It appears that the solution is... when the lines FG and AG are symmetric about CG... proof of that would be great!
So I have had the past 3 days off and I have been working on a pet project of mine... designing a radial engine.
Yup. not a model one either. 7 cylinder probably about 500 cubic inch displacement.
So anyway... it has a REALLY nasty geometry problem I cant seem to figure out. I'm no wizard at math... but I do run a program called solidworks and am pretty good at figuring out the "graphical solution" to problems... which solidworks calculates out to .00000001 inch which is more than enough seeing as how my machines cant hold much better than .0002in manufacturing tolerance. but this one I cant seem to figure out...
7 cylinder radial engine. each piston/cylinder is evenly spaced around the engine. 360°/7~ 51.428° so lets just call it (360°/7).
The design calls for a "master link" this link is the one that all the other link rods attach to. Google search "radial engine master rod" if you're not familiar.
Assume the #1 cylinder is vertical at the top. #2 is the next one clockwise and so on... so #1=#7.
See the attached picture: It is showing the master link "green" at maximum top dead center for cylinder 6.
Line CE and line CG have to be the same length... thus the top dead center circle has to be the same... otherwise the engines compression is erratic and I will never get the thing balanced.
In the picture a crank CA is constrained to rotate around the point C. Link AB is the master rod and B is the slider that slides along CE. Link AF and AB are constrained in angle to 360°/7.
I cant figure out... how to get point G on line FG to be on top dead center circle... thus what the length of AF needs to be...that is where the adjustment needs to occur (Line FG needs to be the same length for all the other cylinder positions).
I initially figured that top dead center would be when point F was on line AG... but it isn't working out that way and the solution isn't apparent to me.
Thanks for looking!
so you want to make sure your cylinder at G can be positioned on this circle while point A revolves around point C in a circle and will adjust the length of AF to do so? I assume the links at F and A allow movement.
I want to make sure I understand what your asking before I dig into this.
Yes. Top dead center circle is circle centered at C with a radius CE. It's actually top dead center of the piston pin.
Here is a video of the system.
as of the post... it has about 10 minutes left to process before it works.
I've got a mathematica sheet going modelling this. I'll have an answer for you in the not too distant future but it is Christmas after all.
Looking at your movie I think AF can be any in an interval of lengths. You'd design it to be the minimum of this to keep moments on your links to a minimum.
YES! You get it!
(GRRR!!! I made a typo earlier: cylinder #1 does not equal #7... #1 would actually be #8... anyway it's useless thinking of it as #8 until I get into timing... I digress) I bring that up because I'm assuming cylinders 2,7 ; 3,6 ; 4,5 are pairs having identical AF lengths... seems to work out. But FG has to be the same for all of the "slave" links that have to match up with the master link and all hit the top dead center circle. This way the master link is the only part to account for the adjustment and all the links are interchangeable and CAN'T be put together in a manner that could destroy the engine by interference... besides cheaper to make a bunch of a single part.
Once I drew everything up it looks like that of the 3 pairs I mentioned above, they are related to each other... so to answer your question... I figured my limiting factor was minimum material required to hold the required size pin. I was working out an estimate of torque when Christmas dinner interrupted. Anyway the smallest AF length occurs on cylinder pair 4,5... so at the moment I have 1 9/16" assigned to it and that fully defines the system for me.