Fusion 360 Rack and Pinion Gear

hey this is Rob I'm going to show you how to make a rack and pinion in fusion 360 and and get you to the point where you can actually see it working using motion links so to start out with I'm going to just do it create a totally new design and first thing I'll do is change my units to be centimeters and I will use for that opinion here the spur gear add-in so this tutorial really is just to show you how to create the geometry for the opinion since the spur gear add-in actually creates the spur gear the pinion gear so you can see the kind of information is looking for diametral pitch pressure angle number of teeth and gear thickness so before I create that I'll just modify my user parameters and add some of those in there so diametral pitch that's going to be just 8 centimeters another one for the number of teeth I'll call that spur teeth there are no units and they're going to be 15 teeth the pressure angle has degrees as its units and that's just going to be 20 and thickness was the other thing that I was looking for so I'll just say that's the gear is going to be one inch thick so everything there is all that you need to create the gear we can get a little more information about it like the pitch circle which is this kind of imaginary circle that goes around the gear face and and anywhere where it contacts a tooth this is sort of the point where gears actually meshed so this is useful for us in creating the the rest of this geometry so I'll calculate that here the way that we do that is just spread your teeth divided by diametral pitch you can see it doesn't like this it's still red and the reason is because we're mixing no units with spur teeth and then some centimeters for diametral pitch so to get around this just multiply it times one centimeter and that kind of puts back in the unit's that this parameter is expecting so for some reason it adds another times one centimeter at the end I don't really know why but it works so there's also you know once we start talking about the actual rack there are some things that we need like backlash so this will basically be the kind of slop or tolerance between the years I'll use centimeters and say it's 0.01 five centimeters I just making that number up that's just so that everything doesn't fit perfectly because that's not realistic so there are a couple other things this is a common terminology between the spur gear and the rack and add addendum and addendum so the addendum is going to mark the top of the gear teeth and we figure that out by just doing 1 divided by diametral pitch again at multiply times 1 centimeter to get that to work and then the D denim is going to be the bottom of the tooth and so these are measured from the pitch circle the addendum is kind of you can see in the background 0.125 centimeters above the pitch circle the D denim is in the other direction and that formula is 1.25 / diametral pitch C we also need to know how many teeth there are on the rack so I'll call that rack teeth there are no units and I'll just make that 10 hello and then we need to know the pitch so the spur gear has a pitch for the teeth and we want to find out basically what the distance is between teeth on the rack so that's our pitch and that's going to be in centimeters and that's just pi / diametral pitch I think that's all we need there is a there is a circle that we draw while we're figuring out the geometry of the the rack teeth and it's may be useful to just add that here call it outer circle diam and there's a formula to it so it's 0.5 times pi times the cosine of the pressure angle divided by the diametral pitch so you'll see where that comes in in a bit okay so I'll use the add-in this is the spur gear add-in and I'll just type diametral pitch here pressure angle here and thickness here for some reason it does not like putting in a parameter here so even though we've got this this parameter called spur teeth I'll just have to put in a 15 here and another thing to note is in fact even though I'm using parameters in there this isn't really parametric if I go back and change one of my parameters you'll see that it actually doesn't change the gear unfortunately so well actually that one that one shouldn't matter but if I make this 18 you can see that the the gear doesn't actually change so we're a little limited in that way if you really need that to work out I think you'd have to draw this spur gear yourself in the same way that I'm showing you how to draw the rack from scratch so this this components all set for now and I'll just call this a pinion and then I will highlight the root component and create a new component called rack okay so now that you can see that's activated and that means anything I do now is taking place within the rack component has its own time line and everything is associated with this including this sketch that's what I'm going to start off with so I'll hit create sketch and I'll just create it on this work plane and actually you know I'll undo let me undo there so I can get rid of that sketch that I just created there's one other thing I want to do which is I want to rotate this gear and the reason for that is because it's it's easier at you know if nothing else is easier for you to fall around along with the tutorial if on the bottom this kind of six o'clock position this green axis meets up with the center of the midpoint of this gap between teeth so you can see it's happening here but not at the bottom so I think what I'll do is I'll just rotate that by 90 degrees and you see now it's it's kind of landing right in the center so you could do that and then go ahead and activate the rack and create that sketch okay I'm going to capture position I don't know why it flips over but I want to see it at this angle and so one of the first things I'll do is just get that imaginary line that that pitch circle and the way I'll do that is hit C for a center diameter circle I'll just draw it out here and I know what that's going to be that's pitch circle diameter and I'll click on it and hit X and that makes it into a construction line you can see this is basically the point where one tooth would mesh with another that's called the pitch the pitch circle from here I will create a line just a horizontal line don't really care about the length right now I'll click on it and make it a construction line by hitting X I'll click on these two and right click and choose tangents so that they're together and the next thing I need is well I'm going to make a center line here because I think it will make life easier for me later so I'll do that do that now and I'll click on it and hit X to make it a construction line and I'll whoops I will make one more line which is going to be right at that intersection and it's going to go some distance I don't really care right now hit tab and change this angle to the pressure angle so there's my 20 degrees click on that and hit X so I've got a bunch of construction lines now so what I need at this point is to have a circle here that is tangent to this this curve of the teeth and that's how that that's how that's that diameter gets figured out now I can either I can either do it that way or I can use the formula so in theory this formula right here outer circle diam should should come up with the same diameter a diameter that lands right tangent to that tooth but you know I'm going to remove that and do it this other way so the way that I'm going to do it is to project some of these some of these curves from the spur gear so I'll hit P for project to include these lines in my current sketch I had okay and what I'm interested in is really this point where that angle the pressure angle line there and this tooth intersect so I'm going to create a point there point me right at the intersection of those two you can see there's the coincident constraint there and I'll just hit C to make a center circle and make sure that it's coincident with that point that I just made so at this point I will also make this a construction line and I'll make another circle I can either offset this or I can make another circle I suppose I could use offset but you can't offset a construction line so I'll hit undo to get rid of that change of making it a construction line and then I'll choose offset and offset it by negative backlash okay I suppose I could now make both of these into construction lines and so there a couple other things one is the you know where the top of the tooth is and where the bottom of the tooth is so I will click on this this line that's tangent to the the pitch circle and I'll make another line I could could make it an offset but again well let's let's make it not a construction line and then try using offset so I'll hit Oh for offset and I'll offset this by D denim which is the bottom of my tooth I'd okay and I'll do the same thing here I'll offset but this time I want to offset in this direction so I'll do negative and this is my addendum so I'll turn these all into construction lines and what you'll see is I have the top of my tooth here and the bottom of my tooth there and the last thing I need to do is to create a line that represents the actual profile of the tooth it starts at the D denim ends at the addendum and the important parts here are that it's tangent to this inner circle and also that it's it's it's pressure angle degrees from the this vertical so I will hit D to dimension it and pressure angle as my is the angle I want so that's that's it that's my tooth and it looks like this isn't coincident with this so I'll just add that constraint and the same here I want to make sure those are actually connected to those lines what I'll do is just use the line tool to make a couple more lines which are these the top of the tooth and the bottom of the tooth and I'll highlight those curves that I just drew and mirror them about that centerline let's try that again so here are my three curves that I'm interested in and the mirror line is here so that's it I've got my tooth and I should be able to just stop sketch and even though I could repeat that to make my complete rack it's better to do that after it's already been extruded so I'm going to still within my rack component I'm going to click on that profile and extrude it by - thickness so it's the same size as my spur gear and at this point I could create and add a rectangular pattern say that this is the body that I want a pattern and the direction is this way I'm going to use spacing not to extend and I will say I need rack teeth number of teeth and the distance is going to be rack tooth pitch I'll hit OK and that's really it if you look at this those are spaced apart properly there are 10 of them if I asked for and you know the last detail would be adding a bottom to this you could do that so that it's parametric as you change the number of teeth in the rack it would adjust I'd recommend doing that in maybe the the the sketch that we just created or you could create a separate sketch but I'll leave that to you also you know we have these as components so it's very easy to start adding joints with an axle you can create a hole in here create an axle for it create a slider for this rack and that's what I've done in this one so I've created this kind of quick base that has a a and axl sticking out of it and there's a slider joint here so that this rack can actually move back and forth and then there's a revolute joint here so that the spur gear rides on that axle turns on an axle so you should in theory be able to turn on contact sets and see that when you turn this spur gear this this rack will move back and forth in practice it doesn't work it's just not able to calculate it properly so instead what I did was use the motion link so it escaped here double-click on this motion link or maybe not edit feature here so you can see that basically for every revolution complete revolution of the spur gear the slider should move how far in that distance is going to be rack tooth pitch times spur teeth so we can see it move here and you can see that the teeth line up that's about it you know if you wanted to you could go into these joints and add limits so that it actually you know you saw that it moved the rack moved when the gear wasn't actually touching it that's easy to do by just editing the joint limits but for the most part this works let me know if you have any questions good luck

Channel: Rob Duarte

Views: 90,645

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Id: khG4Zk5XZrw

Length: 16min 3sec (963 seconds)

Published: Wed Jun 08 2016