<!doctype html public "-//w3c//dtd html 4.0 transitional//en"> <html>   John Hartman wrote: <blockquote TYPE=CITE>Richard Brekne wrote: > That seems clear enough, and I find it curious that the quantity of Balance > Weight so well conforms to measureing all three levers very much  in this > fashion. In fact, when you think of it,  that the Stanwood measurements yeild > the correct quantify for BW so well is kind of odd given the fact that the > weight measuments taken have all the parts in an orientation they never all > three find themselves in at the same time in the action itself. The Stanwood method works out like this because it is based on weight measurements not lever arm measurements. The two are related but not the same.  </blockquote> Pretty interelated I would say. One way or the other a lever can alway be reduced to its vertical and horizontal components, which is to say that no matter which way you turn it.... d1 x W1 = d2 x W2.  If the Stanwood method works at all, then you can sure as heck find appropriate lever arm measurements that describe it. <blockquote TYPE=CITE>  > Dont you also have to take into consideration the orientation of the parts at > the their starting point. In the example I gave, it seems clear that the > amount of purely vertical movement in the back of the <<key>> compared to the > front is going to vary dependent on where in their respective arcs each point > is at the start of motion. If the <<key was tilted forward enough... grin... > the back end would actually pass through the top of its arc,... or if it was > tilted back from horizontal it could rise more with downward motion at the > front. In that sense it almost seems meaningless to talk about a ratio which > mixes change in vertical movement with a lever that moves in an angular > fashion. Yet this is exactly what we do all the time. I am not clear about what you are saying. Are you saying that the key ratio changes depending on its angle of inclination?. You should sketch this for us.</blockquote> Look at it this way John. Take two circles with the same point of origon, one of them 14.14 radius, the other with a 11.18 radius. Then fit the triangel "keystick" I posted last into it such that the top is horizontally oriented, and the "fulcrum" (bottom point) is at the point of origion to the key. Look at the two circles for a bit, and imagine this triangle tracing the two circles with the fulcrum always at the point of origion. It should be clear immediatly that as the point on the small circle moves progressively further towards its highest point, its' change in vertical position becomes less and less while the point on the larger cirvle experiences an increasingly larger change in vertical position. For example, if the front of this key starts out 10 mm above that horizontal line, the back of the key will be about 6mm below the horizontal.  But if instead you move the front 10 mm below the horizontal line, the back will only be about 4mm above it. So looking at strictly the change in vertical positions, yes... the orientation of the key at its starting point does determine (along with the respective radiai of the two arcs)  the rate of change both points will experience as the key moves. Now in a real key, the angles are not anywhere near as extreme of course, yet the same thing applies. Lowering the back of the key at rest will increase the vertical rise of the back for the same amount of verticle drop in the front... just slightly... but just so.   -- Richard Brekne RPT, N.P.T.F. UiB, Bergen, Norway <A HREF="mailto:rbrekne@broadpark.no">mailto:rbrekne@broadpark.no</A> <A HREF="http://home.broadpark.no/~rbrekne/ricmain.html">http://home.broadpark.no/~rbrekne/ricmain.html</A> <A HREF="http://www.hf.uib.no/grieg/personer/cv_RB.html">http://www.hf.uib.no/grieg/personer/cv_RB.html</A>  </html>