How to make a 2D gantry to move chess pieces?

I am designing a chess board that allows players to play remotely! The intention is to have 2 boards, such that if one player (white) moves a piece on her board, then the white piece moves on a different board. I would like to move the pieces using an electromagnet that sits on a 2-dimensional gantry system. The gantry would move in the XY plane, turn on, grab and piece, move, and then turn off.

As a software engineer, the programmatic part I can determine. But I do not know where to start when it comes to building a gantry system. Other than buying some chains, a wheel, and a motor? Any suggestions on other DIY projects? Or tutorials?

*I am not sure that grabcad was the appropriate place to ask this but was hoping somebody might have good mechanical design input. I saw that grabcad is where mechanical engineers get info, but this is not a purely cad modeling question.