How can I cut regularly spaced 45 degree grooves in a piece of wood?

Question

I'm making a coat rack to hang behind a door, but there isn't room room for a hanger between the door and the wall when the door is opened so it's parallel to the wall. My solution to this is to have the hangers align on a 45 degree angle between the door and the wall. So I need a way to make a bunch of regularly-spaced, parallel grooves in a bar of wood which will act as my hanger bar. Here's a rough pic of what I want to make:

I'm hoping to avoid the "table saw a bunch of times where you want the groove and then chip/chisel the remaining wood out" technique because it doesn't seem like that will give me nice, neat grooves easily. I'd love to find a way to use a router (I have a small portable router table if that will help) to do this, but I can't think of a way to produce a bunch of exactly parallel grooves. Anyone have any ideas?

Answer 1

You could use a router set in a router table, with a crosscut sled set at 45 degrees.

Building a jig with a "pin" that fits into the previously cut groove, will make sure all the grooves are cut an equal distance apart. The "pin" will be attached to the sled in some way, and will sit against the edge of the work piece for the first cut. After the first cut, the "pin" will sit in the groove produced by the first cut. The board is then lifted and moved, so that the "pin" sits in the most recently cut groove. This process is repeated the length of the work piece.

I'd make a jig similar to this.