Our design consists of two rings, which are connected to separate pieces of spacecraft by welding or any other necessary connection method. This mechanism can be applied on any scale, but works better for larger spacecraft as the power taken by the electromagnets costs a lower fraction of the energy budget of the spacecraft (it does require each spacecraft having at least a small power source). The diagrams linked below demonstrate the connection process (the gear's size is exaggerated so it's easier to see):

https://drive.google.com/file/d/1NkDHNJ8UQOq2fh1eD61n_Dx0OIfNJv_-/view?usp=sharing

The material we chose for the rods was titanium, because it is stiff, lightweight and strong, with a lower coefficient of thermal expansion than aluminum (which will make them less likely to not fit in the holes due to thermal expansion). We chose aluminum-copper alloy 2219 for the rest of the components because it's strong, lightweight, non-ferromagnetic so it won't get involved in the electromagnetism system, and will only oxidise on its outer layer (atomic oxygen in LEO can oxidise materials quickly). As a lubricant for the tips of the hooks that will slide around the ring as it rotates, we can use molybdenum disulphide - a commonly used dry lubricant for space vehicles.

In order for the electromagnetic pre-positioning system to work, which will roughly align the two spacecraft before contact with small, adjustable impulses of magnetic force, each spacecraft will have 3 magnetometers arranged in an equilateral triangle around the ring. The magnetometers can detect differences in magnetic field strength across one side of the incoming spacecraft and hence which part of that side is closest to the target spacecraft. This is a simple way to let the incoming spacecraft know how it is oriented relative to the target spacecraft. It can then alter the forces exerted by its electromagnets to properly align itself before contact. We chose a triangle formation for the electromagnets and magnetometers because it gives the computer flight control system that coordinates the impulses the most maneuverability in 3D space. It's also important to know that the magnetic field generated by the target spacecraft's magnets will be weak and constant. The force exerted by each electromagnet also doesn't have to be large, because the objects can move towards each other slowly over the course of minutes or hours, since there's no force other than gravity acting on them when the electromagnets are off.

The simplicity of it is that there's no human input needed, what with most of the mechanism being automatic on contact, and the rest being computer-controlled.

We should also state that we're assuming that the two spacecraft can be put within a few meters of each other before this mechanism is put to use, as magnetic field strength decreases proportionally to the square of the distance from the magnet, so this is not a long distance application.

Another assumption would be that the incoming spacecraft would be pre-programmed with data on how massive its target spacecraft is so it can use an appropriate degree of magnetic force to pull itself towards and attach itself to the target without knocking the target out of its orbital path due to the change in momentum on contact.