and this one these two circles and we put 10 teeth on there and 20 teeth on there they will mesh because they're the same size and they will have the ratio of two to one because we've made sure that the circumference is twice this circumference and that's the same as the distance it moves so we can work all of that stuff out just from if you like to a degree common sense yes it does take a little bit of thinking through but once you think this thing through then actually it begins to make a lot more sense if you just go back to your circle and the fact that the circumference of the circle is identical to a straight line that's been moved i've probably rambled on long enough about that really but just to remind you gears whether they're tooth gears flap gears peg gears or even just straightforward circles are all the same thing so are pulleys sprockets chains and belts they all have that same relationship of distance traveled once you've got distance traveled in your head it's just about the ratio of the distance traveled the ratio of the distance traveled is the same as the ratio of the radius it's that easy to work out what the ratios are constructing gears with teeth you just need to remember the size of the dip and the hollow that's all you need to know if your um tooth size is the same which it has to be in order to engage you have a bigger wheel you'll have more teeth if you have more teeth the ratio will change but only in relationship to the two circles that i showed you so it's that easy to remember all of this stuff and really to work all of this stuff out and it terrifies a lot of people including me to some degree actually but it isn't that challenging to actually do there is one other little point to remember if i have a circle and i'm turning the circle that way because it's rubbing on that one it will turn in the opposite direction and that can be quite confusing to people but because they're going that way they turn opposite to each other anyway as i say enough of being burbling on i think the next thing to do is do what i was asked and that is make some peg gears and do something with those peg gears and peg gears and caged gears are very similar so i'm going to make some peg gears next i think and we'll have a look at how we make those and how we can use them i hope this was of interest i hope it'll clear up some of the confusion around ratios and gears and thank you very much for watching

Channel: Robert Murray-Smith

Views: 7,672

Keywords: gear, cogs, ratio, introduction, robert, fwg, maths, engineering, design, technology, wood, work, working, motor, diy, d-i-y, math, dt, murray-smith, science, fair, project, mechanics, mechanical

Id: wnmdNlCiF74

Length: 21min 7sec (1267 seconds)

Published: Sat Sep 05 2020