A planer will not take the cup or twist out of a board. I am not getting into that argument, just research and google and take it from someone that planes 100's of bd ft a week. A planer simply will not do it.
A planer does nothing more than making a thinner version of the exact same piece of wood. Put in a twisted piece it comes out twisted. With a drum sandier it will eat away one side until the wood is flat and many times that leave the wood 1/8" thick.
Just think of a piece that is severely twisted the only way to get it flat is to take some of the wood away and leave other parts intact. A planer takes the same amount leaving a constant thickness throughout the piece. Which in itself makes it impossible to remove twisting and severe cupping. A planer will make the opposite side parallel so how could it ever take the twist out? You can take a very small amount of cupping and twisting out with a planer, but only a very small amount.
If you want to get the items flat with a planer you need to prop up one side of the material shimmed on a sled.
I guess I could take the time to draw some pics and explain it and I am positive the light bulb will come on for those that can't wrap their head around it.
I knew it was a matter of time before someone would bring it up.
Here is one way a guy on wood web used to get a planer to get his boards flat:
"I had some 5/4 maple that had quite a bit of twist that I was able to flatten without having to resort to a hand plane on the opposite corners. I made "running boards", say 1 x 3, out of pine. I then propped the maple up on the bench so the maple was higher than the 1x3 on edge and the maple was approximately even in the amount of twist in all directions. I then screwed the running boards to the maple and then could run the whole works through the planer for as many passes as needed. One disadvantage is that all the finished maple boards had screw holes on the edges, but in my case they hadn't been jointed anyway, so it wasn't a problem for the most part."
You have to do something like this with a planer, not with a drum sander.