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<DIV><FONT face=Arial size=2>Bernhard:</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>You don't want your pivot point to be =
at the center
of percussion. Actually that's physically impossible since your =
radius of
gyration would have to be zero. The whole point of using the =
center of
percussion is that you want it to be where you strike the rotating =
object
(hammer) so that it results in zero force on the pivot.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Don A. Gilmore<BR>Mechanical =
Engineer<BR>Kansas
City</FONT></DIV>
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style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
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<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>
<A title=b98tu@t-online.de =
href="mailto:b98tu@t-online.de">Bernhard
Stopper</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A =
title=pianotech@ptg.org
href="mailto:pianotech@ptg.org">Pianotech</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Thursday, December 18, =
2003 6:57
PM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: Cockeyed hammers / =
Don
Gilmore</DIV>
<DIV><BR></DIV>
<DIV><FONT face=Arial size=2>Don, Sarah</FONT></DIV>
<DIV><FONT face=Arial size=2>my last post has to be =
corrected(fat
cursive):</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV>
<DIV><FONT face=Arial size=2>To design a hammer so that its =
pivot
coincides with the center of percussion is THE way to get a free sound =
and the
maximum of energy transfer to the string. it also allows the hammer to =
reject
the fastest way possible because oscillations in the pivot =
produce
friction and slow down hammer movement at contact point.
</FONT></DIV>
<DIV><FONT face=Arial size=2>i did several simulations with =
software called
pro/mechanica and reshaped hammers after results found. one could say =
that
actual hammer with heavy felts have their center of percussion much =
far away
from the pivot than lighter hammers have. putting a small lead in the =
tail of
the hammer can make them come closer to that point. center of hammer =
mass
should ly on a line along the center of the hammer shank and =
<STRONG><EM>the center of percussion coincides with the pivot, when =
hammer
shank length x is</EM></STRONG> calculated by the formula =
x=I/(m*y)
with I= moment of inertia, m=mass, y=distance pivot - =
center of
mass</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>regards,</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Bernhard</FONT></DIV></DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>
<A title=eromlignod@kc.rr.com =
href="mailto:eromlignod@kc.rr.com">Don A.
Gilmore</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A =
title=pianotech@ptg.org
href="mailto:pianotech@ptg.org">Pianotech</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Friday, December 19, =
2003 12:22
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: Cockeyed hammers =
/ Don
Gilmore</DIV>
<DIV><BR></DIV>
<DIV><FONT face=Arial size=2>
<DIV><FONT face=Arial size=2>Well, I didn't mean to imply =
that the
impulse at the pivot is all absorbed; but it is all lost as far as =
the
string is concerned.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>The center of percussion is one of =
those
counter-intuitive phenomena in dynamics. For the multitude of =
college
students that only take a semester or two of physics, the concept of =
forces
on a free body acting at the center of gravity is a paradigm that is =
hard to
dislodge. For an object in free space or translating in a =
straight line, which comprises most situations, the center of =
gravity
is always used. But for an object pivoted at some location =
other than
its c.g., all bets are off. The most publicized version of =
this is a
baseball bat's "sweet spot" as you described.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Think of a wooden board hung from a =
pivot point
at its top. If you strike the board up near the hinge, the pin =
will
experience a force coming from the direction of the strike. =
But if you
strike the board at the bottom, the pin will experience a force in =
the
opposite direction as the board tries to spin about its =
center. There
is a point in between these two where the pin force is neither =
positive nor
negative and the pin will actually see <EM>no</EM> force. This =
is the
center of percussion and is <EM>not</EM> located at the centroid of =
the
board. It's not usually even particularly close.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>It would seem to be a good =
idea to design
the hammer so that the string contact point of the head passes =
through
the center of percussion. That way the maximum amount of
energy would be transmitted to the string...like dropping a =
ball on
it. But I'm not sure if they actually design them that
way.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV>Don A. Gilmore<BR>Mechanical Engineer<BR>Kansas City</DIV>
<DIV> </DIV>
<DIV></FONT>----- Original Message ----- </DIV></DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; =
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<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: =
black"><B>From:</B>
<A title=sarah@gendernet.org =
href="mailto:sarah@gendernet.org">Sarah
Fox</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A =
title=pianotech@ptg.org
href="mailto:pianotech@ptg.org">Pianotech</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Thursday, December =
18, 2003
2:38 AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Cockeyed hammers / =
Don
Gilmore</DIV>
<DIV><BR></DIV>
<DIV><FONT face="Courier New" size=2>Probably any baseball =
player would
know that it's not smart to hit the ball with the very tip of the
bat. It makes for a nasty shock to the hands (and to the =
extent that
the hands are not rigid in space, it takes away from the power =
transferred
to the ball). Why do they do this with piano hammers? =
More to
the point, is this not considered an unneccessary demand to put on =
the
hammer flanges and bushings? Perhaps it's also a drain on
efficiency? Wouldn't it make sense to have some sort of =
asymmetrical
molding whose center of mass is on the far side of the action =
center, so
as to put the center of mass of the hammer assembly closer to the =
line of
strike?</FONT></DIV>
<DIV><FONT face="Courier New" size=2></FONT> </DIV>
<DIV><FONT face="Courier New" size=2>Also, wouldn't it at =
least make sense
to angle the head of the hammer inwards slightly, so that the =
radius to
the head's center of mass is perpendicular to the strike axis =
of the
head? It seems to me that this would help to control wobble =
in the
hammer</FONT></DIV>
<DIV><FONT face="Courier New" size=2></FONT> </DIV>
<DIV><FONT face="Courier New" size=2>I'm not sure I agree =
about part of
the impact being "absorbed" by the pivot. Sure, there would =
be force
against the pivot, but for impact to be absorbed, the pivot would =
need to
be compliant and inelastic. I realize that's true to an =
extent, as
no system is ideal. However, do you think this would be a
substantial drain of energy? It seems to me that the hammer =
felt and
the strings are far more compliant and are closer to the center of =
mass,
such that almost all of the energy would be dissipated there =
(rather than
at the comparatively rigid center). Have you ever measured
this?</FONT></DIV>
<DIV><FONT face="Courier New" size=2></FONT> </DIV>
<DIV><FONT face="Courier New" size=2>Just curious on your =
take. I
can't do much more than scratch my head about this one. If =
the
hammer were perfectly rigid and the center bullet proof and =
noncompliant,
there'd be nothing to worry about. But considering that it =
does the
hokey pokey and shimmies all about... Well, I don't
know.</FONT></DIV>
<DIV><FONT face="Courier New" size=2></FONT> </DIV>
<DIV><FONT face="Courier New" size=2>Peace,</FONT></DIV>
<DIV><FONT face="Courier New"
=
size=2>Sarah</FONT></DIV></BLOCKQUOTE></BLOCKQUOTE></BLOCKQUOTE></BODY>=
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