NOTE: If you don't care about achievements, use the basic puzzle solution instead.
As you approach the SYMBOL WHEEL, you unlock a new notebook entry (34/62): "Refer to field notes for diagram of the lock mechanism."
To solve the puzzle, you need to manipulate the puzzle wheel and the 4 levers around the corner to the right. The crank at the center of the wheel rotates the symbols. Each of the levers allows you to lock one of the symbols in place. The goal is to get the correct sequence of symbols lined up between the metal brackets on the left side of the wheel.
You (hopefully) located two of the symbols earlier. The printouts should be in the Items section of your Inventory. The other two are among Von Croy's notes, on page 19 of the Notebook in your Inventory. You should now have all four symbols. (According to Werner, the FIRST ANCIENT SYMBOL you discovered will be third in the puzzle sequence. The SECOND ANCIENT SYMBOL will be third in the sequence.)
The "Jackpot!" achievement/trophy adds a challenge: "Unlock the gate in the Archaeological Dig with no blocked rings on your last turn." To do this, you must position the symbols so that one final crank will result in the correct combination.
If you make a mistake, just use the levers to unlock any/all of the rings and try again. If you manage to solve the puzzle but don't unlock the achievement/trophy, you'll need to reload an earlier save and try again.
Here is the configuration before moving any of the symbols. The correct symbol for the first position is the Moon/Silver, so use the crank twice...
...to move the outer ring until the Taurus/Bismuth symbol (the one before the Moon) is selected (i.e., positioned between the metal brackets on the left). The other rings also move, but this doesn't matter. We're concentrating on the outer ring for now.
Follow the walkway around to the 4 levers, and use the leftmost lever...
...to lock the first ring in place.
Return to the puzzle and use the crank once so the flaming sun symbol on the inner ring (i.e., the one before the fourth symbol in Von Croy's notes) is selected.
Go around to the levers and pull the rightmost lever...
...to lock the inner ring in place.
Use the crank twice to rotate the third ring so the Jupiter/Tin symbol (the one before the Sun/Gold symbol from your notes) is selected.
Use the second lever from the right...
...to lock the third ring in place.
Use the crank once more to rotate the second ring until the Cobalt symbol (the one before the second symbol in your notes) is selected.
Return all levers to the up position, so all of the rings are unlocked.
Check to make sure the symbols are correct. They should look like this.
Now when you use the crank one last time, the final symbols should rotate into place.
...and the achievement/trophy should unlock, along with the ancient trapdoor.
Return to the lift platform.
Jump back to the stone ledge below the walkway. Climb onto the wooden platform, then the walkway.
Head past the lift control to the open trapdoor and drop into to the next level.
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