What is the most efficient machine for translating gravitational potential energy of one mass into kinetic energy of a different mass? As the question states, what is our current best machine for translating falling gravitational potential energy, such as a large weight, into launching a smaller projectile vertically? A lever? A trebuchet? What sorts of efficiency levels have been achieved?
What I'm looking for is the best way to translate:
$$ g * h * m_{\textrm{weight}}  * \textrm{efficiency} = \frac{1}{2} * m_{\textrm{projectile}} * v^2. $$
Edit
Here's an example: I want to launch a 10kg mass at 100m/s using only gravitational energy (no chemical rockets, no rail guns, etc.). What's our most efficient machine to do this, and what percentage of the energy of the falling weight will actually be transferred to the projectile? This would get me an idea of the size of the weight and how much it has to fall to accomplish this. The only machine I know of that does this on a large scale and for decent size masses is a trebuchet, so this might be a good starting point unless there are others I'm unaware of.
 A: This question was asked four months ago, but none of the existing answers mentions trebuchets.
To my knowledge the trebuchet design is the only design that is purely mechanical. Other projectile throwing devices store elastic energy and on release transfer that to the projectile.
So a trebuchet it is.
(In effect 'lever' and 'trebuchet' are synonymous. A trebuchet gets its leverage by being a lever (pun intended)).
It may be worthwhile to research the noble art of pumpkin chunkin'. There's a town in the US where there is a yearly pumpkin chunkin' contest that also features a trebuchet category.
Can a trebuchet deliver close to 100% efficency?
For one thing, frictional losses can be kept quite low, that's good.
The problem is this: to throw the projectile the lever arm must be accelerated to a large angular velocity. After the projectile has been released the lever arm is swinging violently. That kinetic energy of the lever arm is energy from the counterweight that was not transferred to the projectile.
The trebuchet design involves trade-offs. A longer lever arm gives the potential for faster throws, but a longer arm also has a bigger moment of inertia.

An ideal trebuchet would transfer all of its kinetic energy to the projectile, so that right after releasing the projectile it would just sit there, nearly motionless. I'm not aware of any trebuchet design that achieves that.
To reduce the inefficiency the mass of the lever arm must be as low as possible. That is what the pumpkin chunkers do: they make the lever arm as flimsy as they dare. For every throw they stand well back, as their machines tend to self-destruct when the trigger is pulled. 
A: Have an insulated cylinder of gas with a piston. Put the weight on the piston and let it press down. Then lock the piston in place and put the other mass on. Then turn the cylinder on its side and unlock the piston and the other mass will be accelerated. By turning it on the side, all the energy goes into accelerating the second mass and not into lifting it. The mass of the piston needs to be small in comparison to the second mass, because it is being accelerated also. But any device will have that problem. To get a vertical direction as requested, then have a curved ramp to convert the horizontal motion to vertical. The size of the curved ramp will consume some of the energy also.
