Sum of torque

[EOW]

Look at images please. The motor accelerates more and more the disk with N intermediate devices. All the device is turning at w1. The motor gives a counterclockwise torque to the main axis (red color) -300 J, the disk win +100 J and with 3 intermediates devices I recover 3*200 J, the sum is 400 J in my example.

The first image shows a basic device motor+belt+disk, I compare the energy when w1=0 and w1=100 at start. I can find the conservation of the energy.

The goal is to accelerate more and more a disk with a motor and have a lot of devices that give the torque from (F5,F6) * (R2-R1) on the main support. An external device recover energy from the support for keep constant w1.

Like I drawn the reductor, it is divided by 3.3, but the rapport motor/disk is 1.45, so this must say with N=100, the disk accelerate very few, so I can guess the energy won by te disk is 0. The motor lost 300 J in my example but I can set N like I want, and each intermediate device win 200 J.

[EOW]

w1 is constant, an external device recover energy from the red axis. I guees no friction with pulleys, belts and gears. I guess a mass as lower as possible with pulleys, belts and gears. The motor gives only energy for the brake. The support receives a clockwise torque from (N-1)F(R1-R2) with N the number of intermediate devices. I think I can take w=2w1. w and w1 are constant.

[EOW]

I resumed the device in the image.

[EOW]

The mass of the belt give Fc1 and Fc2, with Fc1 > Fc2, like that the support has a net torque on it. An external device recover energy from the main axis, like that w1 is constant. A motor on the support drive the Pulley1 but with a mass = 0 for the belt the torque is 0 on the support. But if the mass is not 0, there is a net torque on the support.

[EOW]

All this device is on a support not drawn. The support is turning clockwise at w1. A method for cancel the torque of the counterclockwise blue disk. There is no torque on 3 disks. But the motor gives a torque to the support. If the support is turning at w1 very high, the energy can be recover.