I've done a log cabin block by hand. It's easy to do. Instead of strips you just cut the rectangles and center square to the exact measurement you need (including 1/4 inch seam allowance) and piece it together in the same order you would paper piece it, working from the center and then attaching the rectangles from small to large.
If you want to do a different type of log cabin than the traditional, that's also possible, but when it comes to something like the pineapple log cabin, where the rectangles end in an angle, you might need to work with templates instead of just a rotary cutter.