1. ## coordinate calculation

hi there.
I'm breaking my head for two hours now on how to calculate de coordinates of te radiusses of the ring shown in the drawing aspecially the cutting point of the 114mm and 6 mm radius.
Not that i really need them i'm just doing a bit of braintraining and it pisses me off that i cannot figure out how to calculate them .
anyone got an idea on how to figure it out with just a simple calculator.

2. Looks like you need to brush up on your trigonometry. (We all do.) Look in the Machinery Handbook, there is a section that covers it.

3. ## Finding the center of the radii

The drawing is not complete and the math problem is indeterminate. This can be shown via the equations. The circle made by the 114 mm arc can be written as two second order equations ((x-a)**2 +(y-b)**2 = r**2) but because both the x and y value at the outer end of the arc are not defined that is 2 equations with 3 unknowns. The circle made by the 6 mm radius is also described by two equations (the one above plus its differential) but that only leads to 4 equations with 5 unknowns.

The same result can be shown with a scale drawing and compass. Draw a 114 mm circle with the center at the inside of the required 114 mm arc. The center of the 114 mm radius must be on that circle. Then draw the horizontal line that sets the outside end of the radius plus a verticle line located 6 mm offset from the tanget line for the 6 mm arc. Then draw a 6 mm circle at the intersection of the two lines. You can them pick any point on the horizonal line that is within the outside radii of the 6 mm circle and draw another 114 mm circle. The intersection of the two drawn 114 mm circles is a possible center point of the 114 mm part arc, but there is an infinite number of possible 114 mm circles and hence a range of intersections. Once you pick a center for the 114 mm arc the 6 mm arc center is determined or vise versa.

There are any number of other pieces of information that could complete the drawing, i.e. the angle between the two arcs at the point of intersection, the distance between the inner end of the 144 mm arc and the outer endof the 6 mm arc, the angular length of the arcs, etc. But without some other detail this drawing is incomplete. (Note, I could not read the top line of the drawing and had to assume it did not add another detail.)

Tom

4. If i was you i have to draw the figure in CAD program and then get the necessary coordinates. You have given all the dimensions i don't know why you are unable to configure the coordinates.

5. Originally Posted by duivenhok
hi there.
I'm breaking my head for two hours now on how to calculate de coordinates of te radiusses of the ring shown in the drawing aspecially the cutting point of the 114mm and 6 mm radius.
Not that i really need them i'm just doing a bit of braintraining and it pisses me off that i cannot figure out how to calculate them .
anyone got an idea on how to figure it out with just a simple calculator.
For R6 it should be simple: circle is tangent to the vertical line.
for R114... simply there isn't sufficient information.

6. I think there is enough information here. Look a little harder. If I have time late this evening, I will post an answer for you.

7. The 114 arcs are part of the same circle. The circle touches each end of the 59 long line. You know the radius and 2 points on the circle so you have everything you need.

Matt

8. Ok. I got to this sooner than I thought I could. See attachments for the path to the answers which you seek.

9. When I teach trig to my students, I encourage them to sketch some construction lines and "find the triangles".

10. Originally Posted by txcncman
Ok. I got to this sooner than I thought I could. See attachments for the path to the answers which you seek.
Correct, that's the process I was describing. I think the others may have missed the fact that the top and bottom arcs were a part of the same circle. If they were not, it would definitely complicate the issue.

Matt

11. damn. figured out there must have been something very simple i'm missing.
the fact that both arcs were part of the same circel never crossed my mind.
feeling a bit shamed to be honest.
very much thanks y'all for your effort.
been out of the industry for some years and am just waking up the necessery brain cells.

greetings from the netherlands