Calculate bolt (pitch) circle diameter

sometimes in life it's necessary to know the bold circle diameter of parts either/or pitch circle diameter of parts either for fabrication purposes or parts replacement in this video I'll show you how to calculate it in terms of a practical application let me give you a visual example here I'm not taking of the tripod I have some parts here on this desk top here that all feature bolt circle diameter or pitch circle diameter this is a sprocket from the motorcycles rear wheel that drives the rear wheel and the chain goes around it and connects to the engine this one here is a gasket material for some plumbing components with four holes this one is a flange between two flanges two identical flanges some gasket material would provide airtight or water tight connection on this side you have four bolt holes but if you turn it around you can see this is some student project not an actual real part it is not a pipe or a tube but you can see this is a flange and it can have eight holes nicely and evenly spaced out bicycle components chain rings from the crank this is where the pedal goes and they are the crank arm goes and the pedal units so these also come with four five four and five are typical but sometimes three according to this menu manufacturer here the chain ring came in this packaging so sometimes three is also a possible bolt pattern and their pitch circle you can vary these numbers are in millimeters sometimes for a spare wheel on a car that you want to fit on a vehicle's hub the hub also has these bolts lock bolts sticking out from it it's really important that the pitch circle diameter or bolt circle diameter be matching the wheel exactly solely this pitch circle or bolt circle is a circle and I'm gonna work with this shape here is a circle that goes through the center point of these holes okay and you can kind of this part here leads the eye you get it it's a circle and it needs to be pretty exact in order to fit the part on a vehicle if you have to fabricate one out of just a scratch and whether you're working with cork plywood sheet metal or whatever you need to lay that you layout needs to start with knowing your pitch circle diameter if you don't have it you can calculate it that's what this video is focusing on if all you have is one measurement the measurement between the bolt holes where the bolt holes line up along a polygon so whether you have five or three or four F and four of course makes a square or I have drawn here eight for an octagon or six whatever number of boreholes you have it makes a regular polygon so if you have a different shape where it's not symmetrical if you have four holes on the chain ring or and they are not symmetrical then it's not gonna work it has to be a regular polygon inside a circle in terms of math this is known as a regular polygon inscribed a circle so in this video I'll show you two calculations one is gonna be 15 seconds and it needs a calculator that's it and the measurement the measurement can be taken with a ruler this centimeters millimeters inches whatever this one is in centimeters and the measurement needs to be taken from Boco Center to borehole Center typically with the Spurs of the caspere's are a pretty good indicator of this of course trying to line up the center of the or the spur to line up with the center of the circle is pretty difficult so go from the left side of the hole to the left side of the hole or to the right side of the hole to right side a hole there about something because it's the same as center-to-center so that makes sense I hope so you need one measurement and one calculation 15 seconds you're gonna get your pitch circle diameter or board circle diameter so let me just put you back on the tripod here a little bit of fiddling there we go so on these polygons that I have here I don't have neither inches or centimeters nothing it's just seven so if you have a measurement from hole to hole it could be any number like like the manufacturer indicates here in the packaging any of those numbers are popular none of them are really industry standard but manufacturers tend to choose numbers that are not unique and not custom-made but parts for which would be widely available so if you are fabricating and of course and even just one measurement you're gonna have a problem if you start with a thin sheet of metal you put a firm you put a mark on it for the first bolt hole and you have a center punch and have a run it so far so good if you have a measurement like fifteen or I don't know four and a half inches whatever number you can lay out the second hole in any direction but when you lay out the third one the fourth one and the fifth one they kind of need to fit on a circle and for this I just put a circle here maybe two of them will line up on a circle if you just randomly try to lay out your board four locations if the only number you have is four and a half inches for example four vehicles how so you need to know the pitch circle diameter along which you can place start anywhere two four five okay there's a six fun on it you get the idea you have to start with the pitch circle diameter if you're fabricating so I'm gonna be working with the trigonometry and just for math sake just put your little further back this is known as diameter of a circle or yeah that has a polygon inscribed into it let's start with the circus up with the regular polygon Pentagon that is inscribed into a circle the blue line is the diameter and the side length of the polygon here is 20 20 anything it doesn't matter the end is 20 is taken by a measurement taken by this vernier caliper or it could be given as a number or a blueprint you know I want five holes evenly spaced 20 that's nice it still needs a pitch circle diameter diameter so the blue is the diagonal sorry the blue is the diameter of the circle the blue line is about this much longer here as it goes from one corner that touches the circumference of the circle there but it's a little longer here it comes out to the circumference so needs to be calculated I put the number 72 out there in this calculation a Pentagon it divides a circle into the 360 degrees of the circle into five chunks each 72 if you find the origin of the circle the center of the circle and connect the corners of the polygon if you have a triangle of course you have three lines three radiuses three radii to run from the corners if you have a square of course you have deep the head when I was thrown and that's where the center of the circle is in this case you have five of these 72 degree slices I'm gonna focus on work with just one of these triangles the 72 degree can be divided by the diameter into two 36 degree angles why would I do that because I want a right angle triangle a right angle triangle can be calculated very easily this blue triangle bisects this original triangle bisects the angle exactly into two equal halves as well as bisects this line the side length which was twenty into two equal chunks ten and ten so we went from one triangle now to two triangles I'm gonna focus on one of these new triangles in the next slide that I have just such this blue line again is the radius of the circular now because that's where the center of the circle is and it comes all the way after the circumference but I don't need the entire diameter in this one or radius what is given here is this 36 degree angle and this side length of the triangle that has a length of 10 in terms of trigonometry that's an angle this is a side opposite that angle this is a side that's adjacent to the angle and this is the hypotenuse of the triangle the math takes place here it's either sine cosine or tangent function that gets it done of course it's a sine function because sine of an angle equals opposite over hypotenuse and then when I replace the words with the actual numbers given by again this as you solve the equation you get 17 point 1 3 for the length of the hypotenuse all right what did we do with the 17.3 figure the 17 point Oh 1/3 is there is again this dream length of the triangle which was the hypotenuse of this triangle triangle but is actually the radius of the circle replacement or substitution make sense the hypotenuse is the same as radius and if you double the radius 17 you get diameter 34 point oh two six there's your pitch diameter so let's review the calculations how do I compress this into a 10 second calculation we had 10 divided by sine 36 to guess radius we need diameter so we need to double something you either her yeah you either double the radius or you double the number that you divide in order to get diameter in one step so if you start with 20 20 divided by sine 36 and it and it works it's just as simple as it looks twenty twenty divided by sine 36 equals 34 that's your diameter here your pitch circle diameter or ball circle diameter now for this little bit here how do I know that it's signed thirty six is the magic number that works for me because once you have your measurement it's a four and a half inches or whatever 63 millimeters between board or on board or whatever number how do you know sign what do you need it's fairly straightforward the Pentagon makes five triangles because it has five corners so it's 360 divided by 5 divided by 2 again so 360 divided by 10 here's what the number 36 are that's a number 36 came about so by this analogy if you have a let's go back to the first time slide a triangle divides the circle into three chunks of 120 degree angles half that is 16 so the calculation for this would be 15 divided by sine 60 if you have for both holes the four bolt holes make four 90-degree corner a 90 degree triangle out of out of one square when you draw the diagonals on a square so because it has four corners you divide the 360 into eight chunks and of course it's 360 divided by eight your number is of course 45 so yeah you would take the boat distance divided by sine 45 to get your pitch circle diameter if you have five it's whatever board all divided by sine 36 because 360 divided by ten five corners times 210 is 36 if you have a bolt holes you're gonna be dividing the circle into sixteen parts so 360 divided by 16 is 22 and a half so you're gonna be calculating me whatever the side length here is I don't know three in this case whatever three inches three whatever so three divided by sine 22 and a half gets you your pitch circle diameter in ten seconds so that's how the calculation goes it's a little bit of explanation about it thank you very much for watch

Channel: apprenticemath

Views: 3,268

Keywords: BCD, PCD, bolt, lug, nut, wheel, sprocket, motorcycle, drive, train, machine, part, calculation, calculate, fabricate, lay out, layout, design, replace, match, find, how, do I, custom, fit, bicycle, chain, ring, crank, power, torque, measure, measurement, trigonometry, sine, cosine, tangent, application, show, explain, explanation, polygon, regular, triangle, applied, math, maths

Id: bfU6ZzG5OgI

Length: 14min 9sec (849 seconds)

Published: Fri Apr 26 2019