@Johnny874 . Many thanks for the links . Fascinating stuff . I need to study this . As regards the 2SO . In order to loop it , on a small scale , I think clockwork could be the answer . Imagine an axle . The axle is fixed and can not rotate . It is supported at its ends . Near each end is mounted a disc which can rotate on bearings . Between the discs is a strong clock spring . The outer end of the spring is fixed to one disc and the inner end to the other . One disc is driven by the output through a linkage . A ratchet prevents it unwinding . The other disk drives the escapement which drives the pendulum . If , as I suspect , the output lever tends to overwind the spring , this will just temporarily stall the lever movement for a few swings of the pendulum . Clockwork is quite efficient , and if the 2SO is as efficient as claimed , this idea stands a good chance .

  @All,
 What I posted in the other thread might work. The adjustment that would need to be made is to have the bottom of the cog near the center of the primary fulcrum.
 If something like this can work, the extra energy will allow the pendul to swing higher where it will develop more force. As an example, if a pendulum swings from 30 degrees before bottom center to 30 degrees after, the force it can develop is 1/2 it's mass. If the pendulum can swing to 45 degrees, then the force it can develop is 70% of it's weight, an increase of about 40%.
 And it's useable power may be for a few degrees of swing where it's torque can compress a spring as Neptune suggested. Even a spiral wound spring like in a clock would work. Then it's energy could be released in a controlled fashion until the pendulum swings to the other side and once again drops down. This would allow for a some what constant release of energy from the device. 
 What I like about this is by limiting the pendulum for a few degrees, this could still allow the secondary weight to maintain the pendulum's  swing height. And then you would have a constant source of power that is consistent.
 
                                                                                                                                          Johnny
 

Jim, once again my cognitive skills proof to be lacking to keep up with you.
 
Could you put in layman's terms where exactly a gain would be extracted? I just don't see it.
Remember that when you increase radius to get a higher velocity, you'll need more input also. In the form of height or torque. It only works when the energy is there to be extracted, and it's never for free.

  Hi Cloxxki,
 You did ask specifically where the free energy comes from.
I don't think I explained it very well.
 When 2 weights swing from 30 degrees as an example, if the top weight
is not suspended from it's fulcrum, but from the fulcrum of the lower weight,
it's force will calculated from the lower axle.
 As the 2 weights swing and the top weight starts to swing from it's axis, then it
will be calculated from a higher point of rotation. And yet both the top and bottom weights would have the initial acceleration of the lower fulcrum.
 I am glad you asked, other wise I might not have thought of this specific reason.
 Now in considering that, a small cog placed above the main fulcrum might be the correct answer. Pretty much what Bessler shows in his drawing.
 
                                                                             Jim

 
   @All,
  Possibly the simplest way to test an idea such as this is by using flywheels, one on each side of the fulcrum.
 It could release the pendulum at 30 degrees. This would mean that torque would cause the flywheel to accelerate. After this, the pendulum could swing from a higher fulcrum.
 With 2 weights, when the top weight is at bottom center, it would be at it's highest point relative to the lower weight's swing. If it stays in this position, then it might recieve the necessary lift so it can be reset and help rotate the flywheels. This would mean that the flywheels would need a ring with a large diameter. It would need to transmit power from the weights on the fulcrum to the flywheels. As such, a wheel could act as a flywheel.
 If so, then it would be a simple system capable of delivering useable power.
 It's odd thinking about it, but with only one weight on the pendulum, it might not work. Just have the shorter pendulum supported on both sides by the axles and the top fulcrum by an over head frame work. Think of a swing. Yep, think it will work just fine. And Cloxxki, one day we will have a beer  :-) Figure somethin' good otta come out of all this.
 
                                                                            Jim
 
  edited to add; it could be as simple as one weight chasing the other.

OK, I am slowly getting what you're on to here.
 
I see 2 weights, one with longer rod than the other, making its period longer, and height gain/los per quarter period smaller.
 
Small side step to help visualize the powers in play.
For human transportation, it's all about getting getting from A to B, mostly horizontal usually. Like the A and B here.
The cost of transport is mostly dependent on the speed you're looking for. Since acceleration is expensive, friction at speed ramps up badly, and decelleration is barely really giving any useful energy back.
If you build a low-friction vehicle with great mass to air friction ratio (freight train), taking a deep dive at the start of the journey, takes up great input from gravity, uses is to bridge the lion share of the distance, and then gravity becomes a cost to arrive back at (sea) level at B.
If the train rides a maglev track in a vacume, transport from A to B is free of charge, and super fast. Much like a 100 mile long pendulum from a 70mile high up fulcrum. http://www.calctool.org/CALC/phys/newtonian/pendulum
Period is less than a quarter of an hour, angle a bit over 46º. Fuzzy math, but a 140 mile single swing in 7 minutes.
Huge energy at the bottom, but what to do with that energy going 1000m/s horizontally? You need it all to reach the height of A-B again. Even if at the bottom you rod turns out to be a rope that hits a pin a A-B height, only period is shortened, distance is shortened, but no height gain is reached.
 
So what exactly is going to give the gain, in height, or at least useful work?
 
If you can make me understand the principle you're on to, you can build it and make it work :-)

    Hi Cloxxki,
 I have simplified the design. Something based entirely on torque.
It has 2 moving parts, both weights. The 90 degree lever we won't worry about.
Why you ask ? The lever is fixed at 90 degrees and transmits force at a 1:1 ratio.
 How it works is weight A when it is at axle level will be in it's outer most position.
Weight B will be as low as it possibly can hang. Since weight A is further from the
center line than weight B, weight A will start dropping. As it does this, weight B
would slowly move closer to center. It's average resistence would be less than the
average torque generated by weight A.
 This idea would rotate 90 degrees in one direction, then 90 degrees in the opposite
direction. What allows this to happen is the cog in my video. It would allow the line
to release from the cog and then the weight could roll outward. one can be used in each
direction. While I can not gaurantee this will work, it does have potential. After this, the
ideas get more complex for obvious reasons. And there is some math to show over balance.
it's 2R*Pi/4-2R=x
 If R=1, then;  2*1*3.14/4-2=x
                            2*3.14/4-2=x
                                 6.28/4-2=x
                                   1.57-2= -.43
  This would mean that if 1 were 1 inch or 1 cm (radius of the cog), that the over balance would be .43cm's or inches.
 http://www.youtube.com/watch?v=ilsB_KtTSAU
@AB Hammer, please remember that you have frequently posted that as a private builder you can not share information with other individuals. I think rlortie is in your build group. Sorry you two  :-(
 
                                                                                                    Jim
 edited to add; the pivot would be centered between the two cogs  :-)

As usual I am only able to comprehend a fraction :-)
 
Perhaps this remark is relevant?
Notice that B's vertical position above it's cross with the 45º centerline is greater than A's position below it.
Although both are seperated by 45º, one (A) approaches it horizontally, the other (B) vertically.
The COM of A+B might lie higher than A's cross with the centerline, depending on how much shorter B's distance from the axis is.

   Cloxxki,
  Normally I would agree with you. Considerations for torque are a little different.
 Because A is able to accelerate for 45 degrees of rotation, it's momentum will help it to maintain the greater potential until B is lifted to it's desired position. That is, if it works  :-)
 I'm not sure, but a trebuchet might use a similar principle.
 
  I did make a mistake on the math. I should have calculated for 1R(adius). This would mean  multiplying the radius by .57 will give the distance the weight being lifted will move towards center. By having the cogs on the same side as the weights, it allows for best initial acceleration.
 
                                                                           Jim
 
edited to add; A few years ago, I was working on a 4 weighted wheel. While trying different things, I tried 2 weights.
                   The rotation was close to 90 degrees. I was very surprised.