This model of the Antikythera Mechanism is made after schematic fig. 5 in Nature vol. 444 and includes a Hipparchos Solar Mechanism of my own design.
However I see a-1 as an output to drive a hypothetical planetarium as illustrated.
The Antikythera Mechanism cannot easily be driven from a-1 as any engineer will understand, taking into account the gear ratios.
My input is the disk containing the lunar phase mechanism.
This works beautifully and allows very subtle setting even with the additional load of my hypothetical planetarium.
From the engineers point of view d-2 would be the perfect input gear.
With a crown gear exactly like a-1 engaging d-2 and a little crank, the Antikythera Mechanism (and planetarium) can be driven smoothly and subtly.
Experiments confirm this.
There is however as far as I know no sign of this arrangement in the original, it is purely my personal curiosity that made me investigate this.
My geocentric planetarium is based on modern data of planetary motion and is realised by conventional asymmetrical spur gear differentials as described in engineering text books.
It is similar in principle to Mr. Wright's but rather different in details.
I do not know of any detailed description of Mr. Wright's excellent work so I worked this out myself.
As it represents the same solar mechanism, with good approximations, the differences cannot be great. Mine has 28 gears, but this simplicity leaves room for improvement.