I need an RS422 multipoint connection. When I tried connecting it as shown in the image the communication didn't work, but when I connected all the devices' pins T+, R+, T-, and R- i.e T+ of one device to T+ of another device, the communication worked. Why is this?
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RS-422 is normally point to multipoint, with only one transmitter and up to 10 receivers. You can make your system work as drawn if your client devices (on the right of your diagram) have tri-state control of their transmitters so that only one client (at most) can transmit at any time.
Typically you would run some higher level protocol over the communications link so that the controller (connected via the DT-9003 interface on the left) grants permission to each client to transmit in turn.
You could also consider using RS-485 interfaces on your clients. RS-485 inherently supports multipoint operation, on a single pair (+ ground). It supports more loads and more robust bus terminations, if needed. Your DT-9003 interface already supports RS-485 operation. You'll still need some protocol to grant each device permission to transmit. Only half-duplex operation is supported so the controller will also need to take turns transmitting. RS-422 allows full-duplex operation with the controller able to transmit continuously.
when I connected all the devices' pins ... the communication worked. Why?
The transmit pins of the DT-9000 also act as the receive pins in RS-485 mode, giving another receive path back to the controller, as well as the RS-422 RXD pins.. How the client transmitters didn't clash is rather vaguer but they presumably have some form of over-current protection (assuming they are all still working).
RS-422 is point to point only in the sense of duplex communication, two transmitters cannot be connected on the same wire. Transmitter is always enabled, and should be at the end of cable, not in the middle, due to requirement for single cable termination. There is no support in RS-422 for full duplex multi-node connection, so what you need is not possible with RS-422.
RS-422 only allows one transmitter at the start of bus wiring to drive up to 10 receivers on the bus and termination resistance at the end of the bus.