Okay - I'm a Mechanical Engineer. The idea has merit. Not necessarily exactly as originally submitted, but using motion / traction to lift the bed certainly has merit. The thought has crossed my mind before.
Here's my thinking.
We build a scissor lift type device under the dump body. Nothing fancy - just 2 pieces of steel and a couple/ three pivots.
We pivot the dump box close to the back of the trailer. The further forward the better, but we want some height here otherwise we're just as well off to unhook from the truck and tilt the whole trailer up.
Now we mount a pulley at the front of the trailer, string some aircraft cable from the scissor over the pulley and down under, and we use the motion of the wheels to wind up the cable. I think a cable drum on the axle is safer than the tire chains and would give more force (in exchange for backing up further) but any way of winding up the cable would work.
Using an axle drum would even allow you to raise the dump box by moving forward or backwards by wrapping the cable over or under the drum. I suppose you could do the same with tire chains by having a second pulley at the back of the trailer- use both for backwards, just the front for forwards.
Why the scissor lift? It gives you more force upwards for the same cable tension than pulling on the rear of the box. This allows you to pivot closer to the back of the box and get a steeper angle. You could just mount a tall post to the front of the trailer with a pulley on the top, but that's not anywhere near as clean a design.
Considerations:
Need to ensure the force calculations are done - don't want to overstress the cable and have it snap - that would be ugly although it would likely only happen when you're in the vehicle so you're relatively safe.(Having a hydraulic hose burst is just as bad and you're standing right next to it!)
Sizing the cable drum needs to take into account expected traction at the wheel. Otherwise if the wheel slips, the whole thing will come crashing down as well.
Scissor lifts take the most force at first. This is a good thing, as if the load is too heavy, the cable would snap or the wheel would slip before the load is raised. But need to design it such that the initial angle, expected load and expected cable force are matched to make it work.
Finally (that I've thought of) as the load slides off, the force on the cable will drop, but so will the friction on the tire. Need to ensure the cable force drops faster. I suppose the weight transfer to the rear would negate this effect to some degree.
As someone else mentioned, the whole thing might be accomplished just as easily with a worm-drive trailer winch instead of crawling under the trailer to hook up the cable to a drum, but then you have to crank instead of drive
wroughtn_harv - I'd be happy to work through calculations with you if you decide to proceed.