Methods and apparatus for automatically coupling stackable modular devices are described. The modular devices may be coupled using electromagnetic forces generated by precisely-timed pulses of electric current through electromagnetic materials that cause a first modular device to screw itself into a second modular device. The modular devices may exchange data through electrical or optical connections after coupling. A method includes detecting that a second modular device is proximately and coaxially located to a first modular device, activating a plurality of electromagnetic elements in an annular electromagnetic array according to a timed sequence, each electromagnetic element being activated at a different time than the other electromagnetic elements in the plurality of electromagnetic elements, detecting that the second modular device is communicatively coupled with the first modular device, and deactivating the plurality of electromagnetic elements after detecting that the second modular device is communicatively coupled with the first modular device.