Math (trig) question

nauga said:
I'd be happy to help if you decide to continue with it.

Nauga,
simplifying terms
Click to expand...
I shall require a sandwich.

--

I'll dig back into that Wolfram page again. I think it has what I need, but I have to work through the formula to figure out my known values and to look at the physical components to verify the drawing above actually matches what I have. I am pretty sure that the link "L" is directly in-line with the Z rod at the zero position. That makes the starting values simple because I can set the rod position at that point as "zero" and then +/- from there.

I had been looking at it as a series of angles and triangles, but the 2-circle intersection approach seems easier. The math is messy, and there is a lot of it, but it's already been done by others that are smarter than I am. And, it uses square roots and cosines, and chicks dig square roots and cosines.
 
OK - finally back onto this. From what I've found, there are plenty of on-line resources with "intersection of two circles" equations and calculators. I need to do this in two steps - calculate the two intersection points and select the one that I care about, and using that point recalculate angles. But I have to work backward because I will know the angles first. Given the angles, I can figure the required intersection point on the large circle, then adjust the Y axis of the small circle until it intersects at that same point.

Simple. Coffee will help.
 
GlennAB1 said:
How accurate does your answer need to be? Make a simple working model and measure the angle.
Click to expand...
Probably down to about 3 decimal places, maybe 2.

I need to write this into a program. Given the point of intersection on the large circle, return the Y value of the center point of the small circle. The X value of the small circle center point will be constant.

I can calculate the intersection point because the large circle radius and (x,y) doesn't change, just the angle of rotation. And for that I can do simple math to find the base and height (x,y) values of the triangle that would give me a point on that circle. Now I know where the two circles have to intersect and I need to work backwards to find the y center point of the small circle.

Here are just a few of the things I found:
https://stackoverflow.com/questions/3349125/circle-circle-intersection-points

http://mathworld.wolfram.com/Circle-CircleIntersection.html

http://csharphelper.com/blog/2014/09/determine-where-two-circles-intersect-in-c/
 
GlennAB1 said:
Free play, fits an clearances or manufacturing tolerances taken into account?
Click to expand...
Yeah - taken into account, and I already know there will be a lot of mechanical slop in the system. But the math can go down into the weeds. I just need to calculate a single position - if the mechanism can't get there within a reasonable tolerance, that's a different problem.
 
[email protected] said:
What I'm getting from your description is that you want rotation α as a function of z, something like this. Correct?

diagram.jpg
Click to expand...
OK - got it figured out, I think. Don't need the "2-circles" things after all...sort of.

I can do it all with triangles, sines and cosines.

nauga said:
I'd be happy to help if you decide to continue with it.

Nauga,
simplifying terms
Click to expand...

I'll PM both of you to explain what I did. Thanks, to both of you. It took some ciphering and drawing, and then I had one of those aha-moments. Of course, I may be totally wrong.
 
Matthew said:
OK - got it figured out, I think. Don't need the "2-circles" things after all...sort of.

I can do it all with triangles, sines and cosines.
Click to expand...

Told ya. (snark, snark, snark)
 
Clark1961 said:
Told ya. (snark, snark, snark)
Click to expand...
Yeah, well. I'm a little slow.

I spent most of yesterday doing all the 2-circle math. I needed to know one point in particular. Given all the info I had, I could calculate all the other points, distances, and angles. Then I would have to work backwards to get that point that I needed. Turns out doing that is a pain. But after drawing all the lines and such, I was able to see the triangles. I'm a little slow and need to "see" things.

I know you recommended using triangles, and that's the original way I was going, but I didn't "see" it until a couple hours ago. Thanks for the hints.
 
Matthew said:
Yeah, well. I'm a little slow.

I spent most of yesterday doing all the 2-circle math. I needed to know one point in particular. Given all the info I had, I could calculate all the other points, distances, and angles. Then I would have to work backwards to get that point that I needed. Turns out doing that is a pain. But after drawing all the lines and such, I was able to see the triangles. I'm a little slow and need to "see" things.

I know you recommended using triangles, and that's the original way I was going, but I didn't "see" it until a couple hours ago. Thanks for the hints.
Click to expand...
I'm just being a snarking bastard. Good job working it out. I've drawn many, many, many triangles doing layout/design work...even once used triangles to measure how much a jack-up barge was listing...I think I still have a little clear plastic protractor in the case with the HP-41c...
 
Fortunately, I was NOT the kid in class that always asked, "Do we need to know this for the test?"
 
You must log in or register to reply here.
Back
Top