Background Information

Some Technical Details

The gears in the mechanism

The gearwheels are referenced by the shaft they are mounted on.

shaft	0	1	2	3	4	5	6	remarks
A		20						drive shaft for simulation
B_0_1_2	20	20	64					Year
B_3				32				Moon
C		38	48
D		24	127
E_1_6		32					50
E_2_5			32			50
E_3_4				223	188
F		53	30
G		54	20					Saros
H		60	15
I		60						Exeligmos
L		38	53
M		96	15	27
N		53	15					Metonic
P		60	12
O		60						Callippic
Q	20
K		50	50					Moon Phase Sphere

total drive train

---> A1 x B1 -------------------------------------------------------------------------------> Year
          =
          =
          B2 x L1             P2 x O1 ------------------------------------------------------> Callippic   
          =    L2 x M1   N2 x P1
          =         M2 x N1 ----------------------------------------------------------------> Metonic x 5
          =         =
          =         M3 x E3
          =              E4 x F1
          =               |   F2 x G1 ------------------------------------------------------> Saros x 4
          =               |        G2 x H1
          =               |             H2 x I1 --------------------------------------------> Exeligmos
          =               |        
          =               |             a)
          =               |          +------+     b)
          =                --------> |b     |  +------+    
          B2 x C1                    |      |  | pin  |
          =    C2 x D1               |   a-b|--| and  |-- K2 x E6
          =         D2 x E2          |      |  | slot |        E1 x B3 ---------------------> Moon
          =              E5 x K1 --> |a     |  +------+                  |
          =                          +------+                            |       c)
          =                                                              |    +------+
          =                                                               --> |a     |
          =                                                                   |      |
          =                                                                   |   a-b|------> Lunar Phase    
          =                                                                   |      |        Sphere
          B0 x Q1 ----------------------------------------------------------> |b     |   
                                                                              +------+

legend

F1 F2: Wheels F1 and F2 are mounted on the same shaft
M2 = M3: Wheels M2 and M3 are mounted on the same shaft
M3 x E3: Wheel M3 drives wheel E3
I1 ---> Exeligmos: Wheel I1 drives the Exeligmos pointer
The Exeligmos pointer is mounted on shaft I

notes:

a): Wheels K1 and K2 are mounted on E3 and E4.
Subtract the (slower) rotation of E3+E4 from the faster rotation of K1.
b): The pin-and-slot mechanism that varies the rotation of the moon pointer and the lunar phase sphere.
c): The bevel gear to drive the lunar phase sphere is mounted on top of the slower rotating year pointer.
Subtract it from the rotation of the moon pointer.

the pin and slot mechanism

The transfer function of the pin and slot mechanism is:

out_ang = atan2 ( r_pin * sin ( in_ang ), r_pin * cos ( in_ang ) - exen )

in_ang: the angle of wheel K1 (the input)
out_ang: the angle of wheel K1 (the output)
excen: exentricity of the shafts of K1 and K2
r_pin: distance between the center of wheel K1 and the center of the pin

Total Speed Reduction

pointer	value	VRML axes	remarks
Year	-1.000000	Z	driven trough 1:1 bevel gear from simulator
Saros x 4	0.221855	Z
Exeligmos	0.018488	Z
Metonic x 5	0.263158	Z
Callippic	0.013158	Z
Moon	-13.368421	Z	Non linear due to pin-and-slot mechanism
Lunar Phase Sphere	12.368421	Y	Non linear due to pin-and-slot mechanism

VRML Coordinate System

The VRML coordinate system is righthanded.

Most rotations are along the displaced z-axes.

Axes of the Antikythera model