Thats a sifter, a little different from what your wanting, I think. With shaker tables, its best to buy one. The stroke and draw is tough to get right. I have seen them done, but it does take alot of playing around with.
Really not worth it if your only running small loads, there are easier ways of doing it.
But if you really want to, start with the ribbed rubber mat and glue that down to a PERFECTLY FLAT piece of something that will not warp. Wood is out, unless you run it dry.
Make your support (table frame, legs) out of some very stiff metal and have all four legs adjustable and tightly locking. Bolt them down to concrete, preferably.
Run a shaft under the middle of the table, and use weights of some sort to offset the spin, making it wobbly. You'll need pulley reduction to hook up to an electric motor, so it's not spinning too fast.
Ideally, a table should draw one way fast, and back up slow, but a cam action is really tough to do for a homebuilt one.
Rain gutter on one side of the table, and another section at the lower end. The section on the side should be split in two sections with a divider, the top part is your good stuff, the lower half is your middlings, and the gutter at the bottom is your waste.
The table should be run almost perfectly flat, let the vibration do the work, not gravity. Adjust the legs so that the corner where the raingutters come together is the lowest, but only by maybe 1/4 inch if your table is say-4 feet by 4 feet.
Getting the right balance between the pulleys (for spin), the weights(for the action) and the legs (for level) is the tough part.
