Twitr_janus' eyeballs are controlled by two servos. Like all eyeballs the two eyeballs must move as a pair (well maybe not chameleon's, granted!). This is done by fixing two eyesockets into the skull. Each one can contain an eyeball with a positioning rod at the rear of the eyeball. The rods for the two eyeballs are then fixed together in such a way that they can only move up down togther or left right together.
Here's what this looks like from the front (this is the skull only. It doesn't have skin yet)
The eyeballs were made from old deodorants. For details on making eyeballs and sockets from deodorants, see this post, and this Instructuble (animatronic head reading lamp).
Here's the underside showing the two servo mounts. The one on the left is the left/right rig. The one on the right is the up down cable controller
The main cranium of the skull here is laminated papier mache, which is strong, and can take a self-tapping screw to affix the plastic servo mounts.
The main construction is in making the rig. This is a collapsing parallelogram frame that fixes the rotation of the control rods into one plane, seen here from above, showing the fulcrums (pivots) maded from split pins with washers. The servo is in the middle and is fixed to one cross-beam, with the end of the servo-horn connected by a free pivot to the other. This is actually not a good design, as the arc it sweeps is not even.
From the front, you can see the servo body
Here it is inside the head. The servo rotates in the left/right direction, causing lateral shearing, but in the up/down direction, the rod moves with the rods. The eyeball/left/right servo rig is clearly visible on the left here, and the cable attached to the rig is the up down mover, attached to the horn of the second servo
The mounts are made from square section PVC cable conduit, which can be cut to shape with tin snips and folded with long-nose pliers.
Here is the up/down servo
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