Key Ratio

[Richard Brekne]

John Hartman wrote:

> Richard Brekne wrote:
>  > I think it was John Hartman that asked me for a drawing of what I
>  > meant about the key ratio changing depending on the starting position
>  > and ending position. Again, here is that exagerated example of the
>  > three points on the key. A is the key front, B is the capstan, and O
>  > is the fulcrum. And remember we are looking at the change in vertical
>  > position for points A and B.
>
> Thanks for the drawing, I see your point. I think the contradiction can
> be resolved looking at the lever arms in relation to their arcs of
> motion. Then the ratios will be correct.

Hmmm..

> As I said before how you
> measure the lever arms depends on what aspect of action mechanics you
> are interested in working on.

This is one of the main points I was trying to make in my article, tho the
insistance to utilize the key ratio diagram and the concept behind it sort
of made that less clear... but its a very important distinction, and a key
point to understanding how to measure with distances the Stanwood Ratio.


> If you are investigating the static
> balance of weights it is easier to use lever arm measurements that are
> perpendicular to the force of gravity.

Yes, and also central to picking apart the Stanwood Ratio into its component
distance measurements. Remember his weight measurements are taken with parts
in a horizontal position. Its a fun exercise to figure out how to measure
the Stanwood arms. And it does result in a different ratio then say the
Overs ratio, or some other convention for measureing the arms does. Which
one is << correct >> becomes a silly question really, at least if you are
looking for a universally << correct >> answer. Better is to ask which one
is appropriate for what we are looking at.


> If you are interested in the
> motion of levers (how far they move) then you should measure the lever
> arms diagonally and use arc measurements for the motion. The two are
> roughly similar but not the same.

Yes, but here another distinction needs to be made and its a bit easier to
miss. Its the one I made above. Total movement, verses vertical, or for that
matter, horizontal movement. Actually spliting the circular motion into
these two components is a good way to start looking at these force vectors
that are brought up from time to time, for those who have little or no real
understanding of what they are and how they work.

>
>
> Let me give you some examples. It is true that for a key with a front
> lever arm of 100mm and a back lever arm of 50mm (measured along the
> length of the key) a 2 gram weight on the capstan will balance a 1 gram
> weigh at the front of the key.

Yes... but this will only create a horizontal balance. What  << weight >> do
you need at the back to balance the key at a say 5 degree offset either way
?. And what << ratio >> will that give ? Comparing this towards the vertical
component shown above can get interesting. Not what we usually do because
everyone is told simply to measure the key stick in the angled fashion no
matter what.


> It is only roughly true that when you
> depress the key 10mm at the front the capstan will rise 5mm (your
> drawing shows this). To measure this motion precisely you need to
> measure the lever arms diagonally and use arc measurements for the
> distances. The two will be very close (In the case of a key) but not the
> same.
>

Thats more or less what I did above, except I did it graphically instead of
using simple trig. The interesting thing is that measuring the length of the
arms diagonally and just leaving it at that yeilds a ratio that doesnt even
come close to comparing with either weight or distance moved. Yet this what
we are told to do all the time. I even had to accept this kind of
measurement and diagram in my article or the editor wouldnt publish it.

The horizontal component of a levers arm is the same whether its measured
directly or calculated using  the <<real>> arm and trig. Actually... given
the keystick... we dont even need trig... Pythagoras will do nicely.


> John Hartman RPT
>

--
Richard Brekne
RPT, N.P.T.F.
UiB, Bergen, Norway
mailto:rbrekne@broadpark.no
http://home.broadpark.no/~rbrekne/ricmain.html
http://www.hf.uib.no/grieg/personer/cv_RB.html