of spline and catenary

[gordon stelter]

Hi Terry,
    I've long pondered the feasibility of what I
imagine to be the best sort of arcing for ribs; that
which would provide the apogee directly under the
bridge line.
     How's this: Build a frame the same shape as the
piano case. Lay in plexiglas strips in the rib
position, but extending out the frame sides for
slippage. Then screw trhe bridge to the plexiglas
strips and load, and using a  very long one of those
thingamabobs with all the little metal rods ( used to
copy moldiungs and other complex shapes ) record the
arcing as it is created. 
      Now, cut a custom set of cauls, or rinbs,
accordingly.
     Send me royalties.
     Thump 
    
--- Farrell <mfarrel2@tampabay.rr.com> wrote:
> No answers for you Ron, but a confirmation. When I
> was trying to figure out
> how to form the various arcs for my rib-to-panel
> clamps, I took a piece of
> one-inch square aluminum tube and bent it as you
> describe below. I used
> aluminum because I know no piece of wood will be
> perfectly (or even nearly
> so) consistent in its composition, and thus bending
> properties, along a
> length (aluminum will have more consistent
> properties throughout). I was
> disappointed right at the get-go when I observed
> that indeed the curvature
> was tighter in the center and tapered out to almost
> no bend at the ends.
> What I ended up doing was every several inches along
> the curve I measured
> and forced the aluminum section into the desired
> curve.
> 
> But your question remains unanswered: just what kind
> of curve results from
> this bending technique, and what are the
> implications of ribs with such a
> curvature?
> 
> Terry Farrell
> 
> ----- Original Message ----- 
> From: "Ron Nossaman" <RNossaman@cox.net>
> To: "Pianotech" <pianotech@ptg.org>
> 
> > I did something similar here, only without the
> clamped end and distributed
> > load examples. What I was wondering is what curve
> was described when you
> > bent a piece of uniform cross section wood. There
> doesn't seem to be a
> name
> > for it. The rebuilders who are cutting rib crown
> in a jig which clamps the
> > center of the rib, wedging the ends out to form
> the curve are obviously
> not
> > cutting a constant radius curve in their ribs. As
> far as I know, this is
> > neither good, nor bad. It just is. But what is
> this curve?  It's close to
> a
> > catenary, but flatter at the ends. As this rib is
> cut by the table saw,
> > these flatter curves at the end will tend to
> spring and bend more as wood
> > is cut away, changing the saw cut line and
> producing a crown more nearly
> > parabolic or catenary than was the case before the
> cut was taken. The
> > bending response of the rib changing as the cut is
> made also means that
> the
> > crown profile will be asymmetric because half of
> the crown will be cut
> from
> > the outside to the center, and half from the
> center out - unless the cut
> is
> > done in two passes, with a bulk removal pass, and
> a light final pass.
> >
> > I'm just trying to figure out approximately what
> is actually being
> produced
> > here.
> >
> > Ron N
> 
> 
> _______________________________________________
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https://www.moypiano.com/resources/#archives


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