Bolt Circle, Layout and Construction Basics

[@jdsstegman]

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!

[@chrisstephens6673]

The secret of learning and also teaching is motivation. If you have it you want to learn, if you don't you wonder what the point is and won't. A good teacher knows how to motivate the pupil, a lot of Joe's pupils are here because they can see the relevance now, which they might not have at school.

[@austinmorris1693]

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

[@rayhosking3927]

That's clever!!

[@mpetersen6]

Remember pie r round, cake r squared.

[@austinmorris1693]

@@mpetersen6 nice one i will remember that

[@RalfyCustoms]

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

[@Breadmason]

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

[@joepie221]

Thanks. So far, so good.

[@Supmang]

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

[@firearmsstudent]

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

[@canberradogfarts]

He knows trig dude.

[@firearmsstudent]

@@canberradogfarts He asked if anyone knew how to do a five hole pattern, and viola! Here it is.

[@1911wood]

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.

[@pmdeutsch]

Tell your guys to download the FSWizard app (or load the website on their computer). Has a bolt circle calculator and can even rotate by any degree to get the holes positioned where you need em. Lots of other great tools on the app too.

[@lextreloar4661]

DRO usually has a PCD function. I use it often.

[@1911wood]

@@lextreloar4661 Their DRO was quite old I’m not sure it had that function. The previous guy would print the patterns from cad. They would read the dims from the drawing or glue the drawing to the stock. They had an early laptop for checking their mail that happened to be spreadsheet capable. This was all many years ago. I just learned the meaning of PCD from you and then again one minute later from. Stefan Gotteswinter. Thanks for the input.

[@marlonsteele9021]

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!

[@joepie221]

Glad to help and thanks for the sub.

[@AJR2208]

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 :)

[@markmonier-williams2508]

Does not work as stated

[@AJR2208]

@@markmonier-williams2508 You're right, I just read over it and I missed a step. I'll fix it up now. Thanks Mark.

[@RonParker]

Hey, thanks. That's the construction I learned in high school drafting class, and none of the constructions I've seen online have felt right because they aren't that one. (They're correct, and some of them are simpler, but they're not what I learned. It feels like trying to tie your shoes some other way.)

[@AJR2208]

@@RonParker same here Ron.

[@mikeconnor702]

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

[@joepie221]

Thanks Mike. We are never too old to learn if we want too.

[@mackdaddy1891]

JOE YOU ARE A Master craftsman But anybody that thinks imperial standard is better than .Eric is too rough d up on national pride Do you agree.? Joe.there us a whole class betting against you thinking you like thousands. More than mils...so what is it national pride or reality? 1/3 , of the class says your to old school to use metric..... but 100% of the class os so proud of your daughter making 1st lieutenant. So it just dont matter. BUT IT METERIC BETTER?

[@josephcitizen4195]

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!

[@laurencep3757]

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.

[@joepie221]

I moved from the north 26 years ago. I'm OK with the arctic blast, but the city doesn't have plows and the stores don't sell shovels for snow. The power grids are all failing and now the water is in short supply. This is truly bad times for a lot of people. My shop is without power and ice cold even if I could get there. Warmer weather coming soon. I'll be back.

[@aceroadholder2185]

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.

[@billchiasson2019]

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!.

[@joepie221]

It makes you better at the bench.

[@sandersn4]

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.

[@brianjohnson217]

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

[@joepie221]

Thank you.

[@OthamJohn]

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.

[@joepie221]

For shop work, there is no hiding from this stuff. You should at least understand the basics.

[@scottb8175]

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

[@DDBerlin]

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!

[@joepie221]

I loved geometry in school.

[@DDBerlin]

@@joepie221 me too, although at that time I did not see what relevance it would have in my "real" life

[@dough6393]

Thank you Joe for taking the time to do this.

[@LeoA-t4z]

I’m not speak in understand very well English, but I get your point and I really appreciate your time to explain this concept working a Machinist for 16 years in a United States but every single day you pay attention you can learn something to improve your skills 🙏✌️

[@joepie221]

Absolutely. Every day is an opportunity to expand your skills in this trade.

[@assabetmetalfabrication6143]

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

[@joepie221]

Thanks for watching, and for your service to our country.

[@christianmccollum1028]

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. 👍

[@euclidallglorytotheloglady5500]

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

[@joepie221]

Thank you very much. We got through it.

[@peteredis7232]

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 👍🏻

[@lextreloar4661]

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!

[@TomZelickman]

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

[@joepie221]

Glad you enjoy it! How do you like your shirt?

[@mathewmolk2089]

That makes 2 of us....Bet nobody can ever tell you what a Rapidagraph and LeRoy was. (No class at all but I'll still take AutoCad )

[@duaneohall]

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.

[@mathewmolk2089]

I have been wining about that for 6 months too, but Joe says he has an input issue with his video editing software. (I even offered to send him a wireless headset)

[@paulkirkup2311]

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).

[@joepie221]

19:00

[@tonyashgrove9512]

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

[@joepie221]

Tough times right now, but better weather is right around the corner. The state has totally failed a lot of people.

[@williamlochhead3211]

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

[@bearsrodshop7067]

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

[@joepie221]

Good luck Bear. A lot of Texans got their asses kicked in this recent weather. Next time your inline behind a power lineman at Rudy's, buy their lunch.

[@peteengard9966]

Another whiteboard lesson from Professor Pie. Thank you.

[@johnferguson2728]

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.

[@ChrisB257]

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.

[@tracylemme1375]

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.

[@donaldauclair627]

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!!!

[@joepie221]

That 5 spoke flywheel was a personal challenge to finesse it into a presentable part. I enjoyed the handwork on it. As for the length of chords, on a hex, the chord is the radius of the bolt pattern. There has to be a similar easy trick for other shapes.

[@dennisleadbetter7721]

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.

[@quadpop4643]

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.

[@richjasica8454]

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.

[@campnut6076]

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

[@SlowEarl1]

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

[@bearsrodshop7067]

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

[@MrClassyChicken]

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.

[@brianhaygood183]

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.

[@34k5]

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.

[@jonsworkshop]

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

[@joepie221]

Right about now, I'd kill for 70 degrees.

[@mathewmolk2089]

Must be that global warming the tree huggers are always talking about.

[@bobhazzard7747]

@@mathewmolk2089 In all seriousness, that's exactly what it is. Global warming is causing the wild fluctuations in what we think of as normal weather. That means greater swings, Severe storms more frequently, and a general change in weather wherever you live compared to 'normal' for the last 300 years.

[@coleenlofgren6385]

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

[@DCFusor]

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 ;~)

[@sferg9582]

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.

[@moorejl57]

Resistance is futile, embrace the -suck- math lesson. Also after retirement, exercising your brain is vital to your health.

[@andylewis7360]

Geometry has a beauty all its own ;-D

[@dennismasi9736]

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.

[@jesperlowinger]

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

[@yohoyoho13]

There are a lot of videos on KZbin 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.

[@joepie221]

I watched it. Seemed to be bullet proof.

[@traitorouskin7492]

I love this channel. Thanks joe

[@stevespra1]

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

[@UncleKennysPlace]

Yeah, as I get older, I'm relying more on that stuff, rather than the old dividing head and careful setup.

[@spehropefhany]

Or lay it out in your favorite CAD program and dimension it. Or both for a double check.

[@spehropefhany]

Never heard of 3-4-5 triangle though. Cool trig-less trick.

[@EverettsWorkshop]

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

[@joepie221]

Thanks. A good teacher can make a big difference in a students life.

[@jameswilliams-tn2sf]

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

[@rtkville]

Good one Joe, thank you!

[@shawncornking9849]

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

[@mpetersen6]

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 KZbin channel called Arthur Geometery where the channel owner takes it step by step how to perform different operations step by step.

[@spock59]

I started the Euclidean Geometry puzzles and now I'm solving all the levels and it's past midnight...I am hooked! I always loved geometry, and now with CAD as a tool to create shapes and solve problems, I am looking at the world in a whole new light... and my mind is blown! Thank you for the recommendation!

[@petarraykov9059]

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.

[@Justamanonamission77]

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 ;)

[@Gravattack]

Iv'e never had to do a bolt hole pattern, now I have 3 holes to match in a Lathe Chuck back plate to the chuck. What's a good way to get the precise radius from the chuck? I know I can do it the woodworking way and be close enough. But I'd like to learn the proper way

[@joepie221]

I'll give you the mechanics, so after you see why it works, the calculation is actually much simpler. Lets assume its a true 3 hole pattern with each hole 120 degrees apart. Thats a valuable starting point. Now measure the hole or post diameters and record this dimension. Also required. Now using pins or blocks, confirm the distance between each hole or post is the same and record this distance. Add the diameter of the hole to the distance between them. This is the length of the sides of a true triangle. Draw it on a sheet of paper to better visualize it. If you now draw lines from each corner to the center ( midpoint of the opposite side ), you should end up with 6 identical inner triangles. Solve just one and the hypotenuse ( the longest side ) of that small triangle is your radius. Good luck.

[@TomokosEnterprize]

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 ?

[@1crazypj]

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

[@joepie221]

Not completely awful.

[@stewartfrye]

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

[@dougberrett8094]

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!

[@davidmyhre2720]

Hey Joe thanks again Love the white board.

[@LabRatJason]

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.

[@christurley391]

Thanks for the video Joe.

[@machineshoprescue6612]

Joe I hope your power is still on. Looking forward to your next mini lathe installment. I Amin northern Illinois and it is going to be -3 tonight. My son is in Houston and his power has been off for several days. His and his neighbors water pipes froze up and split the ceiling fell in. Good luck with the weather Kevin

[@joepie221]

So far, so good. Thanks for the thought. This weather is unbelievable, and I'm from the north.

[@mathewmolk2089]

@@joepie221 1 below on the East side of Cleveland this morning and we got a couple inches,,,,but what the heck, It;s the middle of February in North East Ohio. If it was 80 degrees outside I'd be worried. Better days are coming (but that doesn't mean I like it. Coolant on the friggin band saw has been frozen solid for 3 weeks!) Seriously, Anybody try RV antifreeze for bandsaw coolant? -

[@ryanjameson2036]

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

[@KevinWoodsWorkshop]

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.

[@andrepienaar6459]

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

[@michaeljohnson-li5nn]

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.

[@mpetersen6]

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.

[@scottlorenz2955]

Great videos thanks for your help to the machining world. If you can do a short on proper reaming techniques. Are the flutes on a reamer a cutting edge or a bearing surface?

[@joepie221]

Both. They do help guide the tool while wiping the cylindrical surface formed by the lead.

[@ronmccabe1169]

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

[@ggordon4127]

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

[@joepie221]

Geometry !!!!

[@kentuckytrapper780]

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

[@mathewmolk2089]

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!

[@joepie221]

We have been iced in all week and the power to the shop is off. I'll get back to it as soon as temps rise and the utilities are back online. Rare storms down here recently.

[@mathewmolk2089]

@@joepie221 Do worry about it Joe,,,,,We got juice but like I said the friggin coolant in the band saw is frozen solid and so am I. Our shop was supposed to be used for just for one offs in our Industrial Electrical/Millwright business so we never used anything more then a torpedo heater,. Now days I think up the damndest reasons NOT to go out there even though I have a couple of jobs for old customers hanging. (I never worked so hard since I retired) March 1st next week. Warmer days are coming!!!!!!

[@mrtom64]

For a 5 sided poly...take your 45° example @ 14:00 The base will be the length of each side. First bisect the base. Then draw an arc with center at the right angle from one end of the hypotenuse to the other. (A segment) Now... The point at which the bisect line crosses the hypotenuse is the center for a 4 sided poly. The point at which the bisect line crosses the arc is the center for a 6 sided poly. Bisect these two points and you have the center for a 5 sided poly. This distance can be extended further up the bisect line for 7, 8, 9...etc sided polygons. Thats the easiest way I know if you have the length of the sides, hope it helps.

[@skipgoryews1356]

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

[@joepie221]

Hi Skip. Thanks. Thats actually one of my favorite movies.

[@gentharris]

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

[@joepie221]

I did. I learned something from it.

[@raymondhorvatin1050]

Thanks for the geometry trig lesson

[@rogueart7706]

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.

[@KevinWoodsWorkshop]

To mark out 5 equally spaced holes simply multiply the PCD by .588

[@joepie221]

360 divided by the number of holes is the value between the spokes as projected from the center axis of the shape. Its one of only 2 locations that holds true.

[@rogueart7706]

@@joepie221 I missed something. Isn’t the degrees the value that we are looking for?...So that I can clock my indexer and get the holes equally spaced?

[@joepie221]

@@rogueart7706 Yes. But start at the centerline of the layout, not the shape it forms around the perimeter. For example, each internal angle on a hexagon is 120 degrees around the shape, measured inside. Only if you draw lines from the very center to each point do you get the 60 degree value you use. Otherwise, you'll have 6 angles of 120 degrees or 720 total. 360 is totaled at the hub.

[@gregorybarrett4998]

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

[@deoncboshoff8676]

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

[@James-fs4rn]

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

[@markramsell454]

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

[@andrewstoll4548]

Great video as usual.

[@KevinWoodsWorkshop]

I think your lens got confused with it’s bolt holes joe, maybe try using manual focus so your lens doesn’t have to figure out where you are. But on a serious note I hope the bad weather clears in Texas.

[@outsidescrewball]

Enjoyed the lesson

[@joepie221]

Glad you enjoyed it Chuck. Send us some California sunshine.

[@henrya3530]

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 ;-)

[@davidhall6712]

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.

[@stevehuntley3089]

For a five hole pattern, set your dividers to .587785 x diameter in inches and walk it off per Machinery's Handbook, 17th edition, page 75 " Lengths of Chords for Spacing Off the Circumference of Circles with a Diameter Equal to 1... "

[@stevehuntley3089]

The factor for six hole pattern is .5, so (.5) (diameter) is EQUAL to the radius - not because it IS the radius. Also, there's a chart for all circles up to 14 inches by 1/16ths (I think) so you don't even have to do the maths. I got my copy off ebay for $20.

[@mickymartinezgaribay4982]

Pure gold Master pie

[@moorejl57]

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@.

[@joopterwijn]

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

[@InssiAjaton]

In the "good old" days (=school) we had to construct the pentagon using a hint that it related to the Golden Ratio. Oh, while I am at it, we also calculated the numerical value of Square Root (2) using just a compass + pencil and paper for the calculations. Hint: The pencil and paper calculations used Continued Division.