Hi there,
This is Bogdan from Romania.
I'm a mechanical engineer, specialized in the industrial robotics, 3D modeler and designer.
I have over 15 years work experience, designing, prototyping and launching different devices/systems across multiple industries.
I could help with your project.
I totally agree with you on the usefulness of such device, but I can't agree with the picture you attached :) - sorry.
I use to have cats (persan and birmanese) and I know what torture was to clipping the claws and clean up the fur.
What is possible to be done, is a kind of bed, made from washable fabric, indeed with velcro stripes (but also with some sponges on the contact faces), held on a metallic (aluminum) skeleton, which to be foldable and also adjustable (the sizes of the cats vary by type, age and life style - some of them are really obese - my persian weight 9.5kg at 2yo).
For any other questions, you may open a chat room here and we'll discuss about the details.
Regards
Bogdan