its joe pie for circles. and joe piethagorus for triangles. got it.

I wish you were my math teacher back in the day. Maybe it's just that your using the knowledge for something I care about or need it to do what I need to do but it makes more sense now than ever. As always I learn things every video I watch of yours! Thanks as always!

Thanks Joe, this was good thank you. [I edited this below as I originally missed out a step] For a "No Maths" 5 hole pattern - Draw a circle & bisect with 000º, 090º, 180º, 270º. Call each point on circumference A, B, C & D with the Centre X. Bisect A-X for half Radius. Call this point P. From point P, set compass to either point B or point D (doesn't matter which)and then scribe a point intersecting X-C. Call this point Q. Set compass from either Q-B or Q-D. This length can now be stepped around the circle to make 5 equidistant points (5 bolt holes or a pentagon) Stay safe and well :)

Always, always have a "light bulb moment " watching you Joe Thank you Sir and keep unloosening

I made a spreadsheet for our machinists. They simply entered the radius of the bolt pattern, the quantity of holes and it would output the X,Y coordinates of each hole. They drove to those positions on their DRO. They loved it.

Dear Joe, Love your videos, I am not a machinist, just an old printer, but have always admired people who make machines to fine tolerances. Hope you and yours are safe in the cold & dangerous weather. Les

1:34 To do a five hole pattern: Let O be the origin/center of the circle, A and B be the start and end of the diameter line, (As shown later in the video) and C be the point on the circle 90 degrees from A and B: 1) Draw the diameter line (A to B) shown later in the video and a radius line (From O to C) at a right angle to that. 2.) Split the diameter line into four equal sections, (Let's call the two bisect points, D and X) so that the A to D, D to O, O to X and X to B line segments are all equal to each other. 3) Set your compass to the distance between C and D, then draw an a circle around C. There will be two points where the circle intersects the main circle, use those two points and with the compass at the same length, draw arcs downwards to intersect the main circle again. Connect all of the intersections with line segments, and viola! A 5 hole bolt circle

Joe, PLEASE get a remote mic for your "chalk talk" sessions. You have such great information to share, but I can't easily understand you when you turn away from the camera, and I'm betting I'm not the only one who has hearing issues.

Hi Joe, I'm a new subscriber and fan of your videos. I have a small machine shop that supported my fab shop ( never really called myself a machinist). I am now retired and my machine shop has become my hobby, I have learned more tricks of the trade from you than you can possibly imagine. Keep up the great work and stay warm!

Holy thank you for this video! I recently started a jeweler’s apprenticeship and this has helped me be more accurate making true squares and marking accurate holes for setting in circles ! Thanks you!! Your an amazing teacher

5 holes - draw the circle with radius R, then set the compass at 1.176R {equal to (R*(2*sin ((360/5)/2)))} and divide the circumference similar as you did with the six hole example (first one) but progressively around the circumference. Close enough for a scribed and center punched layout. Or points 72 degrees apart with a protractor (0, 72, 144, 216, 288). To layout with a protractor - 360/n (number of equal sides). Inside angle of any point on an equal sided polygon is ((n-2)*180)/n, n= no. of sides. ex. square is 90, triangle is 60, pentagon is 108, hexagon is 120, octagon is 135, etc.... (Edit 2: outside "turn angles" = supplementary angle to inside angles, i.e. 180 - the inside angle, example for a pentagon, supplementary is 180 - 108 =72, and 72* 5 turns = 360 degrees, and the sum of any closed figure is always = 360 degrees because if you turn a total of 360 you end up facing the direction you started at) Also - for anyone using the properties of the unit circle to draw the pentagon, the length of the sides, for a radius R, work out to ((5/2)*R^2-(SQRT5)/2*R^2)^0.5

Joe you are an inspiration, I am now the wrong side of 60 and your videos are great , I have learned so much, Keep up the good work. I wish you tube and your videos were about when I was an apprentice.. Mike C from the UK

For any bolt hole pattern greater than two the compass can be set by using the following: Compass setting = Bolt circle diameter x sin (180 / N) where N is the number of bolt holes. For six holes the compass setting = Bolt circle diameter x 0.5 or the Bolt circle radius.

I've been using CAD (2D and 3D) for 28 years to design and create drawings for machinists and fabricators. I still love the basics of geometry that got me into the business in the first place. Great basic/fundamental information. Love the videos and unique style. Keep it up Joe!

My old "American Machinist's Handbook" has a table for the x-y table moves for hole patterns of various numbers. The patterns are for a base diameter of 1". Multiply the given numbers by the diameter of the circle required. Very helpful for odd bolt hole circles, e.g. seven or eleven. On a manual machine you always have to remember to come up on the desired move from the same direction to keep the back lash in the same direction for each move.

Hi Joe, great explanations, easy to follow, nice to know that the old mathematicians (Pythagoras et al) are still useful. Hey what's happened to your weather? I thought we in the UK were having it bad!! you have power outages, frozen wind turbines, not good, keep safe

5-hole patterns are just as easy as any other bolt circle. Load it into the DRO... LOL Nice work as always sir.

Seeing the sin and cosin of 30 degrees laid out like that was the greatest thing since sliced bread. It clicked and really made sense. Thank you for the lesson, Joe. Now, if I can only remember the values in the future when I need them. 👍

Hi Joe, just seen your weather news on The BBC. Looks COLD. Keep yourself as warm as you can. There are some of us out here that need the inspiration that you give.

My 1892 'Practical Plane and Solid Geometry' text book tells me that to draw an inscribed pentagon, draw any radius, then draw another radius 72 degrees from it, join the two points where the radii meet on the circumference, set the compasses to the length of that chord just drawn, and step this out around the circle. (also works for any regular polygon if you calculate the angle required).

My 17th edition Machinery’s Handbook has a section on this.They make it very easy. To layout five it takes a bit of basic trig. That doesn’t mean it is difficult. By drawing two lines at right angles, one point can be drawn on one of the lines. There is 72 degrees between points,so by using the sine and cosine of 72degree two more points can be laid out. Similar with the last two points. Sine and cosine of 36 degrees. This is the easiest way I know besides the machinist bible. .866 is one of the most useful number I use. When adjusting a three jaw chuck,the diameter time .866 is the distance between similar points of two jaws. The distance between flats of a hexagon divided by .866 is the distance between peeks. Every machinist should know how to lay out bolt circles. Thanks for instructing the less experienced how this can be done. Of course most CNC machines will do this for you. I myself like the feeling that I did it by myself without help from computers.

Thank you Joe for taking the time to do this.

Always learn something from your videos! Don’t ever think to skip on the math stuff it’s just as important as the machining info!.

Love it! Math is everywhere! When they ask in school "what do I need that for?" this is! Just one of the million things in life. I just the other day needed it the other way around. I had a diameter and needed to construct a hex that that the diameter just fits into. So I did it just the other way round. Thumbs up, Joe!

Hi Joe , another great video regarding bolt circle layout. I still love the engineering world but maths has always been a grey area . Wish you'd been around 60 or so years ago , you have the gift of being able to explain and keep it interesting at the same time . BRILLIANT

Great layout I am a sheet metal worker teacher You taught me something new Life time of learning Thanks usn ret vet

Before I had a mill, I’ve manually laid out a 12 bolt pattern, as you did with the 6 bolt pattern (with extra steps) and drilled and countersunk with a mag drill. The manual markup was a headache! But got the job done. Now have a mill, with insert drills and a DRO. Happy days!

Keep banging on about these geometric shapes, eventually it will sink in and we will realise the power of maths. Then we will be truly grateful. Keep them coming please.

Another whiteboard lesson from Professor Pie. Thank you.

Bringing back fond memories of doing drafting work on actual paper rather than all of the CAD work I do these days. Thanks for sharing! Stay warm, sir. - TZ

I’m not a machinist and unlikely I’ll ever get to be but I know who I’d like to be my teacher. Another interesting and informative video Joe. Thanks for all you do 👍🏻

I'm a retired toolmaker, I live in AZ, it's beautiful outside and 68*F and I'm watching a lesson on geometry? I'd say I'm sick, but I feel okay..... what's going on here? Someone help me! I should be out on the motorcycle..... I guess some things are in my blood forever.

Hey Joe! 🎸🎸 I just wanted to wish you and everyone in TX well. Your content has been invaluable!

Hi Joe, I do basically the same thing as you've shown, but for 30/60°, use 1:2: sq root 3 (1.7321) and for 45 1:1: sq root 2 (1.4142). For odd layouts, work out a baseline and go straight to trig, and always reference all holes to the single base position, not to the previous position. I do that in case I do make an error, and only the hole I've made the error will be wrong, not all holes past the error. You should also close out your pattern to ensure there is no closing error, so if you had say a 13 hole pattern, when you calculate the coordinates for all the holes, also calculate the the coordinates for the first hole from those of the 13 hole. Regards Dennis.

Tom's Techniques has a chart of constants times diameter to give you the x and y positions for bolt circles 3 -12. Recently used it for a 5 holer and it worked fine. Just another way to skin the cat. Thanks for the videos Joe, I would be lost without them willie

Can you do a video on adjusting the gib screws correctly I'm a hobby machinist and love your channel and have learned so much please keep it up.

Finally got power and internet back on after 4 days here in Boyd TX. and have you back on my PC screen. Would love hang out and watch, but now going out to play plumber and assist the damage,,,Great bolt pattern tutorial, will come back to watch later, Bear

Knowing how to do the math is very helpful. I regularly do 20-30 bolt hole patterns. Did the math way for many years, but can get confusing, especially with odd number patterns. If you don't have a DRO with PCD function, nowadays they have great free smartphone apps, where you enter the diameter of bolt circle, number of holes, and starting angle. Instantly gives x and y coordinates for all the holes.

Good info Joe. Boss finally upgraded old Bridgeport with a DRO 6 years ago, I've gotten rusty at manual BC layouts.

Good one Joe, thank you!

Great explanation Joe, thank you. A little addition, it is worth pointing out that 0.70711 and 0.86602 are also known as ½√2 and ½√3 respectively.

Nice Joe. I keep .8660 and .5 permanently etched in my brain. With the compound set to 30 degrees most of the time .8660 and .5 can come in handy sometimes.

For all of those who struggle with geometery and layout. 1) There is a game app called Euclidea. It's all about puzzles in Euclidean Geometery. It makes you realize just how much you forget about geometery once you're done with the class. 2) There is a KZfaq channel called Arthur Geometery where the channel owner takes it step by step how to perform different operations step by step.

Well, Hello "Sunday Joe". 5 hole, no problem. Unless it has to be within a couple thou I would simply draw the circle with a very fine line and go at it with a pair of dividers or the compass till it was very close. Redo the circle and refine it. So far that has served me well. The lines must be very fine. I did this a few times for laying out a 18 in, 20 hole rotator bearing plate for excavator type tools. I eventually made a clear plastic pattern that centered on a 1/8 pin. Centerpunch and drill away. This is a great tour back to GR 10 math my friend. These rules built the tech that has made our world what it is today. Just like a grade 8 bolt eh, LOL. Take care. How's the lathe coming along ?

Here I was laying out a bolt circle for a new toolpost grinder I'm making, take a break, and...Here's Joe Pi telling me a better way to do it. But Joe - you shouldn't have gloated about your nicer weather than we are having up here in the North. At least we're used to it ;~)

NIce that you were able to go out to your shop today,,,We got and continue to get blasted here in Boyd. Guess on could say "We are in the hole",,, up here, heh!! and thx for showing up there and keep us viewers watching,,,Bear

Joe thanks for getting us back to the math, some of us (me) have become to reliant on the dro to do the math !! Mark

Well presented Joe, any machinists will find this useful if they have forgotten it. Dead simple and straightforward, yeah there's loads of ways to skin the cat, but the simple stuff is just what you want in the workshop. 70 degrees lol.... Yesterday was our first day above zero deg C since Christmas in Scotland! I'd kill for 70 lol. Cheers, Jon

Joe, I want to suggest that you invest in a clip-on mike, so that we can hear you better.

Very handy refresh Joe - you are always giving super useful geometry/math info. Pythagoras is king :) My approach to a five hole would be entirely math oriented using a published formula - work out the co-ords for each hole etc.

Hey Joe awesome content again!! The most important and often overlooked dimension on a bolt circle is the length of the chord.... how do you inspect those hole locations when it matters? Most likely you are making two parts that need to mate together through your bolt circles. Radius and diameter are a start but then each hole needs to be an equal distance from each other..... That 5 spoke flywheel is a thing of beauty!!!

Tom Lipton at oxtools just put out a video that includes 5 hole bolt circle layout. Great companion video to this.

When dealing with a BC, treat the radius as a constant. Use sine and cosine to find the distance along the x and y axes. From center the distance along x is R * cos(angle). The y offset is R * sine(angle). If you follow proper protocol and measure the angle counter clockwise from where the centerline (x axis) crosses the right edge of the circle, the signs of the sine and cosine will take care of themselves. IE 45° cos is .707, sine is .707. 135° cos is -.707, sine is .707. 225° cos is -.707, sine is -.707. Etc. This may sound difficult at first, but it allows dealing with BC’s that are not symmetrical. Just calculate hole by hole. Any number of holes can be figured, with any angular spacing. Today there is no excuse for not having a calculator with built in trig functions. I often use the HP41 app on my phone. I liked the way you set the right angle with the compass. For small stuff it is better than the 3,4,5 method. Or the 6,8,10 method. Keep up the good work!

For layout/drawing N hole circles with radius R, arcchord is the straight distance between the points along the circumference 2*R*sin(180/N). To get the X,Y offsets to drill such a pattern on a mill (without a dro), each hole (n:1,2,3,4,5) offset from the center is (x,y) = R*cos((360*n)/N, R*sin(360*n)/N) -- for radians, use pi and 2pi for 180 and 360 respectively.

Reading through comments and following links got me completely side tracked into geometry video's :o)

U just made me go AHA! Thanks from Sweden 👨‍🏭

I love this channel. Thanks joe

There are a lot of videos on KZfaq on how to draw a pentagon inside a circle with ruler and compass. The one on the *Arthur Geometry* channel is pretty straight forward. He uses a triangle to draw a perpendicular line, but it simple enough to do it without the triangle, by bisecting a line segment with a compass as Joe described in the video above.

Joe, in the U.K. it is more common to use the term PCD (Pitch Circle Diameter) as opposed to Bolt Circle. Having said that I understand that both terms are of equal status on engineering drawings.

Joe, I wish you were my high school math teacher. You make so much sense that she didn't.

I got one for you. I once needed to make a spur gear differential where pairs of pinion gears were engaged with each other and with a shaft. The pairs of pinion were 17 teeth and the shaft was 24 teeth. I never did figure out a good way to set all of the hole centers precisely with backlash in mind. I ended up doing something different.

Somebody might have noticed already... 5 bolt pattern is on your back as a "lone star". Think of it in this way. Plus have in mind that the star, (as in a circle) will have peripheral and center angles, with ratio 1/2. Then play with the radius again.

Got another number for you to write on your toolbox. To mark out 5 equally spaced bolt holes , multiply PCD by .588. Works every time.

Does anybody here remember the little trig handbooks that Illinios Tool Works used to have that would fit in your tool box. The first one I got was in a high s hool trig class cir a 1969 It is possible to have a triangle with more than 180 degrees. But that's getting into spherical geometry.

Twelve thumbs down? Drop-outs 4-sure. Great info joe.

Love the videos and I will be buying a shirt to support the channel. Plus you had me with the American flag!

Trigonometry got a lot easier for me the day I realized this: degrees 30, 45, 60 90 = 1, 2, 3, 4 in this way: sqrt(1)/2 = 30, sqrt(2)/2 = 45, sqrt(3)/2 = 60, sqrt(4)/2 = 90. Once I memorized that I can easily solve those triangles, and it helps me remember the rest.

Hey Joe hope your fairing well after that cold spell cant wait for the next video on the lathe

Hey Joe! Let me say that as a hobbyist who waches quite a bit of YT vids for knowledge, i have been waiting for one of you guys to help me learn how to do the math to do basic bolt holes on a mill. In my case without a table. I see how you have explained the math but i was hoping you would show this and how it applies to a random round part on the mill. I still dont understand how to do a simple layout for an even or odd number of holes, evenly spaced apart. To be honest i am very bad with math, but i still feel as though what you showed still cant be translated into a part. What i mean by that is...you show the edges of the raduis but what about when you have to come in a certain amount into the part? Wouldnt that change everything? Hope i am making sense and I would really love to see you out in the shop and help show us rookies how to get a bolt circle on our machines. PS without a DRO? Lol. That might be tuff but i really hope someone does a video on it. Thanks for all your tutelage! PPS the sound was really bad on this one ;)

I understand you right could you take the 360 degrees and divided by the number of autos and get your number two

5 hole easy (pcd is 63mm) = 360 degrees / 5 = 72 degrees, Sin72/2 = 0.58, Sin.058x63mm = 0.59, 0.59x63mm again = 37.17mm is the distance between holes around 63mm pcd circle, use that divider/ compass

Thanks for the video Joe.

At 5:56, you are constructing a "perpendicular bisector." That's a really powerful technique for making a perpendicular line right between any two points. One of the most useful geometry tricks out there. Draw enough of them and you turn your square into an octogon, or double the number of sides in anything. The pependicular bisector between any corners gives you a radius line to the corners between them. 4:33, squares and parallelograms have 360 degree interior angles. Every closed shape, including those two, have 360 degree external angles. That is, if you walk around anything and end up where you started facing the same way you started facing, the total amount of turning you have done is 360 degrees. Works for any number of turns. For the pentagon, 360/5=72. 3-4-5 triangles are great, as are its multiples. 5-12-13 is another good one, but 3-4-5- is usually more accurate. I remember more of this stuff from my 7th grade wood shop teacher than I do from geometry class or my entire engineering curriculum.

Search YT for "General method to divide a circle into any number of equal parts" I can't get link to be accepted.

the method below works for any space pattern, it's quick and accurate, but it does take the correct dividers, a set with a fine adjustment screw

Joe’s challenge was to find a quick and easy way to use triangles to identify the locations of the centers of five holes, equally spaced about a center. I agree that a simple solution does not appear. Here’s what I’ve come up with. For convenience we can name the centers P1 through P5, with corresponding locations (x1,y1) through (x5,y5). We can orient the work so that one of the holes, call it P1, is aligned with the x axis. This will give it location (0,R), where R is the distance from the center. Then the remaining four holes will be symmetrically located about the x axis. Name them incrementally as we progress clockwise around the center, so that P2 and P5 are each 360/5 = 72 degrees away from P1, with locations (x2,y2) = (-x5,y5). Similarly, P3 and P4 are each 144 degrees away from P1, with locations (x3,y3) = (-x4,y4). To find the locations of P3 and P4, notice that the triangle formed by P4, center (call it O), and P3 is isosceles, with base P3-P4 and equal sides O-P4 and O-P3 of length R, with included angle 72 degrees. We can drop an altitude h from O to P3-P4 at A, which will give us two congruent right triangles, P4-O-A and P3-O-A with hypotenuse R and included angle 72/2 = 36 degrees. We can solve this right triangle. This gives us h = R*cos(36) = R*0.809017, and (P3-P4)/2 = R*sin(36) = R*0.587785. This already gives us the location of P3 and P4: P3(0.587785*R,-0.809017*R) and P4(-0.587785*R, -0.809017*R). There remains P2 and P5. P2 (and P5) is 72 degrees from P1 which is on the x axis, with distance R from the center O to P2. This R is the hypotenuse of a right triangle. We can solve this right triangle, giving y2 = y5 = R*cos(72) = R*0.309017, and x2 = R*sin(72) = R*0.951056, with x5 = R*-0.951056. After all the math, the locations for a set of five equally spaced holes about a center at the origin are P1 ( 0, R) P2 ( 0.951056*R, 0.309017*R) P3 ( 0.587785*R, -0.809017*R) P4 (-0.587785*R, -0.809017*R) P5 (-0.951056*R, 0.309017*R) One sequence for progressing on the mill would be 0, R 0.951056*R, 0.309017*R -0.951056*R, 0.309017*R -0.587785*R, -0.809017*R 0.587785*R, -0.809017*R

thanks joe

Thanks for the geometry trig lesson

I was suppose to learn this in Algebra, I remember most but I guess I forgot some too. So thanks for the tutorial.

👍 good stuff. Hopefully all upcoming machinist will learn to do this on paper and not rely on a computer.

Hey Brother Joseph, For me that was a trip back to 11th grade Trig class. Good thing too because I forgot how to find the length of a cord of a circle. I haven't done that since I got a DRO that did bolt hole circles. - I hope you keep doing things like this every now and then. To rest is to rust and after not actually having to think and do some trig and even algebra for a lot of years it's good to have a guy like you put a boot in my keester and give me a much needed refresher course. (I'm betting some of the kids have never done anything like this. Good to show 'um how) Hey, when is the next installment due on the little lathe? I get more smiles to the mile out of that then anything else on the net. = You get much smaller and you are going to have to get a lathe and mill with dials that read in tenths!

Hey Joe thanks again Love the white board.

Hey Joe did you see Tom Lipton's latest video that shows how to describe a pentagon/5 hole bolt circle?

Pure gold Master pie

5 bolt pattern check inscribed pentagon "Carlyle's Circles"

I use a Zeus chart for working out bolt holes on a PCD. With a Zeus chart it is very easy to calculate the co-ordinates for locating odd numbered equally spaced holes - e.g. 5, 7, 9, 11. Just multiply the values shown in the chart by the diameter of the pitch circle to arrive at the correct co-ordinates. Obviously a rotary table makes life easier but in engineering there is ALWAYS more than one way of doing everything ;-)

Hi Joe. Some years ago I built a spreadsheet to do bolt circles (N

Protractor? I guess you unloosened your thought :)

360/5 equals 72 degrees on the indexer for a pentagram...360 divided by any number of bolt holes will give the temperature. There is another method for using a compass but I can’t figure out how to explain it here. I butcher bolt circles almost daily so I had to click on this to see what master Joe can teach me. Thanks Joe.

Hello Joe if i can equate or compare your skills and brain to a movie it would be TOP GUN ! thanks for being out there for us . Skip

LoL, revisit classroom 35 years ago,... you know it,... but always nice to have confirmation of your knowledge 😂😎

Great lesson

Great video. Thanks

Hmm, my technical drawing book has methods for circular patterns, even odd ones. If there's any interest I could go look.

How to divide circle by any number -easy do it by dividing straight line ,the circumference. Circumference= Diameter multiplied by 3.14.Divide it by any number you want and use the result in a compass.I do it for the bolt pattern on a lathe for example on flanges.If you use a sharp tip knife ,like 60° threading knife (sometimes i use actual tungsten el cheapo scribe in a toolpost )you can scribe a small line.Divide it with a compass ,use a center punch ,drill it on a drill press -no DRO needed.Fast and simple. If you use a peace of paper as long as xircumference you cna make a template for drilling pipes for example,or notch a tube if you fold it in half (i still havent figured out a way to do it under angle lets say 45° on paper,but there are programs online for that that you can enter dimensions and it prints out template www.blocklayer.com/)

Heres a good way to divide a circle into any number of segments using a pair of dividers. www.woodmagazine.com/woodworking-how-to/shop-tips/a-simple-way-to-divide-circles

Great video as usual.

Enjoyed the lesson

A golden rectangle can be drawn with ruler and compass. The angle between the short side and the diagonal of a golden rectangle is 360/5 = 72 which the same as the angle between consecutive bolt holes on a 5 hole pattern, which means that a 5 bolt pattern can also be drawn wth ruler and compass.

Use polar coordinates for each bolt hole, then convert to Cartesian. Given a bolt hole at lets say radius 5 and angle at 72 (part of 5 hole pattern) you get X = rcos@ and y = rsin@.