All of our CNC machines can carve at that depth without a problem and do 3d carving. Our typical application is cutting sheet materials, but a good percentage of our customers cut 3D bas reliefs or even more complex 3D objects using reference points and jigs.
Most of our CNC machines have a Z travel of at least 6 inches for the smaller machines and 7 to 10 inches for our larger machines. The Fabricator Pro has a Z travel of 10 inches.
Depending on your application, you will need to consider the length of the end mill (more than the deepest depth of the 3D carving) and the stock that you will be using. If the stock plus the length of the end mill exceed the clearance with the Z axis raised to the top extent, then you will need to consider the way the table/bed of the machine is formed (maybe with a depression to take advantage of the greater need for clearance).
The greenBull has the capability of Z axis travel of up to 36 inches, but I would recommend, if milling wood, that the Z-axis not extend more than 12 inches to reduce deflection.
Most of the CAM software on the market will have 3D profile machining operation capabilities. CAMBAM has a very nice 3D prpfiling feature. The Vectric line of software can definitely handle this as well.
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All of the pics and videos show your cncs cutting sheet materials, I'm interested in carving 3d images in plastic and hardwood slabs up to 2" thick. What machine and software would you recommend?