A Sine Bar Walks Into a... wait

today on this old Tony let's talk about angles stuff okay fine hold on a minute the plan was to avoid using this word at all costs but in this video we're basically talking about trigonometry wait wait I know you hate that word you've probably hated it since high school I can't blame you and that's why it was renamed shop math let's talk about sine bars maybe sine tables potentially angle blocks why they work and how you use them we may get into cosine error and if there's time how to use all this math to take finer cuts on your ly than you thought you could all of this stuff or all of the things I just mentioned come down to trigonometry I mean shop math if you put my back to the wall I tell you trigonometry is actually pretty cool totally worth giving it a second chance and my personal theory they hit you with trigonometry right at that point in life where boys and girls start well maybe thinking about other stuff and let's be fair no subject in school is going to top that so trigonometry takes the backseat no wait in that case the backseat would probably be occupied it would take the front seat now I've gone confused my seal ice trigonometry is a big words got a lot of letters maybe that's why I shot math works so well but that said will be very little math here I'll leave that part up to you anyone that might be allergic to numbers well no hard feelings if you want to skip this video let's start the beginning trigonometry comes from two words Trigon who was a famous Targaryen mathematician and inventor of the Trigon insert and OMA tree I have no idea what that means but there's probably good Irish joke in there alright enough screwing around settle down now do you know what this is it's a sine bar come on I literally said that not two sentences in this magical indispensable piece of shop equipment if you do your part can set crazy precise angles machining is in all square parts or round parts you know sometimes there are angles and I'm not talking about those out of square parts you usually make I mean intentional angles precise intentional angles need to make or measure a surface to exactly I don't know ten point one two three degrees well this is your ticket use it on your surface plate on your mill surface grinder lathe back seat of your car wherever and whenever you need to make or find an exact angle I know what you're thinking this old Tony how does that chunk of metal doing anything at all then make me even more money I don't have well I'll show you if we put this down on a flat surface imagine for a moment my bench is a flat surface maybe like your surface plate it doesn't do much of anything at all it's a good paperweight at best but once you put fresh batteries in it if you stick something under one side check out what happens the top magically is not horizontal anymore it's at an angle walked right into that if instead you put something under one of the pins and the top isn't at an angle if it looks like this check your batteries but of course just whatever that random angle is isn't very useful is it heck we could have cut an angle like that on the mill without the dumb sine bar but here's the thing with just a little bit of effort and maybe a calculator we can know what that angle is just by measuring how big or high that something is we stuck under one side in this case that's about 2 inches or 50 millimeters more or less which can only mean one thing the angle that this sine bar is now set to is exactly twenty-three point five seven eight degrees all thanks to a little bit of tree shop math the thing that really blows my mind is that those two things the height and the angle they are related you can't change one without the other changing how on earth does the sine bar know that the height change how does it convert it to an angle and how does it do it so precisely well I wouldn't be so bold as to claim to know the will of the Gods but what I can tell you is this and don't panic hopefully it should make more sense in a minute the angle the sine bar makes with the table in this case is the inverse sine of the stack height divided by the length of the sine bar in other words the height of that stack is the length of the sine bar times the sine of that angle I mean technically those aren't other words those are the same words just said in a different order and don't freak out if sine or inverse sine sometimes nicknamed arc sine scare you it shouldn't take a deep breath let that highschool trauma fade away and you'll see they're right there on your calculator it's a button just like any other button push it and the calculator will tell you the sine of whatever number you entered put in 30 push the sine button and the calculator will tell you it's 0.5 and fun fact the shift key on your calculator isn't just for typing capital numbers push the shift key or the second function key in my case and the sine button becomes the arcsine button the inverse sine put in 0.5 asked for the inverse sign you get 30 degrees back out of it if you'd rather not put your life in the hands of a calculator you can also find these numbers in the back of the Machinery's handbook or probably any old high school math book I guess I lied it's not in the back it's somewhere up near the front but if you still trust me have a look the sine of 30 degrees is 0.5 just like the calculator said since we're here and we're both just sitting around doing nothing waiting for the next really cool this old tummy video and to distinguish this a bit from other sine bar videos let's have a very quick look at exactly what sine and cosine means since I'll probably be dropping those words the rest of this video that and with any luck we'll drive home the sine bar equations we just saw so you're not just taking my word for it you're not just trying to memorize something somewhere about three or four thousand years ago people were dying left and right from their ladders slipping way out from underneath them those were brutal times to solve the killer ladder problem and ensure the survival of the human race invented trigonometry coincidentally that's where the whole bad luck from walking under a ladder comes from check this out this sine bar has two pins attached to it there are a very specific distance apart the distance between those pins is exactly five inches in theory anyway depends on the quality of the sine bar you buy or you make so does this sign table the pins on this table are also five inches apart we'll talk about why that's five a little bit later but for now these two things are exactly the same except one of them is bigger can you guess which one but let's just look at the sine bar sine table is exactly the same thing if we keep one pin still and only stack stuff under the other pin the whole bar table moves in a circle a circle with a radius equal to the distance between those pins like a compass right when you're drawn a circle in the higher we raise it the larger the angle gets let's now take my fake flashlight and shine it at the sign bar or a sign table or a life-ending ladder whatever note that I'm shining the light in from behind the angle of interest in this case along the length of the bench it's sitting on because of that light imagine for a moment our sign bar casts a perfect shadow this isn't a perfect example because our sign bar has some thickness to it so imagine just the top surface that line is casting the shadow that shadow it's casting the length of that shadow is related to the angle the steeper I make the bar the longer the shadow gets there's a relationship there and the relationship between the angle of that line and the length of that shadow it makes was given a funny name sine the length of that shadow is the sine of that angle now if I shine that flashlight down from the top 90 degrees to what we were doing before I get another shadow this time next to the angle instead of opposite the angle since they were evidently running out of names back then that shadow is called the cosine so as we change the stack height as that bar moves up and down through whatever angle the length of both of those shadows changes now since our bar isn't changing length hopefully it's apparent that the length of those two shadows are related if the sine shadow gets longer the cosine shadow has to get shorter and vice versa now since there wasn't all that much to do 3,000 years ago and most of their friends died slipping on ladders they had plenty of time to give that relationship its own name to in any given position of our sine bar or ladder the length of the sine shadow / the length of the cosine shadow they decided to call the tangent and that's exactly what this is the tangent so let's get back to sines and cosines probably doesn't take too much imagination to see that there is a special point I can rotate this bar to such that the length of this sine shadow is the same length as the cosine shadow can you guess what angle yes 45 degrees at 45 degrees the sign in the cosine are exactly the same let's check the book this lists sine cosine and tangent all in the same line for any given angle you could see it 45 degrees this sine and the cosine is the same and now we know why the tangent is one since sine and cosine are the same those two numbers divided by each other is one this is fun let's keep going so you don't sound like an idiot when you're explaining this to your friends down at the bar the shadows we've been talking about are usually called the projections this is the projection of the height and this is the projection of the length while we're here there's one last thing I'd like to reinforce sine and cosine depend on which angle you're talking about in our case we were talking about the angle between the table and the top of the sine bar if you wanted to talk about this angle up here you'd have to switch your projections that angle shadow or projection would now be down here and that would be the sign and it's cosign would be over here that is sometimes tricky to keep track of so be careful if you decide to start projecting yourself onto your triangles just make sure you're doing it right for the three of you that are still watching there's one last thing we should talk about so these numbers actually make sense in the real world back when Trigon was trying to help Erin out with their ladders there was one big problem he couldn't quite crack everyone's ladders in sine bars were at different lengths trigons calculators slide rules and tables didn't work for everyone and tragically even more people were dying now then it hit him yes it was probably a ladder he would assume everyone's ladder sign bar sign table giant Christmas tree lookout tower cable car wire or whatever he would assume they were all one long just one unit doesn't matter what one inch one foot one meter one mile if everybody agreed on one the sign in the cosign could work let's see how that works for our five inch sign bar since our actual sign bars five times longer than the one that Trigon got all hung up over now we have to multiply by five if we wanted to construct say a perfect 30-degree angle using a 5 inch sign bar just like before we need to figure out the stack height so stack height is the sine of 30 degrees which we saw a 0.5 times the length of the bar times 5 inches 0.5 times 5 is 2.5 since we're working in inches that's a 2.5 inch stack height if our sign bar was 5 millimeters that would be a two point five millimeter stack height if it was five miles that would be a two and a half mile stack height so now that we've packed five years of math classes in five minutes let's talk about what you might stuff under your sign bar now although for the stack you could technically use anything you wanted usually and especially when you don't want to get fired you build the stack up with gauge blocks this is a set of precision gauge blocks where it used to be anyway now they're more like my fabrication blocks but anyway you pile these up like Legos to get to the dimension you need for our 30-degree example on the 5 inch sine bar we need to build up a two and a half inch stack so I'd grab the two inch block and the 1/2 inch block a 1/2 inch block make sure your surface plate is meticulously clean get the blocks that you need clean them wring them together mine don't really ring anymore and set up your sign bar now of course you don't need to use a two inch block and a half inch wok you could use two 1 inch blocks and a half inch block 5 half inch blocks 25 tenth of an inch blocks machining knows no creative limits as long of course your stack is the right height to get you the angle that you're hoping to work with now you take the part that you want to inspect something that has a 30 degree angle like this 30 degree angle block this out of an angle block set these are really handy to have not that expensive not as expensive anyway is the gauge block set you'll need to go with your sign bar but whatever you got you put the part on the sign bar and now we can come in with an indicator this tenths indicator each division there is I guess two and a half microns I'm just gonna zero it out and then sweep the leg sweep the surface frankly I expected that to be worse given how I just threw everything out here on my surface plate but that's reading half of a tenth of a thousandth of an inch aka half a tenth that would be one point two five microns now of course it depends on what you're measuring but it often helps to build your sign bar fortress up against an angle plate of some kind and usually the back of your surface gauge will have pins that you can deploy they'll stick out the bottom it's hard for me to show you but you can use that to ride along the edge of your surface plate and that way you can be sure everything is nice and straight you're doing a nice clean sweep across the surface you don't want your stuff falling over or introducing weird compound angles that could give you errors in your reading working with a sign bar to actually do machining is in principle the same exact thing you'd set up your stack horizontally or vertically however you need to get the work into the position to make your cut that sometimes is easier said than done take this five-inch sign bar for example on my mill there's really no way to get it in the vise it's just too big this worked well when I had the Bridgeport had a larger vise but in this smaller vise the sign bar is just too big I could potentially use a parallel in the bottom of the vise but it doesn't take very much to get out of the clamping range of these jaws I could clamp onto the sign bar and there's really not much room left for my work if you imagine that on a parallel with some angle to it I just couldn't clamp the work ideally I guess I'd be using a smaller sign bar here to what we saw on the surface plate I'd probably set something like this up on an angle plate I could clamp the angle plate down and clamp the sine bar in the work to the angle plate there is a course a limit to how big the work can be so your setup would likely change a bit in practice most of the time I can work with this little angle block set not as flexible as the sine bar but I can mix and match these to get you know the more popular angles and they're much smaller more compact in this case fit nicely in this vise for bigger work I've taken to using this sine table though I bought that mostly to work on the surface grinder again the function is exactly the same the only difference is this has sort of this sub plate one pin is hinged at the front and there's a pin at the back you can build the gauge blocks under and just lock down all the screws and attach your work to the top if and when you go shopping for sine bars you'll find that one of the most popular sizes is 10-inch twice the size of this one I'm not totally sure why but I'm willing to bet it's because 10 is an easy number to multiply by any answer you get on your calculator is a lot easier to multiply by 10 than say 9 this perhaps was in the land before calculators but practically the sine bar can be any size at all though the longer it is the more precise it usually is and of course you should match it to the size of your work you wouldn't want to use a one inch sine bar to set up a 24 inch block of material on your mill after 10 you'll find a lot of 5 inch bars like this one and smaller two and a half inch bars again I think the idea used to be you multiplied by 10 because that was easy then divided by 2 in the case of the 5 inch bar or divided by 4 for the 2 and a half inch bar on top of that I think most like mechanical trades books manuals that sort of thing already lists sign tables based on bar lengths it's been a while but I think I've seen those before buying mine I actually made one of my own I don't remember exactly what I needed this for but I made it wider than your usual sign bar I did my best to set these pins 5 inches apart but they're braised in place and they moved a little bit figure out that Center distance I just put a reference angle on the top and built a stack until the indicator sweep over that read zero from one side to the other very similar to that 30-degree angle block we saw a minute ago except I have a small granite standard when that indicator sweep we're at zero I could just do the math backwards I knew the angle I can measure the stack height and it turns out the distance between centers on this is 5.0 - oh then I just stamped that into the bottom and use that number anytime I use this sine bar one last thing before we wrap up the sine bar topic you'll often hear that sine bars are only good - about 45 degrees that's not really true if I were to venture a guess that maybe rooted in the fact that most sine tables in the back of old machining books only went to 45 degrees now they only went that far I believe to save on printing anything over 45 degrees and people used to know how to do the math if you needed to know the sine of 60 for example and your chart only went to 45 well you knew that the cosine of 30 was the same value so you'd find it that way though there is an upper practical limit to the sine bar and that's about 60 degrees in fact on most sine bars if you try to go above 60 you'll run into the actual body of the bar down around here below the pin I haven't measured this but that looks like it's pretty close to 60 the real reason goes back to the fact that the sine bar as you lift it traces out a circle you remember this bit down in the lower range up to about 15 maybe 20 degrees sine bars can be crazy precise because the change is almost linear double the stack height and you almost double the angle but as you wrap up around the circle you're getting less bang for your stacking buck as you approach 60 and Beyond the curve of the circle starts to flatten out a lot very small changes in stack height up there can result in big angle changes my leave is smarter than me it's way better at math which admittedly might not be saying much but it doesn't need a pencil it doesn't need a calculator and is never wrong never this is the cross feed this handle pushes the tool in or out I wind the handle in to take deeper and deeper cuts making my parts smaller and smaller until they're scrapped that's how I know I'm done now the lathe has graduated dials in this case in inches to give me a better shot at making my parts the size I want lathes are made with one of two types of dial direct read and indirect read direct read means whatever you dial in on the hand wheel is how much smaller the diameter of the work gets state the oblivious lathes make round parts and nine times out of ten you're interested in the finished diameter not necessarily how much your tool moved so on a direct read leaf the hand wheel graduations and the diameter of the work are directly related move one whatever on the hand wheel and your diameter would end up being one whatever smaller this lathe happens to be indirect reading I think all coal Chester's are but I can't be certain the dials don't tell me what the diameter of the work is doing they tell me how far the tool is moving if I move the hand wheel say 20,000 see the tool post moves 20,000 so in this case we're reading the radius and the diameter the work gets two times smaller than what I dialed in neither is really better or worse just different though it does stink when you're used to one type and you have to move to a different type taking a closer look at my graduations we see that the smallest division is one thousandth of an inch so if I move the tool 1,000 I'm cutting 1,000 the radius and the work gets mm oh I'm almost done with my part really close to done and all I have left to do is to remove 1,000 I am etre and then what do I do now on my dials I'd have to do my best to split those divisions by eye but how do I know that's half of that what if it's 4/10 we're six tenths well for one you could use an indicator set up just like this one and not trust the dials at all but that's still a really small move on a hand wheel that and taking a 1,000 isn't as easy as it sounds we in the quantum realm here spooky stuff can happen but that's a topic for another video instead let's see if a little math can't save the day this here is the top slide where the compound goes by a lot of names and by a lot I mean to it set 90 degrees to the Cross line so that means no amount of turning this hand wheel will reduce the diameter of the part of course if I turn my top slide to 90 degrees then it works just like my cross slide and I have the same problem one division results in two thousand or change and I'm right back where I started but check out what happens if I set my top slide to say 30 degrees the scale reads 60 that's just how my lathe is laid out but in this case that 60 means thirty degrees off of 90 like 30 degrees off of parallel from delayed axis we've got ourselves a nice little triangle with the motion of the top slide now 30 degrees to the axis of the lathe if I wind the top slide in now say a full turn a hundred that the cutting tool moves 86th out in towards the Chuck and only 50,000 towards the work towards the lathe centerline it moved the tool half of what I dialed on the hand wheel if you didn't see it coming that's because the sine of 30 degrees is 0.5 so now set up at 30 degrees if I move the dial one division the tool only moves towards the work half of a division I can now more confidently anyway dial in a cut that would peel 1009 to grease the sine of 15 is pretty darn close to 0.25 so that's four times less than what I turn the handwheel now to get the same one that the diameter I can move two full lines on the hand wheel which is a ton easier to read than trying to split the divisions by I dialing in 1000 is a lot different than actually getting a 1000 attack since you know separating boys from men is no longer politically correct anyway that's it that's how your lathe does tree shop math all on its own with no stinking calculator hey so while we're here you could also use a sine bar to set up your top slide by eye it looks pretty close to the 30 degrees we set on the scale but here you could run an indicator along your sine bar and tweak your top slide angle until that indicator reads zero I've also heard of people setting sine bar up against either like a test bar in the chuck or the quill of the tailstock and mounting an indicator and the tool post I guess and sweeping this until the angle is correct again until you had zero indicator reading I've never done this and frankly I don't know how you would hold this in space to even pull that off in theory I guess it's possible oh yeah I would just load an indicator in the tool post and just watch the indicator eating as you move the top slide so if this is set to 30 degrees and you wind it in a hundred thou if your indicator tells you 50,000 then your angle is dead-on if it tells you 49 or 50 1000 to do alright I'm super excited about this I saved the best part for last cosign err okay fine it's kind of dull I was going to skip it but I mentioned it earlier in this video and I wasn't able to edit it out like a good time-traveling using shop math so let's give this some lip service now I'm not a big fan of the term cosine error it's not the cosines fault it's your fault come on own up to it like a real wheat from the chaff cosine error is the error you can get from not aligning your measuring tool with the actual dimension you plan on measuring maybe it sounds obvious enough when stated like that usually it sneaks in more with test indicators than it does with dial indicators but the concept is the same and it's easier to demonstrate with a dial indicator so we'll use this it's actually a lot easier to demonstrate with a tape measure but that'll just confuse everyone even more say we're trying to measure the height of this block you'd be doing this on a surface plate of course don't let anybody see you do this on a welding bench if we're trying to measure the height of the block it means we want to know this dimension of course it doesn't have to be height maybe you're trying to measure run-out whatever it's not important but we have some dimension that we're interested in measuring and in this case we're using a dial indicator now a dial indicator measures how far its stem moves in line with the stem right if we put the indicator nice and straight perpendicular to the top surface we get a good measurement but if we're not paying attention didn't get enough sleep or you got the whole shop heckling you for that karaoke bit you tried to pull off the night before you might end up setting the indicator a little crooked I mean come on it's not that much what's the big deal say it's off 10 degrees for argument's sake that'd be a lot but let's say 10 degrees to your blurry eyes it looks good enough well now you're no longer reading the height of the block you're reading this line this crooked line moral the story keep your indicator perpendicular to the dimension you're trying to measure this is a 4-inch block of aluminum in the long dimension you measured it like a normal person says four inches but if you insist on measuring it like a knucklehead it's a four and a quarter inch block this is cosigner the rule is reading one over the cosine or whatever that knucklehead angle is you're trying to measure the width of the block at my apologies I didn't mean to insult anyone's intelligence with those last two examples but I wanted to convey just exactly what cosine error is earlier I said this comes up more with test indicators because most people are pretty good at using dial indicators or a tape measure the way they were meant to be used you know there are all types of test indicator by nature it turns an angle into a straight measurement you move the arm a few degrees but it tells you inches or millimeter it's not giving you an angular measurement there it's not reading out degrees so here cosine error can be a little bit trickier it can sneak up on you you have to know how this thing is meant to be used how the manufacturer designed it to be used well so you know what direction it's measuring it every test indicator is different so read the manual for yours for inter Rapids like this one they're designed to read properly when the stylus is about 12 degrees I think to the work if you lay it flat you're not going to get a real number on the dial if for some reason you do have to lay it flat or that close to the surface maybe you're trying to get inside a tight spot you'll have to add the cosine error for 12 degrees in the case of the inter rapid and of course if for some reason you change the stylus on the end if you use a longer one or a shorter one well you have to accommodate for that too usually they come with or you can find little charts and tables to help you out this is pure speculation I've never really cared much to look into it but I guess that's 12 degrees because 12 degrees is how much you need to clear the sort of that knuckle or the hinge in the back of the indicator you can sweep an entire part get accurate readings and not run into anything like you could if you held it flat also that 12 degrees isn't super critical if it's 10 if it's 14 if you're close it's probably going to be good enough that said though test indicators like this are usually used to compare things not to take a direct real measurement of course you could if you took into account how it was designed maybe you're trying to use this to center work in a four jaw Chuck or Center your mill over some existing bore or feature you might not really care what the dimensions are there just don't want the reading to change or not very much anyway well that's it I think that concludes our breathtaking spine-tingling on inspiring deep dive into the world of trigger thanks for watch [Music]

Channel: This Old Tony

Views: 801,467

Rating: 4.9478946 out of 5

Keywords: sine bar, cosine error, shop math, trigonometry, interapid, indicator, test indicator, dial indicator, sine, cosine, sine table, angle blocks, machinist angle blocks, lathe math, cutting tapers, setting lathe taper

Id: PO-Ab7YfBzY

Length: 26min 17sec (1577 seconds)

Published: Sun Dec 09 2018

Reddit Comments

[u/juxley]

I watched this earlier today, and I have to say I learned more about trigonometry from this video than I ever did in high school. Thank you!

[u/Eldias]

I didn't really learn to appreciate math until I was hit with beginning calculus. That was really the first time everything seemed to have a use and point and where it all finally worked together, rather than being disparate parts in a toolbox. I really looked at Trig before that as a dirty step cousin to - you know - useful math, like algebra.

[u/DeathMonkey6969]

That little cross slide at an angle trick is how we climbed the ladder of precision.

[u/Guysmiley777]

I'm strongly in favor of re-branding trigonometry as "shop math".

[u/Tradyk]

Started watching this video on youtube, and at about the same time, saw this gif from /r/dataisbeautiful on my other screen. Thought it might be relevant/interesting to anyone watching this vid:

https://www.reddit.com/r/dataisbeautiful/comments/a4l0ta/the_unit_circle_oc/