There are two Wirt patents for retractable nib pens. The patents are one number off from each other. Presented here is an example of each type with photos and the patents. My nomenclature of type 1 and type 2 is based on patent order.
Both use a point on the cap to push out the nib.
The type 2 mechanism pushes a wire to push the nib and feed carrier out. When the cap is replaced, a rod inside the cap pushed the feed back into the barrel.
The type 1 mechanism is more complex. A segment of sac or rubber tube is tied to the filler at each end. Pushing with the cap top advances the nib and feed carrier, and also stretches the sac. The sac is used as a seal and as a spring. When the cap is removed, the nib retracts on its own as the sac returns to its resting position.
Type 1 Wirt retractable nib safety pen
Type 2 Wirt retractable nib safety pen
A simpler version. But there needs to be a seal around the wire.
Below: Type 1 patent 526426. Instead of a spring, the production pen uses a sac as both a spring and a seal
Below: Type 2 patent 526427. In production, there is no spring. A rod inside the cap pushes the nib carrier back into the barrel.