Do you mean "I know how to wire switches II and III for non-derail" ?
And "How do I wire switch I for non-derail?" ?
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Gary is absolutely correct. A diode matrix, (using DC,) is the way to go.
However, the length of the outer rails between II and I, and III and I, probably is too short to allow safe travel, at anything above a crawling speed.
Using DC, it just takes a few diodes, at $0.10 each. Using AC, you need 4 relays, at $10.00 each.
A-C solution:
You need four relays, each with one form A contact*, and whose coils are rated at the same voltage as the switch machine supply. Wire each relay coil in parallel with the control rails of both switches II and III, respectively.
Call them Relay 2L, 2R, 3L and 3R. The relays operate whenever a control rail is energized. Call the control rails 2L, 2R, 3L, and 3R for convenience.
Case 1: train traveling from right-to-left through switch II.
Whenever *EITHER* rail 2L *OR* rail 2R gets energized, (either one operates switch II) the associated relay operates, and the relay contacts, wired in parallel, operate ONE coil (call it "Top") of the switch motor of switch I.
Case 2: train traveling from right-to-left through switch III.
Whenever *EITHER* rail 3L *OR* rail 3R gets energized, (either one operates switch III) the associated relay operates, and the contacts, wired in parallel, operate the OTHER coil (call it "Bottom") of the switch motor of switch I.
The operation is as follows:
Assume trains traveling from right-to-left in your diagram.
A train setting switch II in EITHER position will also set I in the proper position ("Top") to accept traffic from switch II.
A train setting switch III in EITHER position will also set I in the proper position ("Bottom") to accept traffic from switch III.
You will get a little relay chatter during operations in either direction, but it's not bad for the relays.
D-C solution:
Use a diode matrix instead of relays.
This is an excellent example of how using DC for signaling and track turnout control is superior to using AC.
What we are building is called a "wired logic" circuit, which uses a simple truth table of choices for switch I operation. Whether you elect to use AC and relays, or DC and diodes, the logic is the same.
Here's how the language will read:
"IF EITHER 2L OR 2R, THEN TOP"
"IF EITHER 3L OR 3R, THEN BOTTOM"
If you also want to ensure that trains will not over-ride the switches II or III when switch I is set against their traffic, you can use relays with an additional Form B contact* to de-energize the center rails at the approaches to the switches II or III, when switch I is set against traffic on those sidings, respectively.
Since I do not have the facilities to do a drawing in my computer, you will need to let me fax the diagram either to you or to someone who can post it here on this Forum.
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* Form A = "make" = normally open = SPST
* Form B = "break" = normally closed =SPST
* Form C = "break before make" = transfer = SPDT
* Form D = "make before break" = transfer = SPDT