formula in geometry

[ticko2]

How to figure out a 3 bolt circle on a 1.500 diameter, traveling on xy axis on a bridgeport. i can easily use a turning index and get it on 120 degree for equally spaced,but my only way of making this 3 bolts circle on this project is using geometry so i can easily travel on a xy axis on bridgeport...if anyone can help me how to get the formula how to figure this out,i'd appreciated...thanks in advanced.

[KTD1]

The XY coordinates can be found using trigonometry.
As an example I will assume your first hole is in the 12 O’clock position.

Hole #1: X0.0000 Y0.7500
Hole #2: X-0.6495 Y-0.3750
Hole #3: X0.6495 Y-0.3750

In this pattern, the X coordinate is equal to the radius of the bolt pattern times the cosine of 30 degrees. (0.7500 x COS 30.0)

The Y axis is equal to the radius times the sine of the angle or (0.7500 x SIN 30)

Hope this helps.

[Geof]

Put the work zero at the center of the bolt circle so you ha X0.0 and Y0.0 here.

You don't specify any orientation for the holes so i will start with the simple approach; put your first hole on the X axis and this means the coordinates for this hole are X0.75 Y0.0

Your next going counterclockwise is 120 degrees away or in other words 30 degrees past the Y axis.

The coordinates for this hole are; X-0.375, Y0.6495 which you obtain by trig; Sin30 is the X coord/0.75 or in other words 0.75*Sin30 gives the X coord which is negative because you are past the Y axis. Similarly 0.75*Cos30 is the Y coord.

The third hole is the second one just reflected below the X axis at X-0.375, Y-0.6495.

[ticko2]

yes it does help me,you gave me the answer as how and where to go and move with x and y axis..but i can't understand how you get all this dimensions,if you can explain it more simple..as how did you get x 0.6495 and y0.750...but thanks again.

[ticko2]

i think geof just gave me a better explanation, but thank you KTD1,i appreciate your help also..this a great site,i can definetly spent quite some time reading and lerning..thanks again guys.

[Avago]

Originally Posted by ticko2 yes it does help me,you gave me the answer as how and where to go and move with x and y axis..but i can't understand how you get all this dimensions,if you can explain it more simple..as how did you get x 0.6495 and y0.750...but thanks again.

I've got to admit that i'm rubbish when it come to maths,but i did find lots of easy to work out examples in this little workshop book.I would recomend it to anyone in engineering and cheap too!

http://cgi.ebay.co.uk/ZEUS-Thread-ta...1%7C240%3A1318

Tim

[Geof]

Also just remember some very simple relationships.

Six holes on a circle are separated by a distance that is equal to the radius of the circle. You calculate the coordinates as we explained using sin and cosine and of course the coordinates repeat around the circle with the sign changing.

Twelve holes are obtained by doing six holes from the three o'clock position like I did plus six holes from the 12 o'clock position like KTD1 did.

Four holes are simple if they are on the X and Y axes but if they are at the 45 degree points it is not really much more difficult; now it is the sin and cosine of 45 degrees that is used. Again 8 holes are obtained by doing four twice from the different starting points.

When you start doing these calculations you will see some numbers popping up regularly. The square root is such a number; 1.41421 half of this is 0.7071 and I will let you discover where this pops up.

Another number is 1.732 which is the square root of 3 and half of it is 0.866 which also pops up in trig tables.

And remember standard triangles. In a ninety degree triangle with two equal side the relative sizes of the sides are 1, 1, 1.4142; this is the 45, 45, 90 triangle. The 30, 60, 90 triangle has sides in a ratio of 1, 1.732, 2.

It starts getting more tedious when your holes are displaced from the axes by a weird number of degrees because then you do need to start looking things up on the calculator but for a lot of calculations not much more than mental arithmetic is needed.

[KTD1]

During my apprenticeship, I ran a rotary head die mill. How many know or remember what that is? To make things more interesting, the machine also had a cross slide rotary table on it. It wasn’t just for giggles, we didn’t have a CNC back then. All of the form punches and dies with contours went across the die mills. The guy working next to me did his apprenticeship at Studebaker Motors. He had a calculator but seldom used it. He would work most of the trig in his head. I learned a lot from that guy.

Today the techniques are replaced with G & M codes. A machinist doesn’t use many math skills and I think we are forgetting an important brick in the foundation.

When I’m working with polar coordinates, I generally work from the base system that all calculators use. Follow these rules and you will never go wrong.

Use a polar center point of X 0.0000 Y0.0000
Zero degrees is always the 3 o’clock position.
90 degrees is the 12 o’clock position, 180 degrees is the 9 o’clock, 270 is the 6 o’clock, etc,

The X axis coordinate is equal to the radius multiplied by the COSINE of the angle.
The Y axis coordinate is equal to the radius multiplied by the SINE of the angle.

In the example pattern from my previous post:

Hole #1 is at the 12 o’clock position so the angle is 90 degrees.
0.75 * COS 90 = 0.0000 (This is your X coordinate)
0.75 * SIN 90 = 0.7500 (This is your Y coordinate)

Hole #2 is 120 degrees from hole #1. (90 +120 = 210)
0.75 * COS 210 = -0.6495 (This is your X coordinate)
0.75 * SIN 210 = -0.3750 (This is your Y coordinate)

Hole #3 is 120 degrees from hole #2. (210 + 120 = 330)
0.75 * COS 330 = 0.6495 (This is your X coordinate)
0.75 * SIN 330 = -0.3750 (This is your Y coordinate)

This method is quite helpful when you have irregular patterns or positions that may be close to the axis zero point. If the calculator is giving you a negative coordinate, that’s where you belong.

[Geof]

Originally Posted by KTD1 ....Today the techniques are replaced with G & M codes. A machinist doesn’t use many math skills and I think we are forgetting an important brick in the foundation. When I’m working with polar coordinates, I generally work from the base system that all calculators use. Follow these rules and you will never go wrong.........

And the knowledge of the G and M codes is being replaced by reliance on CAD/CAM.

Just a detail I will agree is picky. You are working with Cartesian Coordinates not Polar Coordinates; cartesian coordinates specify a point by three linear numbers typically x, y, z but polar coordinates use a distance r and an angle.

[KTD1]

And the CAD/CAM is sometimes the most inefficient way to program.
Before anyone here programs on the CAM they must first program G code at the machine. Drives me nuts when someone goes back to the computer to adjust a peck drill increment or feedrate. So often a program is a simple do loop or subroutine and they spend an hour drawing the part in CAD.

[Geof]

I agree that knowing hand coding is essential at least to a certain level. Doing all the tedious trig calculations by hand I draw the line at an instead use a simple 2D sketching program to get coordinates for tangent points, etc.

I have been impressed, however, with the improvements in CAM from ten years ago when I got involved in CNC after 40 years manual machining. Back then if something could be hand coded it would probably be much faster than the best CAM program. Now the two programs can be neck and neck but if you have a situation where trochoidal toolpathing can be used for very fast material removal rates in steel CAM pulls ahead because it is virtually impossible to duplicate this by hand.