Corrdinate points for arc segments

[eliot15]

Just playing with programming arcs of circles and was wondering...

Lets say I have a circle with a radius of 1.5". If I wanted to cut the full 90 degree arc from X0. Y1.5 to X1.5 Y0. I could do:

N1 G41 X0. Y1.5 D1 F30.
N2 G2 X1.5 Y0. I0. J-1.5

This will give me an arc length of 2.3562 (90/360*2pi*1.5).

Now suppose I want to cut an arc half that length (45/360*2pi*1.5 = 1.1781).

Is there a way to calculate the coordinate point (XY) for the arc end point. Or say I wanted any arbirarily long arc segment on a circle (a 2" arc, for example). The end point coordinates obviously have to be on the arc, but how does one arrive at them.

Thanks,

eliot

[Chrliev]

To find the end points on an arc try; sine of the angle * radius, for one axis and cosine * radius for the other axis, X or Y axis and + or - depends on where in the quadrant of the circle you are at, if 0,0 is the center...

[eliot15]

Hey, thanks very much. That worked great!

The sine and cos of a 45 degree angle are both 1.0607. So the following draws an arc segment with a 90 degree start angle and a 45 degree end angle in the 1st quadrant:

G41 X0. Y1.5 D1 F15.
G2 X1.0607 Y1.0607 I0.0 J-1.5

And if I want to work with a given arc length - say 2 inches - I can use the following:

central angle = (arc length * 360)/(2pi * radius)

A 2" arc yields a 76.3944 degree angle with sine of 1.4579 and cosine of 0.3529, which can be drawn with:

G41 X0. Y1.5 D1 F15.
G2 X1.4579 Y0.3529 I0.0 J-1.5

Thanks a million!!!

[eliot15]

Actually realized I have another question around this. The previous example worked fine, but it uses a 90 degree start angle and an arbitrary endpoint.

But suppose I wanted to use an arbitrary start point as well? Say I wanted to start a 2" arc segment with a 1.5" radius at 18 degrees instead of 90 degrees.

I there a way to calculate the start point and endpoint of a 2" arc segment in this case?

Thanks for any more time you may have to burn on this. I really appreciate it.

eliot

[eliot15]

OK...I figurrrrrd it out.

sin(18) * 1.5 = 0.4635
cos(18) * 1.5 = 1.4266

This is my arc start coordinate point: X1.4266 Y0.4635

Then find the central angle for a 2" arc segment with a 1.5" radius.

(2 * 360) / (2 * pi * 1.5) = 76.3944 degrees

76.3944 degrees - 18 degrees = 58.3944 degrees

Now find the arc end coordinate point.

sin(58.3944) * 1.5 = 1.2775
cos(58.3944) * 1.5 = 0.7861

This is my arc end coordinate point: X0.7861 Y-1.2775

G-CODE

G41 X1.4266 Y0.4635 D1 F15.
G2 X0.7861 Y-1.2775 I-1.4266 J-0.4635

[kendo]

make an excel calculator
like this:

[kendo]

OOPS!

OK, not like that....
like this:
(I fixed it, and, you get the idea....)

[eliot15]

Awesome. Thanks!!