At 08:58 -0500 6/1/10, jiimialeggio wrote: >Unless I'm completely missing something, the reason the right side >of the equation can't make proper sense with the left is that the >action actually has a variable ratio. 5.0 is @ half but considerable >higher at the beginning of the stroke, fallingand 0 at letoff. As I >see that equation, it is assuming the ration @ 1/2 stroke is >constant throughout the entire kestroke=not true. Action rations >seem to me to be confusing designations, since you really are >talking either about an average (I don't see that factored into the >left side), or a fictitious static number. No? The class handout posted by Joe, misleadingly entitled "Action Geometry: Truth and Consequences", has no truth in it at all and the consequence will be that any reliance on it will lead to wrong results. No accurate expression of the "action" ratio can be obtained without taking into account the angles involved and the "losses" due to circular motion and that requires the application of simple, and sometimes not quite so simple, trigonometry. The result thus calculated will differ _significantly_ from the result derived from this uselessly simplified equation. Generally speaking, the traditional ratio in European actions, whether upright or grand was established long ago at 5:1, that is to say that for a _perpendicular_ depression of the front of the key of 10 millimetres the _perpendicular_ displacement of the nose of the hammer will be 50 mm if escapement is disabled. Certainly there are variations in the velocity ratio at different points in the touch, but it is the ratio of total distances travelled by hammer and key that gives the ratio in question. A well set-up keyboard/action unit needs to have all the centres/fulcrums and "contacting profiles" (places where arcs should coincide at some point in the leverage) in precisely the relative positions dictated by the keyboard/action design. Any deviation from these positions will not only make a difference to the ratio but also, in most cases lead to friction, difficultied in regulation and a less than optimal touch. Suppose that the front lever of the key (top front of ivory to centre of balance point is 2 and the back lever (centre of balance point to mid-point of capstan top) is 1, then following the logic of the above handout the profile (capstan top) will move up 5mm for 10mm of touch-depth. This is nonsense, and the same facile pseudo-geometry is applied to every subsequent stage in the leverage, with the result that an actual ratio of, say, 5:1 will be grossly overestimated. JD
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