Key Ratio

[Richard Brekne]

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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.

This drawing was done on a shareware CAD program. One triangle was drawn
with coordinants that gave a triangle 15 units across (A2 B2) 14,14
units down (A2, O), and 11.18 down (B2, O). Two circles were then drawn,
both with O as their center, one with a radius of 14.14, the other with
a radius of 11.18. Then the triangle was rotated at copied at both 5
degrees, and -5 degrees from the origional (A2,B2,O).

The net change in vertical position for the front of the key compared to
the back of the key gave the following two ratios

A3,B3 moved to A2,B2 yielded a 0.511 ratio
A2,B2 moved to A1,B1 yeilded a 0.436 ratio

This is kind of easy to see from an intuitive perspective if you just
look at the diagram a bit and follow the << Key >> as it traces the two
arcs. You can prove this using some basic trig as well if you like. In
anycase, defining the arms of the key as key top front, down to balance
rail bottom, up again to capstan top results in this same tendancy for
the change in vertical position of the capstan compared to the key
front. Tho of course due to the dimensions of a real key the difference
in vertical ratio is not nearly as pronounced.. but just so. Tilting the
key backwards (front up) increases the vertical rise of the capstan for
the same degree of movement at the front of the key.

Cheers

RicB


[Image]


--
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


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