Cockeyed hammers / Don Gilmore

[Don A. Gilmore]

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Bernhard:

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.

Don A. Gilmore
Mechanical Engineer
Kansas City
  ----- Original Message -----=20
  From: Bernhard Stopper=20
  To: Pianotech=20
  Sent: Thursday, December 18, 2003 6:57 PM
  Subject: Re: Cockeyed hammers / Don Gilmore


  Don, Sarah
  my last post has to be corrected(fat cursive):

  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.=20
  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 the center =
of percussion coincides with the pivot, when hammer shank length x is =
calculated by the formula x=3DI/(m*y) with I=3D moment of inertia, =
m=3Dmass, y=3Ddistance pivot - center of mass

  regards,

  Bernhard
    ----- Original Message -----=20
    From: Don A. Gilmore=20
    To: Pianotech=20
    Sent: Friday, December 19, 2003 12:22 AM
    Subject: Re: Cockeyed hammers / Don Gilmore


    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.

    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.

    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 no force.  This is the center of percussion and is =
not located at the centroid of the board.  It's not usually even =
particularly close.

    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.

    Don A. Gilmore
    Mechanical Engineer
    Kansas City

    ----- Original Message -----=20
      From: Sarah Fox=20
      To: Pianotech=20
      Sent: Thursday, December 18, 2003 2:38 AM
      Subject: Cockeyed hammers / Don Gilmore


      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?

      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

      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?

      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.

      Peace,
      Sarah
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