What would be the easiest and most intuitive way to do the following?

Well you need a simple system where you choose items from an inventory and click two spots to place them. On top of that, to make it easier for the player to design things, you should have a way to view the range of motion. You could do that by (upon placing a new link) moving the connected parts in a random set of directions, turning around if any link/prismatic is at its limit.