Length of a helix vs composition of forces

[activ25]

I redrew the device, the nut is circular in top view. When I said the center of mass of the bolt don't move, I mean, its radius ! The center of mass of the bolt rotates because the bolt is inside the nut and because the nut is fixed to the black arm and because the black arm rotates around A1. But, the radius is always the same, like that for the calculations and for the real device it is easier. The energy recover is very few in comparison with the energy needed to rotate the bolt around A1, it is not a problem IF friction = 0, but in reality it is not possible, so I need to reduce the looses from the rotation of the bolt around A1, reduce air pressure and take ceramic rolling gears.

[activ25]

I don't need the nut. I drew like the cylinder is transparent. All the motors are fixed inside the cylinder. The bolt never rotates around itself, I brake it from the green brake fixed on the cylinder. The motors inside the cylinder are fixed of the cylinder. The cylinder has no helix, only the bolt has an helix. On the helix are fixed magnets of electromagnets. The violet support is fixed on the cylinder. I recover an energy from the translation of the motor. I recover an energy from the rotation around A1. I need an energy for the motor.

[activ25]

I drew the device in 2 positions. The center of mass is always at the same radius except for the motor but the size of the motor is in relation of the force F so directly link to the energy recovered. Remember the energy recovered is less than 1% of the kinetic energy inside the rotation around A1, so the device must be build to reduce all the friction, especially from air and rolling-element bearings.

I took simplifications to simplify the calculations but it is possible to have an external gravity, to have friction, w not constant, another angles phi and theta, and even the bolt can rotate around itself even the efficiency is lower, etc. all the geometry is an example.

For an angle of rotation δ (around A1) the sum of energy during the step1 is:

(+√3/2-√3+3/4*√3)*δRF

δ could be 2pi or more. δ is the angle of rotation of the helix relatively to the cylinder.

With R the radius of the bolt (or the radius where the force is applied) and F the force.

[activ25]

With a 3d multibody simulator, the sum of energy is not conserved, exactly like my calculations proved it. But I'm force to move the motor in the longitudinal axis of the bolt. That device is impossible to test in reality, except, maybe, in a lab, but it is possible to simulate it. And the equivalent electric must be possible to build and test in real. The advantage with the electricity, it costs nothing to have an alternative current, but here, in mechanics, it increases so much the losses that it is not thinkable to reverse the rotation of the bolt around A1, even 1 time each second. With electricity, it is possible to have a 10 Mhz signal without any problem.

[activ25]

2 cylinders