Good morning all, Thanks to John Davis and Patrick Powers (and a reply off-list) for their suggestions. It is obvious that linkages have been used, but they are quite uncommon, suggesting that the traditional graphical / geometric delineation was simpler. But if you were intending to make a batch of dials, then some form of lay-out jig would be ideal if the effort of constructing the jig was less than marking out in the traditional way for each dial.
Nomograms are one way of calculating the required angles etc., and have a rich history themselves. Two interesting papers on nomograms are by Doerfler: http://myreckonings.com/wordpress/wp-content/uploads/JournalArticle/The_Lost_Art_of_Nomography.pdf (1.3 MB) http://www.myreckonings.com/pynomo/CreatingNomogramsWithPynomo.pdf (2.8 MB) There's also a 1918 book by Joseph Lipka on Internet Archive (https://archive.org/details/graphicalandmec04lipkgoog) (6.2 MB) I confess to not having much of a clue about the mathematics behind either the linkages or the nomograms, but I really like the way they work. Nomograms remind me of those wonderful analogue devices that many of us grew up with: slide rules. If you remember using a slide rule, then you probably also used meccano. And as Noel Ta’Bois demonstrated, meccano would be ideal for constructing linkages, but apparently Lego is now used for such prototyping (see the examples in the paper by Alexander Slocum that I sent earlier (http://web.mit.edu/2.75/fundamentals/FUNdaMENTALs%20Book%20pdf/FUNdaMENTALs%20Topic%204.PDF) (And I am still battling to understand the linkages in my wire strainers, and trying to calculate their mechanical advantage. I thought that this was a rather simple question, but it turned out to be a lot more complex than I thought. Oh well, life’s like that!) Cheers, John John Pickard [email protected]
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