I've been looking at this drawing for an hour and am still confused. It's a school chess piece problem. Everything was fine till I got to the deep radius in the middle. They seem to have left out the Z coordinate at the start and end of the radius. I'm sure there must be a way to figure it out from what IS given, but I'm not sure how. Up till now, we've been doing radii that are 90 degrees, so the arc radius tells you how far it travels in the X and Z directions. This one though, I don't think you can do that! Anyway, take a quick look at if you wouldn't mind, and give me a hint. Don't tell me the answer, just tell me how to figure it out!

The numbers they have given you are inconsistent (slightly). They show the minimum diameter as .394. Add half of that to the radius of the arc (.630), and you get .827 -- which is not equal to the .823 that is shown.

You can solve this by a little trig, geometry, and algebra. Or, you can sketch up the known parts in a cad system and have it tell you where the intersection is.

Ken

If I were making that I wouldn't need to figure it out.
In the lathe I would program the arc using the center point. It doesn't need to know the Zs you are looking for.

If you are doing it by hand you can work equal distance from the 1.299 dimension keeping your rad on the small size untill you get the center to the finished diameter then feather out the radius equally (Z) untill it matches your radius gauge.

To solve this geometrically, draw the following lines:
1 from the center of the radius to the left most unknown point
2 from the center of the radius to the right most unknown point
3 connecting the two unknown points
4 from the center of the radius to the centerline of the part (the perpendicular line)

Call the left most unknown point A, the right most B, the center of radius C, and the intersection of line 4 and line 3 D.

The, you have two triangles to find the short sides of (they are symmetric). You need to find the length of AD and BD. The length of AC = BC = the radius of the arc. The length of CD = the radius of the arc minus the difference of the part radii (.552-.394)/2. Now you should have enough information to solve of BD.

You didn't want me to answer the question, so I'm leaving out the final steps.

Ken

Well...hopefully you're using a CNC lathe....if I read the numbers correctly the Z at the 642 dia. is 58 and the Z at the 552 dia. is 103 and the radius doesn't seem to be centered (can't read the 1.2xx dimension).

thanks guys! the numbers didn't come out very pretty but I think I got it.

The hieght of the cord is given between the .394 and .552 difference in radius. The radius is given also. This leaves the length of the cord = 2 sqrt[h(2r-h)]. Applying that to the location of the radius centerline will give the runout points of the radius relative to the origin.

DC

One of Many.....I don't think the height of the cord is given....

"Given" was a misnomer. Derived would have been more appropriate, but I did reflect the way it was given by the difference in radius between the 2 diameters per print.

By given, although not in print it is there with some pretty basic math.:o

DC

Well.. you have 2 choices.. If youre using cutter comp you can program the part edge..If not then you have to identify the tool tangent on x and z as related to the part tangent relative to the .630 radius. email me if you want some tool path geometry layout help..
Drum.