[Ri...] Posted July 5, 2022 Share Posted July 5, 2022 I am trying to determine the sin error for contact of the stylus radius to a radius. The attached image shows what I am currently doing, but of course the result will be in error. Any help is appreciated.thumbnail_image0.jpg Link to comment https://qualityforum.zeiss.com/topic/10054-need-some-math-helpagain/ Share on other sites More sharing options...
[Al...] Posted July 5, 2022 Share Posted July 5, 2022 Hi Rick, Are you just looking for a general formula to calculate the error due to probing direction? Normally it's R * cos(theta) for the offset in one direction, and 1 - sin(theta) for the other. R is the stylus radius and theta is the angle between the nominal probing direction and actual direction. If I've got something wrong I'm happy to be corrected, but I hope this helps. Link to comment https://qualityforum.zeiss.com/topic/10054-need-some-math-helpagain/#findComment-47836 Share on other sites More sharing options...
[No...] Posted July 6, 2022 Share Posted July 6, 2022 Please sign in to view this quote. My old UMESS manual says it's R * (1- cos(theta)) for the offset in the probing direction. I didn't check which one is true, but I guess both are meant for slanted planes. But this is a radius, so it needs further correction by some more trigonometry. But it's too early in the morning for me to puzzle this out. 😭 Link to comment https://qualityforum.zeiss.com/topic/10054-need-some-math-helpagain/#findComment-47838 Share on other sites More sharing options...
[Ma...] Posted July 6, 2022 Share Posted July 6, 2022 Wouldn't it be better to scan this as curve or circle and then make intersection? This can be tricky because raceway radius can vary ( in both directions + radius ) After determining actual radius and position you could be able to touch with right vectors Link to comment https://qualityforum.zeiss.com/topic/10054-need-some-math-helpagain/#findComment-47840 Share on other sites More sharing options...
[Da...] Posted July 6, 2022 Share Posted July 6, 2022 Please sign in to view this quote. Curve would be best, but a circle pattern would get really close ! Intersect to a Theo plane, then recall Intersections into a circle Link to comment https://qualityforum.zeiss.com/topic/10054-need-some-math-helpagain/#findComment-47842 Share on other sites More sharing options...
[Al...] Posted July 6, 2022 Share Posted July 6, 2022 Please sign in to view this quote. You're right Norbert, I forgot the R in my second formula and it should be cosine rather than sine. R* sin(theta) would give the offset perpendicular to the probing direction. I think, regardless of whether it's a slanted plane or a radius, these equations should still apply. They're only giving the offsets between points on the ruby tip, not points on the part. Link to comment https://qualityforum.zeiss.com/topic/10054-need-some-math-helpagain/#findComment-47844 Share on other sites More sharing options...
[No...] Posted July 6, 2022 Share Posted July 6, 2022 Please sign in to view this quote. Yes, but you need to know where those points are. The actual contact point on a radius is not the same as on a slanted plane. The formula above is based on the assumption that the connecting line between the sphere center and the actual contact point is perpendicular to the slanted plane. Then you can calculate theta from the angle of the plane. But on a radius this angle constantly changes, so the problem is how to get theta. Link to comment https://qualityforum.zeiss.com/topic/10054-need-some-math-helpagain/#findComment-47846 Share on other sites More sharing options...
[Is...] Posted July 7, 2022 Share Posted July 7, 2022 You will lose accuracy, better to intersect a theoretical element with a curve. Link to comment https://qualityforum.zeiss.com/topic/10054-need-some-math-helpagain/#findComment-47848 Share on other sites More sharing options...
[Is...] Posted July 7, 2022 Share Posted July 7, 2022 anyway...formula.png Link to comment https://qualityforum.zeiss.com/topic/10054-need-some-math-helpagain/#findComment-47850 Share on other sites More sharing options...
[Ri...] Posted July 7, 2022 Author Share Posted July 7, 2022 Please sign in to view this quote. Appreciate the assistance 😉 I added "diff2" Its what I was trying to figure out, and now I see I was doing it wrong.formula diff2.png Link to comment https://qualityforum.zeiss.com/topic/10054-need-some-math-helpagain/#findComment-47852 Share on other sites More sharing options...
[Er...] Posted July 8, 2022 Share Posted July 8, 2022 I would go with a radius intersected by an offset plane. Then use that point to take an actual point for increased accuracy. Link to comment https://qualityforum.zeiss.com/topic/10054-need-some-math-helpagain/#findComment-47854 Share on other sites More sharing options...
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