HI Frank Excellent work Frank, & thank you! for taking the time & spending your passionate curiousity on this question. How very cool! Well I think you have proved something that we were all looking at & that is increasing ratio changes thru the range of motion which was the initial premise, and isn't the wippen & key ever arms changing lengths un-proportionally the key to the puzzle? I read it twice & it still sounds like the angled arrangement is an advantage. I'd love a clearer image of the drawing enclosed. Not sure I'm getting all of this yet. I'll keep looking. What if most of the range of motion happened 3/4 below the magic line? Thanks Dale Erwin -----Original Message----- From: pianoguru at cox.net To: pianotech at ptg.org Sent: Mon, 23 Mar 2009 8:20 pm Subject: [pianotech] Point of contact between capstan and wippen heel 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 hread, but it stimulated a lot of rethinking and research on my part. Not to eat a dead horse, but I think I have something new to add, for those who are nterested. In fact, what I found pretty much contradicts everything that had een said on the subject, including what I had said. To invoke the term “involute” with respect to the relationship between the ovement of the capstan and the wippen can be nothing more than metaphorical. till, there are=2 0some surprising similarities. The inescapable fact is that the rown of the capstan is a true arc, not an involute curve, and likewise for any adius of the wippen heel. The wippen could be calculated to produce an nvolute shaped if there were any reason to do so, but not the capstan, since it ust be free to turn to any degree of rotation. It seems to make intuitive sense that the line of excursion of the point of ontact would be centered between the arcs representing the movement of the ippen and the movement of the capstan. If this were true, it would also be rue that the length of one lever arm would get shorter as it moves up to the agic line, then lengthen as it moves above the magic line, and the reverse ould 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 ine, but it is not centered between the arcs. Being a straight line mimics the nvolute curve. This line would not be centered even if the lever arms were of qual length and the arcs of equal radius. The attached file shows the actual xcursion of the contact points. The determination of this line is derived from D computer models of the lever arms in 3D modeling software, with the parts oved to a half dozen positions and a line plotted between the points of contact t each of these positions. I cannot explain why it is a straight line, or why t is at an unexpected angle to the magic line. I can only say that the model roves to my satisfaction that it is what is illustrated. The key lever arm continues to lengthen throughout its full range of motion, and he wippen lever arm continues to shorten throughout its full range of motion. hat happens when the motion crosses the magic line is that the key lever arm ontinues to lengthen but at a faster rate, while the wippen lever arm continues o shorten at a slower rate. This would be true well beyond the normal range of otion. In fact, the motion would have to extend 17mm below the magic line or mm above the magic line before the lengthening or shortening will reverse irection. The lengthening of the key lever arm is exactly the same amount as the wippen is hortened, 0.69mm in the most typical configuration. Still the rate of change n length is faster on one side of the magic line than the other, which means hat the contact points, relative to each other do move apart and then together, ven though the overall movement through the range of motion is consistently in he direction of lengthening the key lever and shortening the wippen lever. his also confirms that there is sliding between the surfaces, even though they ach end up the same distance from their origins. In one configuration the capstan and wippen heel were tilted forward, to make he arcs tangent with the magic line. This increased the change to 0.71mm. ilting the capstan=2 0the opposite direction, away from the front of the keys, educes the change to about 0.61mm. This is probably not enough difference to ake a difference, but that is not to say that there might be an advantage to ilting the capstan in terms of staying closer to where you want to be in spite f action wear over time. If you depart from having the magic line at half blow, the changes in lever arm engths are no longer the same for the key lever and the wippen lever. If the ey travel ends at the magic line, the key lever is lengthened by 0.56mm, while he wippen lever is shortened by 0.82mm. If the key travel begins at the magic ine, the key lever lengthens by 0.82mm, while the wippen lever shortens by .54mm. It’s too early to draw too many conclusions from this data. I’m just putting it ut there to solicit reactions to it. Frank Emerson [Image Removed] -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/pianotech_ptg.org/attachments/20090324/a30de24f/attachment-0001.html>
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