12 times more output than input, dual mechanical oscillation system !

[Cloxxki]

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 :-)

[johnny874]

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  :-)

[Cloxxki]

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.

[johnny874]

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.

[johnny874]

   A simple way to have 2 levers in a repeating behavior.
  The picture shows the line from the weight moving in a straight line to the cog.
This is to reduce friction. By having a line tethered to the arm the weight is on and wrapping around the axle of the weight, the weight will roll when it's line is pulled. Mimimum friction.
If as the 2nd drawing shows, the line pulling on the weight is tethered behind the direction the weight is moving, more resistence. This is because the weight will exert extra force on the lever when it is being lifted.
As pendulms swing, their motions are very efficient. If a lift equal to the drop of the lever falling happens, then perpetuality can happen. It is not lifting higher but in repeating the motion.

                                                                                   Jim

  Alan, if you and Ralph want, you guys can build what I post. I'm not you guys  :-)