There is such a thing, for shearing alpacas. They are quite spendy, but they exist.
I used to shear alpacas and at that time there were no tilt tables available. We just had to get enough people (usually three) and lay the animal on the table. Now they have a table that turns until it is perpendicular to the ground. You lead the animal up, and secure it to the table (it looks more like a small wall at this point). Once the animal is tied on, you use the hydraulics and the table tilts until it is parallel to the ground.
If you do a search on alpaca shearing table, I'm sure you'll find one. But like I say, they are not cheap!