Frank, Thanks for sharing your work with us. What shape and angle of capstan and wippen heel did you use? Got a drawing that shows them? thanks Mike pianoguru at cox.net wrote: > There was a thread over the last week or so, with the subject line “capstain/wippen angle, was: key position at rest.” I contributed to this thread, but it stimulated a lot of rethinking and research on my part. Not to beat a dead horse, but I think I have something new to add, for those who are interested. In fact, what I found pretty much contradicts everything that had been said on the subject, including what I had said. > > To invoke the term “involute” with respect to the relationship between the movement of the capstan and the wippen can be nothing more than metaphorical. Still, there are some surprising similarities. The inescapable fact is that the crown of the capstan is a true arc, not an involute curve, and likewise for any radius of the wippen heel. The wippen could be calculated to produce an involute shaped if there were any reason to do so, but not the capstan, since it must be free to turn to any degree of rotation. > > It seems to make intuitive sense that the line of excursion of the point of contact would be centered between the arcs representing the movement of the wippen and the movement of the capstan. If this were true, it would also be true that the length of one lever arm would get shorter as it moves up to the magic line, then lengthen as it moves above the magic line, and the reverse would be true of the other lever arm. However, that is not what happens. > > The line representing the excursion of the point of contact is indeed a straight line, but it is not centered between the arcs. Being a straight line mimics the involute curve. This line would not be centered even if the lever arms were of equal length and the arcs of equal radius. The attached file shows the actual excursion of the contact points. The determination of this line is derived from 3D computer models of the lever arms in 3D modeling software, with the parts moved to a half dozen positions and a line plotted between the points of contact at each of these positions. I cannot explain why it is a straight line, or why it is at an unexpected angle to the magic line. I can only say that the model proves to my satisfaction that it is what is illustrated. > > The key lever arm continues to lengthen throughout its full range of motion, and the wippen lever arm continues to shorten throughout its full range of motion. What happens when the motion crosses the magic line is that the key lever arm continues to lengthen but at a faster rate, while the wippen lever arm continues to shorten at a slower rate. This would be true well beyond the normal range of motion. In fact, the motion would have to extend 17mm below the magic line or 9mm above the magic line before the lengthening or shortening will reverse direction. > > The lengthening of the key lever arm is exactly the same amount as the wippen is shortened, 0.69mm in the most typical configuration. Still the rate of change in length is faster on one side of the magic line than the other, which means that the contact points, relative to each other do move apart and then together, even though the overall movement through the range of motion is consistently in the direction of lengthening the key lever and shortening the wippen lever. This also confirms that there is sliding between the surfaces, even though they each end up the same distance from their origins. > > In one configuration the capstan and wippen heel were tilted forward, to make the arcs tangent with the magic line. This increased the change to 0.71mm. Tilting the capstan the opposite direction, away from the front of the keys, reduces the change to about 0.61mm. This is probably not enough difference to make a difference, but that is not to say that there might be an advantage to tilting the capstan in terms of staying closer to where you want to be in spite of action wear over time. > > If you depart from having the magic line at half blow, the changes in lever arm lengths are no longer the same for the key lever and the wippen lever. If the key travel ends at the magic line, the key lever is lengthened by 0.56mm, while the wippen lever is shortened by 0.82mm. If the key travel begins at the magic line, the key lever lengthens by 0.82mm, while the wippen lever shortens by 0.54mm. > > It’s too early to draw too many conclusions from this data. I’m just putting it out there to solicit reactions to it. > > Frank Emerson > > ------------------------------------------------------------------------ >
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