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Research Papers

Coupling Mechanics of Antikythera Gearwheels

[+] Author and Article Information
F. Sorge

DICGIM,  University of Palermo, Viale delle Scienze, 90128 Palermo, Italyfrancesco.sorge@unipa.it

J. Mech. Des 134(6), 061007 (Apr 27, 2012) (10 pages) doi:10.1115/1.4006530 History: Received September 08, 2011; Revised March 22, 2012; Published April 27, 2012; Online April 27, 2012

This paper discusses the gear coupling mechanics of the ancient Antikythera mechanism, among whose distinctive characteristics was the triangular shaping of the teeth. The engagement of the tooth pairs is analyzed in detail, estimating the temporal variation of the speed ratio due to the back and forth shifting of the relative instant center. The admissibility of the theoretical contact points is carefully checked, and the magnitude of the successive tooth collisions is calculated together with the energy losses arising from the particular nature of the coupling. Some interesting results are that only one tooth pair turns out to be active at each time instant and the real path may belong only to the approach or to the recess region entirely, or may split into separate subphases, in approach and in recess, or may even straddle both regions. The occurrence of each of these conditions depends on the average speed ratio (tooth ratio) and the assigned clearance between the wheels. It is also found that the speed oscillation is roughly contained in a ±10% range and the efficiency may reach rather high values, despite the presumable crude finishing of the ancient gearwheels due to the rather rudimentary technology used in the construction of the tooth profiles.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Main fragment of the Antikythera mechanism at the National Archaeological Museum of Athens. (b) Site of the Antikythera wreck. (c) Presumed scheme of the whole planetary mechanism (Ref. [10]).

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Figure 2

Scheme of tooth coupling, z2 /z1  = 2 and β = 30 deg: (a) approach phase; (b) profile matching; and (c) recess phase

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Figure 3

Geometry of the tooth profile

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Figure 4

Meshing diagram α2 (α1 ) indicating admissible and inadmissible contact configurations

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Figure 5

Interference of inactive profiles. The diagram reports an interference-free coupling case, because the plots of the following and preceding profiles are on the left of the inverse motion plot.

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Figure 6

Minimum tooth angle for several clearance values. Example with z1  + z2  = 120.

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Figure 7

(a)–(f) Diagrams of rotation angles for β = 30 deg (Δα1  = 2π/z1 ; Δα1a  + Δα1r  = Δα1 ; a, approach; m, matching; r, recess). (a) and (b) z1  = 48, z2  = 96; (c) and (d) z1  = 96, z2  = 96; (e) and (f) z1  = 96, z2  = 72. (a), (c), and (e) D/Dmin  = 1.01; (b), (d), and (f) D/Dmin  = 1.025.

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Figure 9

(a)–(f) Diagrams of rotation angles for β = 30 deg (Δα1  = 2π/z1 ; Δα1a  + Δα1r  = Δα1 ; a, approach; m, matching; r, recess). (a) and (b) z1  = 48, z2  = 96; (c) and (d) z1  = 96, z2  = 96, (e) and (f) z1  = 96, z2  = 72. (a), (c), and (e) D/Dmin  = 1.01; (b), (d), and (f) D/Dmin  = 1.025. (a) (Δv2⊥ /v1⊥ )r  = 0.1582. (b) (Δv2⊥ /v1⊥ )r  = 0.1457. (c) (Δv2⊥ /v1⊥ )a  = 0.0876, (Δv2⊥ /v1⊥ )r  = 0.0095. (d) (Δv2⊥ /v1⊥ )a  = 0.0696, (Δv2⊥ /v1⊥ )m  = 0.0119. (e) (Δv2⊥ /v1⊥ )a  = 0.1117. (f) (Δv2⊥ /v1⊥ )a  = 0.0682, (Δv2⊥ /v1⊥ )m  = 0.0314.

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Figure 8

Meshing with three subphases

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