One of the first things I built myself was a plate drying rack. It can be made quite easily, with very little tools and some scrap wood. Basically all you need is wood, a triangular file, a saw, wood glue, and ideally glue clamps. I made the triangular cuts by making a small cut using the saw, just deep enough, and then filing it out with the triangular file, which gives you a nice 60 degree angle. You could use a router with a conical bit instead, but I realize not that many people have one. A triangular file is cheap, and it works just fine for this particular task.
You can use two screws instead of the pinions. This particular design will nicely hold 20 plates up untill 10×8 inch.
You can download a 3D Sketchup model here, or play with the model in the viewer below: