Re: Using linkages to draw curves on sundials
Hi all, I just receveid a message from Gigi Ghia (luigi.g...@gmail.com), an italian gnomonist, about this matter. I translate for him. Gigi reports a website of Francis Ziegeltrum, where he shows a mechanic device to reproduce the ‘8 curve’, as it is called by french gnomonists, obviously a bit approximate. http://francis.ziegeltrum.perso.sfr.fr/octographe.html The same author published an articol on Cadran Info n.29 (2014) of the french gnomonic association. ciao Fabio Fabio Savian fabio.sav...@nonvedolora.it www.nonvedolora.eu Paderno Dugnano, Milano, Italy 45° 34' 9'' N, 9° 9' 54'' E, GMT +1 (DST +2)--- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Using linkages to draw curves on sundials
Hi Tony, Thanks for your note on Neville Shute and the engineering principle that you cannot push a rope (or chain). I have read and reread all of Neville Shute's books, the most famous being "On the Beach". My favourite is "No Highway" about a boffin studying metal fatigue in aircraft. His actions causing a hard grounding of the plane was based on based his esoteric research. This book was written around the time of the Comet crashes due to metal fatigue and the stress risers in the corners of the square windows in the Comet. At the NASS conference in Portland ME, we were described in the media as "boffins". I took no offence but recognized it as an apt description recognizing that our arcane abstruse interest sometimes leaves people bemused. Regards, Roger Bailey From: tonylindi...@talktalk.net Sent: Friday, September 09, 2016 1:58 AM To: john.pick...@bigpond.com ; Sundial List Subject: Re: Using linkages to draw curves on sundials Hi John, This query immediately brought to mind an interesting aside from the autobiography of Neville Norman, who wrote novels under the pen-name of Neville Shute, as he did not wish to trivialize his main profession as an aeronautical engineer. Working in the team of Dr. Barnes Wallis designing the airship R100, (the successful commercial opponent of the fatal government-controlled R101), he was given the job of stressing its 16-sided lightweight polyagonal frames, held rigid by wires. Working in pairs, to avoid careless inputs to their mechanical calculators, they would take many weeks to assess the stress pattern of each assembly of girders and wires based on an initial assumption. When, after much tedious labour, they found that one of the wires based on their first proposal was 'in compression' (have you ever tried pushing a chain?) he said "We would moisten our lips and begin all over again". Electronic computers would have achieved the ultimate solution to this problem in microseconds both almost within my lifetime. http://www.century-of-flight.net/Aviation%20history/coming%20of%20age/R101%20disaster.htm Original Message From: john.pick...@bigpond.com Date: 07/09/2016 0:14 To: "Sundial List"<sundial@uni-koeln.de> Subj: Using linkages to draw curves on sundials Good morning, While researching mechanisms of wire strainers used to tighten wires in fences, and trying to find the theoretical mechanical advantages of the different mechanisms, the first thing I learned was that "linkages" are the key to many of them. There's a whole branch of mechanics devoted to the theory of these things which involve a zillion combinations of pivots and links to achieve various purposes, usually to transmit motion in a specific manner. The best explanation I found was Slocum, A. (2008). Fundamentals of design. Topic 4. Linkages (http://web.mit.edu/2.75/fundamentals/FUNdaMENTALs%20Book%20pdf/FUNdaMENTALs%20Topic%204.PDF). 3.3 MB But my curiosity lead me further, to a more mathematical treatment. Unfortunately and for unknown reasons, the Jefferson Lab Library has removed the title page. Bizarre! I contacted the library and they gave me the full title etc. Svoboda, A. (1948). Computing mechanisms and linkages. MIT Radiation Laboratory Series, Volume 27. New York, McGraw-Hill. (https://www.jlab.org/ir/MITSeries/V27.PDF) (CAREFUL: 40.8 MB) Among other things, this book shows how you can use mechanical linkages of various forms to draw the curves of mathematical functions. And seeing that the curves on sundials are all defined by equations, I was wondering if anyone knows of any attempts to make a mechanical device of links and pivots specifically for generating sundial equations, and thus drawing sundials? It seems to be a feasible but complicated way of doing it, with some serious mathematics behind the linkages. I don't include sundial rulers in this, as they are not physically linked and pivotted. Similarly, I don't include CNC machining as this involves moving the tool / work using a pre-programmed series of x, y and z coordinates. And of course, 3-D printing is out. (And I still haven't figured out what sort of linkages are used in the wire strainers I'm studying!) Cheers, John John Pickard john.pick...@bigpond.com --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Using linkages to draw curves on sundials
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 john.pick...@bigpond.com --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Using linkages to draw curves on sundials
Hi John, I can offer: J. Davis: ‘Alightweight laser trigon for layout of sundial lines’, BSS Bulletin, 11(iii), pp.144-146, (1999) which included drawing analemmic hour lines, and for an earlier purely mechanical example (built of Meccano!) there was Noel Ta'Bois: 'Sundial Line Drawing Jig', BSS Bulletin 92.3 pp 28-30 (1992). Regards, John DDr J Davis Flowton Dials http://www.flowton-dials.co.uk/ BSS Editor http://sundialsoc.org.uk/publications/the-bss-bulletin/ From: John Pickard <john.pick...@bigpond.com> To: Sundial List <sundial@uni-koeln.de> Sent: Wednesday, 7 September 2016, 1:14 Subject: Using linkages to draw curves on sundials Good morning, While researching mechanisms of wire strainers used to tighten wires in fences, and trying to find the theoretical mechanical advantages of the different mechanisms, the first thing I learned was that "linkages" are the key to many of them. There's a whole branch of mechanics devoted to the theory of these things which involve a zillion combinations of pivots and links to achieve various purposes, usually to transmit motion in a specific manner. The best explanation I found was Slocum, A. (2008). Fundamentals of design. Topic 4. Linkages (http://web.mit.edu/2.75/fundamentals/FUNdaMENTALs%20Book%20pdf/FUNdaMENTALs%20Topic%204.PDF). 3.3 MB But my curiosity lead me further, to a more mathematical treatment. Unfortunately and for unknown reasons, the Jefferson Lab Library has removed the title page. Bizarre! I contacted the library and they gave me the full title etc. Svoboda, A. (1948). Computing mechanisms and linkages. MIT Radiation Laboratory Series, Volume 27. New York, McGraw-Hill. (https://www.jlab.org/ir/MITSeries/V27.PDF) (CAREFUL: 40.8 MB) Among other things, this book shows how you can use mechanical linkages of various forms to draw the curves of mathematical functions. And seeing that the curves on sundials are all defined by equations, I was wondering if anyone knows of any attempts to make a mechanical device of links and pivots specifically for generating sundial equations, and thus drawing sundials? It seems to be a feasible but complicated way of doing it, with some serious mathematics behind the linkages. I don't include sundial rulers in this, as they are not physically linked and pivotted. Similarly, I don't include CNC machining as this involves moving the tool / work using a pre-programmed series of x, y and z coordinates. And of course, 3-D printing is out. (And I still haven't figured out what sort of linkages are used in the wire strainers I'm studying!) Cheers, John John Pickard john.pick...@bigpond.com --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Re: Using linkages to draw curves on sundials
Hi John, Would you include Nomography in such a study? After all nomograms might (just) be considered as mechanical devices Patrick From: John Pickard Sent: Wednesday, September 07, 2016 1:14 AM To: Sundial List Subject: Using linkages to draw curves on sundials Good morning, While researching mechanisms of wire strainers used to tighten wires in fences, and trying to find the theoretical mechanical advantages of the different mechanisms, the first thing I learned was that "linkages" are the key to many of them. There's a whole branch of mechanics devoted to the theory of these things which involve a zillion combinations of pivots and links to achieve various purposes, usually to transmit motion in a specific manner. The best explanation I found was Slocum, A. (2008). Fundamentals of design. Topic 4. Linkages (http://web.mit.edu/2.75/fundamentals/FUNdaMENTALs%20Book%20pdf/FUNdaMENTALs%20Topic%204.PDF). 3.3 MB But my curiosity lead me further, to a more mathematical treatment. Unfortunately and for unknown reasons, the Jefferson Lab Library has removed the title page. Bizarre! I contacted the library and they gave me the full title etc. Svoboda, A. (1948). Computing mechanisms and linkages. MIT Radiation Laboratory Series, Volume 27. New York, McGraw-Hill. (https://www.jlab.org/ir/MITSeries/V27.PDF) (CAREFUL: 40.8 MB) Among other things, this book shows how you can use mechanical linkages of various forms to draw the curves of mathematical functions. And seeing that the curves on sundials are all defined by equations, I was wondering if anyone knows of any attempts to make a mechanical device of links and pivots specifically for generating sundial equations, and thus drawing sundials? It seems to be a feasible but complicated way of doing it, with some serious mathematics behind the linkages. I don't include sundial rulers in this, as they are not physically linked and pivotted. Similarly, I don't include CNC machining as this involves moving the tool / work using a pre-programmed series of x, y and z coordinates. And of course, 3-D printing is out. (And I still haven't figured out what sort of linkages are used in the wire strainers I'm studying!) Cheers, John John Pickard john.pick...@bigpond.com --- https://lists.uni-koeln.de/mailman/listinfo/sundial --- https://lists.uni-koeln.de/mailman/listinfo/sundial
Using linkages to draw curves on sundials
Good morning, While researching mechanisms of wire strainers used to tighten wires in fences, and trying to find the theoretical mechanical advantages of the different mechanisms, the first thing I learned was that "linkages" are the key to many of them. There's a whole branch of mechanics devoted to the theory of these things which involve a zillion combinations of pivots and links to achieve various purposes, usually to transmit motion in a specific manner. The best explanation I found was Slocum, A. (2008). Fundamentals of design. Topic 4. Linkages (http://web.mit.edu/2.75/fundamentals/FUNdaMENTALs%20Book%20pdf/FUNdaMENTALs%20Topic%204.PDF). 3.3 MB But my curiosity lead me further, to a more mathematical treatment. Unfortunately and for unknown reasons, the Jefferson Lab Library has removed the title page. Bizarre! I contacted the library and they gave me the full title etc. Svoboda, A. (1948). Computing mechanisms and linkages. MIT Radiation Laboratory Series, Volume 27. New York, McGraw-Hill. (https://www.jlab.org/ir/MITSeries/V27.PDF) (CAREFUL: 40.8 MB) Among other things, this book shows how you can use mechanical linkages of various forms to draw the curves of mathematical functions. And seeing that the curves on sundials are all defined by equations, I was wondering if anyone knows of any attempts to make a mechanical device of links and pivots specifically for generating sundial equations, and thus drawing sundials? It seems to be a feasible but complicated way of doing it, with some serious mathematics behind the linkages. I don't include sundial rulers in this, as they are not physically linked and pivotted. Similarly, I don't include CNC machining as this involves moving the tool / work using a pre-programmed series of x, y and z coordinates. And of course, 3-D printing is out. (And I still haven't figured out what sort of linkages are used in the wire strainers I'm studying!) Cheers, John John Pickard john.pick...@bigpond.com --- https://lists.uni-koeln.de/mailman/listinfo/sundial
