[python] Re: General Formula for the position of the virtual pivot point
- From: Michael Rienstra <ageless@xxxxxxxxxxxxx>
- To: python@xxxxxxxxxxxxx
- Date: Thu, 26 Aug 2004 22:38:31 -0700
Dirk,
I figured out how to obtain the formula you speak of while riding
around town on my bike early this morning, but it will take me a little
head-scratching to fit the pieces together -- I had a ridiculously long
day -- left for work at 4:50 am and didn't get home until around 7:30
pm! Luckily the middle 4 hours of the day was office stuff instead of
bike riding so I got to relax, but I was really hoping to take a nap!
At any rate the sunset made it all worthwhile. Enough about that!
We start with this page:
http://iel.ucdavis.edu/chhtml/toolkit/mechanism/fourbar/fourbarpos.html
It shows us how to derive equations for the angles of the right Side
link and the Coupler link, for known values of G, S, C and the angle of
the left Side link. The math is a bit confusing to me, although I'm
sure I once would've understood it. I need to get a better math
reference book -- my old physics book has a math appendix but it's
pretty basic!
Anyway, using this example, we need to derive two equations for the
angles of the left Side link and the right Side link for known values
of G, S, C and the angle of the Coupler link.
Then we can convert those equations to line equations, which is much
easier than the first step, since we know a point on each line (the
fixed pivots on either end of the Ground link) and then we just convert
degrees to slope. Then it is very simple to combine the two line
equations into a equation which gives you the intersection of the two
lines, which is the virtual pivot!
After that, it's not too hard to come up with an equation that relates
the angle of the Coupler link to the position of the wheel axis, and
another to relate the angle of the Coupler link to the angle of the
wheel axis. It's frustrating when one's math skills are rusty! I can
almost taste those equations but they are just out of my grasp!
If anyone wants to give this a try, please feel free! Otherwise I will
try to understand the math, possibly search for some online tutorials
to remind me of what I once knew, etc. I think I can do everything
without too much study except for the first step, although with a bit
of luck I could find a good tutorial quickly and it would suddenly make
sense.
Time for bed once again! Tomorrow is another long day -- 5 am bicycle
delivery route (more pastries and bagels and such) followed by a
bicycle landscaping route (a local business which uses bikes, trailers
and electrical landscaping equipment), followed by a another bicycle
route delivering some mail!
Michael
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