Sum of torque

[EOW]

I tested on Algodoo for look at all angular velocities, it seems ok. I done a video :

https://www.youtube.com/watch?v=_zsx3ehhUto&feature=youtu.be

The stem move a little, the mass of the stem is very small, there is friction between the purple stem and red disks. The support has only an angular velocity at start, not disks.

Need the spiral for test the sum of the energy. The spiral is fixed and I think forces can be like I drawn.

The gif:

http://imageshack.com/a/img903/8053/6oVzC4.gif

And a bigger video:

http://youtu.be/TVv2GTwHhY0

The purple stem must block at the point B not A, because the distance move by the stem is not very big.

[EOW]

I think the length travelled by the purple stem is not enough for reach the spiral. But I can fixe one part of the stem to the spiral, like forces F1 are always reported to the center of the support like I drawn, this could say the red disk accelerate counterclockwise. But at start, the red disk don't turn around itself, so this is an additionnal energy. The purple stem has no mass.

2 Cases:

1/ the length travelled by the stem is greater than the "step" of the spiral, in this case I can block the stem and red disk increase their angular velocity clockwise
2/ the lenght travelled by the stem is lower than the step of the spiral, in this case I can attach the stem to the spiral, red disks increase their angular velocity counterclockwise.

The support don't receive a torque in case 1 nor in case 2.

Cycle:

Accelerate more and more the support, but at start angular velocity of the red disk is 0. The purple stem will accelerate the red disk in the counterclockwise direction.

[EOW]

Maybe instead of use a spiral I can use another circle with the center just aside just for a transcient analysis.

[EOW]

I can unroll a roller chain from one disk to roll up to another disk. Red disks don't turns at start in the labo frame reference = turn counterclockwise in the support frame reference. Like I unroll and roll up the roller chain, the support don't receive a torque. But there is friction and red disks decelerate in the support frame reference = accelerate in the lab frame reference. Think with the same diameter for disks (think in 3D, disk can have depth). The roller chain has no mass (or as lower as possible). Disks can be very close from one to other like that the torque on the support is very small.

Cycle:

1/ Turn clockwise at w the support
2/ Unroll and roll up the roller chain from one disk to the other => win energy
3/ Decelerate the support and recover energy

I can repeat the cycle because the roller is roll up to the left disk. I need to change the position of the disk left <-> right only.

The friction can be asymmetric, no friction when I unroll and friction when I roll up or the other.

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Or the idea with a pipe and a container of water, the idea is to move down the container with a higher weight from the volume of the pipe. There is air inside the pipe. For the shape of the reel : http://en.wikipedia.org/wiki/Spiral_of_Theodorus, like that the up force from the water to the pipe is always perpendicular to the trajectory, there is no torque on the reel from the force up.

[EOW]

With 2 spiral of Theodore of Syrene, the force Fp from the water is gave to the spirals but this sort of spiral has Fp/2 at the center of rotation. I can full spirals with water inside, like that Fp = 0. I need energy for move up the water but that energy can be recover later.  I move up the water from the bottom spiral to the upper spiral and I move down the container full of water. Or move up the water only, but need to change the step of the spiral more and more lower when the diameter increase. With d1< d2 < d3 < d4 < d5 < d6.