Do you need to cut from the middle of the piece or just take slices off?
I'm thinking a band saw might be a good choice but finding one that can use small blades to cut the curves might be a challenge. The old Inca band saws were advertised the take a 1/16" blade but good luck finding the saw or the blades.
Can you post more details about your project or maybe some pictures?
Saw something in the net that might work... The scroll saws. My problem is that I will cut wood 1" thick. Dont know if those machines will work for it.
I do not have pictures of the project as this will be the first one. And the drawings I made is just for my understanding. No one could understamnd such drafts. :)
A scroll saw could cut the wood but I think it's going to be really, REALLY slow going. Maybe one of the premium machines could do it? Before you go that route try to find a scroll sawing forum and see if anyone has a recommendations.