This circuit is designed to reliably control two solenoids (represented by the relays here) of a door latch mechanism by a single momentary input.
The first solenoid releases the door latch before the second one releases a counterweight-driven mechanism to open the door.
The double delay prevents that the latch solenoid has to work against a side load caused by the opening mechanism as solenoids generally don't work well under such conditions.
The circuit is just a proof of concept on an experimental level. If actually built it will be adapted to 12VDC (24VDC for the solenoids) and most likely mosfets rather than transistors.
Edit: Connected power for the second relay directly to the 5VDC rail as it’s not required to run it across the PNP-transistor. Added forgotten diode at second timer; the simulation doesn’t require it but IRL it’s necessary.
There is a weird glitch with the transistor for the second solenoid opening for milliseconds on power-up of the second timer. I think it’s a simulation issue; I have used the second timer design in the past for other purposes, like turning on speaker outputs with a delay, and have never seen this glitch IRL. In the simulation a diode with a resistor in parallel to the relay help. I have added them on the schematic together with a test switch if you want to observe the glitch. As soon as I got access to an oscilloscope I’ll test the real circuit for this.
Simulation runs at half speed.