<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; = charset=iso-8859-1"> <META content="MSHTML 6.00.2800.1276" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff background=""> <DIV><FONT face=Arial size=2>Don,</FONT></DIV> <DIV><FONT face=Arial size=2>indeed you are right, i did a confusion = with what is also called the "sweet spot". The sweet spot (no reaction forces) coincide with the pivot when the center of = percussion is at the point where the hammer hits the string.</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>Bernhard</FONT></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> Saturday, December 20, = 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>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> <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=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; = BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <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></BLOCK= QUOTE></BODY></HTML>