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[DCSB] Duncan Keenan-Jones (Glasgow) Digital Experimental Archaeology: Hero of Alexandria and his Automata in CAD

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A key claim made by Hero of Alexandria in his work Περί αὐτοματοποιητικῆς (On the making of the Automata, hereafter Automata) is that he has improved upon previously described automata, making them more feasible and more easily reproduced in practice. A three-year, Leverhulme-funded project is testing Hero’s devices and his claims. Working from a fresh analysis of the Greek text, the two automata described by Hero are being built, initially in the computer-aided design (CAD) package SolidWorks, and then in the physical world. A primary objective is to determine to what extent the Automata is a technical treatise, exaggeration/self-aggrandisement and/or a jeu d’esprit.

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[DCSB] Duncan Keenan-Jones (Glasgow) Digital Experimental Archaeology: Hero of Alexandria and his Automata in CAD

  1. 1. Digital Experimental Archaeology: Hero of Alexandria and His Automata in CAD Duncan Keenan-Jones Classics, University of Glasgow Digital Classicist Seminar, Berlin 15th November 2016
  2. 2. Overview • Introduction – Hero & his automata • Project aims – Hero and his predecessors – Libation mechanism • Methods – Computer-aided design (CAD) – Mathematical simulation • Hydraulic simulation • Conclusion
  3. 3. Hero of Alexandria • First century AD • Large number of surviving treatises • Περί αὐτοματοποιητικῆς: (On the making of the) Automata Woodcroft 1851 (wikimedia commons) Schmidt 1899 (wikimedia commons) …ἥτις ἁρμόσει πάσῃ διαθέσει πρὸς τὸ δύνασθαι τὸν προαιρούμενον ἑτέρως διατίθεσθαι ….so that whoever chooses to arrange differently will be able to do it (Hero, Automata 1.1, trans. Grillo)
  4. 4. Hero’s mobile automaton ναοὶ ἢ βωμοὶ σύμμετροι αὐτόματοί τε προσαγόμενοι καὶ κατά τινας ὡρισμένους ἱστάμενοι τόπους, καὶ τῶν ἐνόντων αὐτοῖς ζῳδίων ἕκαστον ἰδίᾳ κινεῖται πρὸς λόγον τὸν κατὰ τὴν προκειμένην πρόθεσιν ἢ μῦθον ἁρμόζοντα, shrines or altars of suitable size, capable of moving forward under their own power and stopping at certain defined locations; and each of the little figures inside them moves by itself in accordance with either the set purpose or the appropriate story (Hero, Automata 1.1, trans. Grillo)
  5. 5. Drive Mechanism
  6. 6. Programmable 6.1 Ἐπειληθείσης γὰρ τῆς σπάρτου περὶ τὴν ἐξελίκτραν ἐπί τι μέρος, περιτεθεῖσα περὶ τὸν Ξ τύλον τὰ ἐναντία ἐπειλείσθω τῇ πρότερον περὶ τὴν ἐξελίκτραν. …πάλιν οὖν καταφερομένη ἡ λεία ἀπειλήσει τὴν πρώτην ἐπείλησιν, καὶ τὸ πλινθίον πορευθήσεται. (2.) εἶτα ἀποστᾶσα ἀπὸ τοῦ τύλου εἰς τὰ ἐναντία ἐπιστρέψει τοὺς τροχούς. καὶ οὕτως ἔσται ἡ ἀποπορεία τοῦ πλινθίου. ἐὰν δὲ βουλώμεθα πορευθὲν τὸ πλινθίον στῆναι…ἐπειλήσαντες τὴν σπάρτον καὶ περιβαλόντες περὶ τὸν τύλον οὐκ εὐθέως τὰ ἐναντία ἐπειλησόμεθα, ἀλλὰ μηρυμάτιον ποιήσαντες καὶ προσκολλήσαντες [ἐπειλήσομεν] ἐπὶ τὴν ἐξελίκτραν καὶ πάλιν τὰ ἐναντία ἐπειλήσαντες ἀποδώσομεν εἰς τὴν λείαν, καὶ ἔσται τὸ προκείμενον. (3.) ἐὰν δὲ καὶ πολλάκις βουλώμεθα πορεύεσθαί τε καὶ ἀποπορεύεσθαι τὸ πλινθίον, πλεονάκις καὶ τὰς ἐναλλὰξ ἐπειλήσεις ποιησόμεθα καὶ τὰ διαστήματα ἡλίκα ἂν προαιρώμεθα καὶ τοὺς τῶν δαιμόνων χρόνους ποιήσομεν διὰ τῶν μηρυμάτων ἡλίκους ἂν προαιρώμεθα. 6.1When the cord has been wound to a certain extent around the cylinder, let it be looped around the knob Ξ and wound around the cylinder in the direction opposite to the preceding one. … So again, the fall of the counterweight will unroll the first winding, and the case will move. (2.)Then, after the cord detaches from the peg, it will turn the wheels in the opposite direction.This is how the case will come back . However, if we want the case, once it has travelled, to stand still… we will wind the cord and put it around the peg without winding it the other way around immediately. Instead, we will form Rossi & Pagano 2011 J.Mech.Design a little bundle, glue it onto the cylinder, wind the cord again contrariwise and attach it to the counterweight, and what has been said before will happen.(3.) If we also want the case to move forward and backward many times, we will make alternate windings more frequently and the intervals between them the size we choose; we will also make the timings of the deities whatever period of time we choose by means of loops of slack.
  7. 7. Libations 13(1)After the sacrifice, milk must spurt from the thyrsus, and wine from the cup. (2) So, this occurs as follows: a pipe is attached under Dionysos’ feet, with two holes near one another on its surface; from these, small pipes extend up into the inner part of Dionysos, one leading to the thyrsus, the other to the cup. (3) Let ΑΒ be the base of Dionysos, ΓΔ the pipe connected to it, Ε and Ζ the holes in the pipe, and ΖΗ and ΕΘ the small pipes stretching from these: ΖΗ to the thyrsus, ΕΘ to the cup. Let ΚΛΜ be a knob (πυρὴν) placed on top of the shrine. Inside this let ΝΞ be a container with a partition ο in the middle. From the container ΝΟ let a pipe ΠΡΣΤ lead to a certain other pipe ΥΦ, fitted tightly (συνεσμηρισμένον) to the pipe ΓΔ and attached from below to the surface on which the shrine rests. (trans. Grillo) σωλὴν (pipe) πυρὴν (knob) ἀγγεῖον (container)
  8. 8. Experimental Strand • Aims – Technical competence presupposed of the reader • How much must be “filled in”? – Practical rather than theoretical? • How feasible? • Had Hero built these automata himself? – Libation mechanism • Could it be constructed? • How impressive in practice?
  9. 9. Hero and his predecessors 1.8 ἐν μὲν οὖν τούτῳ τῷ βιβλίῳ περὶ τῶν ὑπαγόντων γράφομεν ἐκθέμενοι διάθεσιν ποικίλην κατά γε ἡμᾶς, 1.8Therefore, in this book I will write on mobile automata and set forth a complex configuration of my own 5.1 Οἱ μὲν οὖν πρὸ ἡμῶν τὴν ἐπὶ μιᾶς ὁδὸν τῆς τε πορείας καὶ τῆς ἀποπορείας παρέδωκαν ἡμῖν καὶ ταύτην κακοπαθῆ τε καὶ ἐπικίνδυνον· σπάνιον γὰρ ἐπιτυχεῖν κατακολουθοῦντα ταῖς ὑπ’ αὐτῶν ἀναγεγραμμέναις μεθόδοις, ὡς ἔστι φανερὸν τοῖς πεπειραμένοις αὐτῶν. 5.2 ἡμεῖς δὲ ὑποδείξομεν, ὡς ἔστι τὴν ἐπ’ εὐθείας πορείαν καὶ ἀποπορείαν γίνεσθαι εὐκόπως τε καὶ ἀκινδύνως. 5.1 So, our ancestors have handed down to us a way of achieving forward and backward motion along a single line, though troublesome and involving danger; for success is rarely achieved by following the methods they have written down, as is clear to those who have tried them. (2.) I will show that forward and backward motion along a straight line can be performed both easily and without danger…. 20.1 …καὶ γὰρ εὐκόπως καὶ ἀκινδύνως καὶ ξένως παρὰ τὰ πρὸ ἡμῶν ἀναγεγραμμένα κατακεχωρίκαμεν, ὡς ἔστι δῆλον τοῖς πεπειραμένοις τῶν πρότερον ἀναγεγραμμένων. 20.1 …for I have recorded methods which are feasible, riskless and innovative compared to those described by our ancestors, as is clear to anyone who has tested the earlier devices. (Hero, On the making of the Automata, translation F. Grillo)
  10. 10. Methods • Quantitative • Reproducible – Documented, available • 3D CAD Model (SolidWorks) – Design – Simulation • Full scale physical model – Performance testing
  11. 11. 3D CAD Model (SolidWorks) – 8 different configurations composed of 29 sub-assemblies – 185 parts • joined by 249 mates • more than 500 sketches made • the housing or plinthion: 512 features (35 seconds to rebuild) Tap (κλεὶς & ἐπιτονίον, kleis & epitonion)
  12. 12. 1) close reading of Greek text • in concert with textual strand (13.5) ἵν’ οὖν στέγῃ τὰ ὑγρὰ τὸν πρότερον χρόνον, κλεὶς ἔστω ἡ ϙ͵Τ ἀποκλείουσα, ὡς εἴρηται, τὰ ὑγρὰ δι’ ἐπιτονίου τοῦ ͵Α, περὶ ὃ ἀγκύλη σπάρτου περιβεβλήσθω χάλασμα †ἔχουσα καὶ ἀποδεδομένη εἰς τὴν λείαν, ὅπως κατὰ τὸν δέοντα καιρὸν ταθεῖσα ἐπιστρέψῃ τὸ ἐπιτόνιον καὶ ἐνεχθῇ τὰ ὑγρά. (13.5) So, to keep the liquids in beforehand, let ϙ͵τ be a key, which, as stated, shuts the liquids off by means of a stop-cock ͵α; let a loop of cord be put around this, with some slack to it and attached to the counterweight, so that when it has been pulled taut at the appropriate time, it will turn the stopcock and the liquids will be conveyed. (Trans. Grillo)
  13. 13. Κλεὶς & ἐπιτονίον • Κλεὶς – Bar, key – tap (Hero Pneum. 1.24-5, 2.2, 22, 24) • ἐπιτονίον – Handle with a shaft that rotates? • Tuning peg (LSJ) • Inner cylinder of a tap: here andVitr. 9.8.11 :ita uti minus tympanum quemadmodum epitonium in maiore circumagendo arte leniterque versetur – Tap (P. Harr. 1.49.9) – Epitonium: tap (CIL 8.23991; AE 1986.25; 1999.169, Dig. 19.1.17.8, Seneca Epistulae Morales ad Lucilium 86.7.1,Varro, Res Rusticae 3.5.16)
  14. 14. 2) Ancient technologies research • to find culturally appropriate design solutions • Context as close as possible to Hero’s (time and space) • Nemi tap: best preserved Kretzschmer 1960
  15. 15. http://rarehistoricalphotos.com/caligula-nemi-ships-1932/
  16. 16. 3) 3-D CAD modelling Kretzschmer 1960 κλεὶς ἔστω ἡ ϙ͵Τ ἀποκλείουσα, ὡς εἴρηται, τὰ ὑγρὰ δι’ ἐπιτονίου τοῦ ͵Α
  17. 17. 3) 3-D CAD modelling • Location within 3D space reveals omissions and inconsistencies • Location of the tap not specified (13.5) ἵν’ οὖν στέγῃ τὰ ὑγρὰ τὸν πρότερον χρόνον, κλεὶς ἔστω ἡ ϙ͵Τ ἀποκλείουσα, ὡς εἴρηται, τὰ ὑγρὰ δι’ ἐπιτονίου τοῦ ͵Α, περὶ ὃ ἀγκύλη σπάρτου περιβεβλήσθω χάλασμα †ἔχουσα καὶ ἀποδεδομένη εἰς τὴν λείαν, ὅπως κατὰ τὸν δέοντα καιρὸν ταθεῖσα ἐπιστρέψῃ τὸ ἐπιτόνιον καὶ ἐνεχθῇ τὰ ὑγρά. (13.5) So, to keep the liquids in beforehand, let ϙ͵τ be a key, which, as stated, shuts the liquids off by means of a stop-cock ͵α; let a loop of cord be put around this, with some slack to it and attached to the counterweight, so that when it has been pulled taut at the appropriate time, it will turn the stopcock and the liquids will be conveyed. (Trans. Grillo)
  18. 18. 3) 3-D CAD modelling Peleg 1996:34 Casa delTorello, Pompeii (LeanderTouati 2011 Opuscula)
  19. 19. 3) 3-D CAD modelling • Not stated that the cord runs through the columns (Hero not always consistent) 13.7 δεῖ δὲ τοὺς ρσ, ψω σωλῆνας δι᾿ ἑνὸς κιονίσκου τῶν ἐν τῷ ναΐσκῳ κοίλου ὄντος ἐνεχθῆναι ὑπὸ τὴν βάσιν τοῦ ναΐσκου, ὅπως ἀφανεῖς ὑπάρχωσιν. The pipes ΡΣ and ΨΩ must run through one of the shrine’s little columns which is hollow under the shrine’s base, in order to be invisible. (trans. Grillo)
  20. 20. Cod. Marcianus gr. 516, XIII c. codex Guelferbitanus Gudianus gr. 19, XVI c. MS Diagrams Differences?
  21. 21. 3) 3-D CAD modelling • Other pulleys are mentioned: – Bacchants (16.3) – pulleys for cords to turn Dionysos and Nike (13.7-8) • No mention of extra pulleys at bottom • Cords for screws 17.2…αἱ δὲ σπάρτοι ἐκ τοῦ κάτωθεν μέρους ἀνενεχθήσονται εἰς τὴν ΓΔΕΖ χώραν καὶ ἀποδοθήσονται εἰς τὴν λείαν τὴν ἐν τῇ ΑΒΖΕ χώρᾳ διὰ τροχίλου· οὕτως γὰρ ἀφανεῖς ἔσονται πᾶσαι αἱ κάτωθεν ἀναφερόμεναι σπάρτοι. 17.2…the cords from below will be brought upwards into section ΓΔΕΖ and attached to the counterweight inside section ΑΒΖΕ by means of a pulley; for all the cords which are brought up from below will thus be out of sight. (Trans. Grillo)
  22. 22. (3b 3D Printing) • Testing
  23. 23. 4) explanatory 2-D drawings • For construction
  24. 24. 3.1 <Ἔστω> βάσις μῆκος ἔχουσα ὡς πήχεος, πλάτος δὲ ὡς παλαιστῶν τεσσάρων, ὕψος δὲ ὡς παλαιστῶν τριῶν, κυμάτιον ἔχουσα περιτρέχον εἴς τε τὸ ἄνω καὶ τὸ κάτω μέρος. ἐπὶ δὲ τῶν γωνιῶν αὐτῆς ἐφέστηκε κιόνια τέσσαρα, ὕψος μὲν ἔχοντα ὡς παλαιστῶν ηʹ, πλάτος δὲ παλαιστῶν δύο, ἔχοντα ὑποκείμενα σπειρία καὶ τούτοις ἁρμοζούσας κεφαλὰς ἐπικειμένας. ἐπὶ δὲ τῶν κεφαλίων ἐπίκειται καθάπερ ἐπιστύλιον κύκλῳ ὕψος ἔχον ὄγδοον τοῦ κίονος ὅλου, ὡς δακτύλων εʹ. (2.) κατὰ δὲ τῶν ἐπιστυλίων κατέστρωται σανίδια καλύπτοντα τὴν ἐπάνω ἐπιφάνειαν, καὶ περίκειται κύκλῳ κυμάτιον. ἐπὶ δὲ τοῦ καταστρώματος ἐφέστηκε μέσον ναΐσκος στρογγύλος περιφανὴς ἔχων κίονας ἕξ. ἐπὶ δὲ τούτου πυργίον κωνοειδὲς ἐφέστηκεν ἐντεταμένην ἔχον τὴν ἐπιφάνειαν, καθάπερ εἴρηται. (3.) ἐπὶ δὲ τῆς κορυφῆς ἐφέστηκε Νίκη ἐκπεπετακυῖα τὰς πτέρυγας καὶ ἐν τῇ δεξιᾷ χειρὶ στέφανον κατέχουσα. ἐν δὲ μέσῳ τοῦ ναΐσκου ζῴδιον Διονύσου ἐφέστηκεν ἐν μὲν τῇ ἀριστερᾷ χειρὶ θύρσον κατέχον, ἐν δὲ τῇ δεξιᾷ σκύφον. παρακαθέζεται δὲ πανθηρίσκος πρὸς τοῖς τοῦ Διονύσου ποσίν. (4.) ἐν δὲ τοῖς ἔμπροσθεν καὶ τοῖς ὄπισθεν μέρεσι τοῦ Διονύσου ἐπὶ τοῦ καταστρώματος βωμὸς ἐπίκειται ἔχων ξύσματα τῶν σανίδων τεκτονικὰ ξηρὰ ὥστε εὔκαυστα εἶναι. κατὰ δὲ κίονα τῶν ἐν τῷ ναΐσκῳ τοῦ Διονύσου παρέστηκεν ἐκτὸς τοῦ ναΐσκου Βάκχη διεσκευασμένη ὡς ἄν τις προαιρῆται. 3.1 Let there be a base approximately one cubit long, about four palms wide and nearly three palms high, with a small wavy moulding running around both its upper and lower part. Four little columns, roughly eight palms high and two palms wide, stand on the corners, with little base-mouldings placed at the bottom and capitals in line with them placed on the top. On the capitals lies a kind of entablature running all around and one-eighth the height of the entire column, approximately five fingers. (2.) On the entablature are laid small boards covering its upper surface, and a small moulding runs all around. On the covering stands prominently, in the middle, a circular little shrine with six pillars. On this stands a little cone-shaped dome with a projecting surface , as stated. (3.) On the peak stands a Nike with spread wings and holding a wreath in her right hand. In the middle of the shrine stands a figure of Dionysos holding a thyrsus in his left hand and a cup in his right.A little panther sits by Dionysos’ side at his feet. (4.) In the spaces before Dionysos and behind him, on the surface, is an altar with shavings made from working the boards, dry enough to burn easily. Outside Dionysos’ shrine, at each column, stands a Bacchante arrayed in whatever way one chooses.
  25. 25. (4.4) καὶ οὕτως τέλος ἕξει ἡ ἐπίδειξις. τοῖς δὲ εἰρημένοις μέτροις ἐχρησάμεθα ἀναγκαίως· μειζόνων γὰρ γενηθέντων ὑπόνοιαν ἕξει τὸ ὅραμα ὡς ἐντός τινος ταῦτα δημιουργοῦντος. (4.4) I employed the mentioned dimensions out of necessity; for the sight, were they any larger, would arouse suspicion as though someone was contriving these movements from the inside. • Performance insights from modelling – Standing rather than reclining – Trade-off between counterweight fall and visibility
  26. 26. Modelling Insights – Poor visibility for lower observers Theatrum tectum (covered theatre, Pompeii)
  27. 27. Simulation • Dimensions • +Vitruvian orders • All mechanisms • In SolidWorks • Provide data for simulation
  28. 28. Pipe size 13.7 δεῖ δὲ τοὺς ρσ, ψω σωλῆνας δι᾿ ἑνὸς κιονίσκου τῶν ἐν τῷ ναΐσκῳ κοίλου ὄντος ἐνεχθῆναι ὑπὸ τὴν βάσιν τοῦ ναΐσκου, ὅπως ἀφανεῖς ὑπάρχωσιν. The pipes ΡΣ and ΨΩ must run through one of the shrine’s little columns which is hollow under the shrine’s base, in order to be invisible. (trans. Grillo)
  29. 29. 14.5 mm (ext. dia., Williams 1893 Quart. Musical Rev.) (Pompeii, www.gettyimages.co.uk/detail/illust ration/italy-naples-museo- archeologico-nazionale-sistrums- organ-stock-graphic/148352858 ) • Spouts with 5mm orifices (Pompeii Herculaneum) • Lead regularly beaten into sheets of 2-3 mm (Dessales 2013, 190–1, 197-9) Wright 2007 Interdisciplin.Sci.Rev. 1 mm thick Smallest ancient pipes? Pipes can’t be bigger, or plausibly smaller
  30. 30. Hydraulic simulation of adequate tank size 1. Bernoulli’s equation: obtain hL(friction head losses) by assuming v2 < v2 without friction loss – p1/γ + z1 + v1 2/2g – hL = p2/γ + z2 + v2 2/2g – P: pressure, z: elevation, g: gravity,, γ : specific weight 2. Calculate initial f (friction factor) using Swamee and Jain correlation (assumes turbulent but close) 3. Darcy-Weisbach equation + minor losses (K): recalculate v – hL = (∑K + fL/D)v2/2g – D (pipe dia), L (pipe length)
  31. 31. Hydraulic simulation of adequate tank size 1. Darcy-Weisbach equation + minor losses (K): recalculate v – hL = (∑K + fL/D)v2/2g – D (pipe dia), L (pipe length) 2. Recalculate f: f = 64/Re (laminar flow), others for turbulent (Colebrook 1939 J.Inst.Civ.Eng.) 3. Repeat from 2 with recalculated f, v until convergence 4. Calculate time to empty tank from Q = vA
  32. 32. 1.73 m/s 1.22 x 10-5 m3/s 4.19 s to empty ~ 2.1 s per performance Hydraulic simulation of adequate tank size • Ancient hL greater? – Nemi tap: smooth • Physical testing • How big could a πυρὴν be? – Nut, (olive) stone, grain, gem (LSJ) – Round head of a probe 1.30 m/s 9.12 x 10-6 m3/s 5.56 s to empty ~ 2.78 s per performance
  33. 33. codex Guelferbitanus Gudianus gr. 19, XVI c. MS Diagrams
  34. 34. Schmidt
  35. 35. Conclusions • 3D Modelling reveals silences in Hero’s text – Lack of pulleys in basis for rectangular motion notable – Had Hero built the rectangular motion? • Data from Hero’s text modelled in 3D CAD are sufficient for a constrained hydraulic simulation of the libation mechanism of Hero’s mobile automaton • Suggests larger tank than could probably fit in the puren • Further testing in physical model
  36. 36. The End

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