Capstan angle

[Ric Brekne]

Grin...

Hi Phil and Dave.  I have to admit to firing off my last just a tad too 
quick. I offered support for David's point about the angled capstan 
making no difference which in fact I do not agree with.  My point went 
to the height of the capstan.  I read Davids post too quickly and 
assumed we were on again about whether or not one had to measure down 
from the top of the keyfront to the balance rail point, and then up 
again to the capstan top in order to get the key ratio. That is what I 
take issue with, as one can in fact analyse the whole thing as a 
straight line with the key horizontal.  Off horizontal simply alters the 
effective arm lengths, something that is also clearly shown on that 
applet I offered a link to.

Angling the capstan changes the distance between the input force and the 
fulcrum and of course alters the key ratio.  If that is difficult to 
think through... just think about a 5 inch extention in the shape of an 
"L" on on the front of the key.    No doubt playing way on on the end of 
that key is going give one more leverage... yes.

Sorry for the confusion Phil.

Cheers
RicB



Well, it's two against one, so you guys must be right.  The 
capstan and key form one solid unit.  This unit is rotating about a 
fixed point.  An applied force on this unit will create a torque 
about that fixed point.  What determines this torque is the distance, 
in a direction normal to the force, to the rotation point, multiplied 
by the force.  See the link that you gave for clarification.  If a 
vertical force of 10 lbs is applied at the top of the capstan, which 
is 5 inches horizontally from the balance point, then the torque at 
the balance point produced by this force is 50 in-lbs (and the torque 
required on the front end of the key to balance this is also 50 
in.-lbs - so, if your measuring point is 10 inches from the balance 
point, then you have a downweight of 5 lbs).  The angle of the 
capstan, or where it touches the key,  has nothing to do with it.
    If you want to take the capstan itself as a free body, then if the 
capstan is vertical and a vertical force of 10 lbs is applied to the 
top of it, then the reacting force at the key contact point is a 
vertical force of 10 lbs.  The capstan will in turn apply this 10 lbs 
force to the key.  Torque about the balance point is 10 lbs x 5 
inches = 50 in-lbs.

................... snip