Sum of torque

[EOW]

I use a continuous track and a road wheel. I suppose the road wheel can receive a torque from Fg (there is an axis of rotation of the wheel). The energy lost by the spring is won by the track but the energy win by the torque on the road wheel is greater than the energy lost by the center of the wheel.

Lg3 is higher than 1/sqrt(2) so the sum of energy is not 0 because the center of the wheel receives always F/sqrt(2) because the direction of the force is always the same: pi/4.

[EOW]

I suppose the force from the spring constant even the length increases.

The center of the wheel is (0,0)
With an angle of rotation of 0.01 rd

Point P1:
At start (2 , 1)
At final (2.02 , 1)

Point P2:
At start (1 , 0)
At final (1.00995000043 , -0.009999833)

At start the angle of the forces from the spring is atan( (1-0) / (2-1)) = pi/4 rd
At final the angle of the forces from the spring is atan( (1+0.009999833) / (2.02-1.00995000043) ) = 0.7853733291 rd

cos(pi/4) = √2/2
cos(0.7853486586) = 0.7071243415

The difference is 1.75e-5 so the force on the center of the wheel change from √2/2 to √2/2-1.75e-5
And the torque is exactly √2/2+(0.01-1.75e-5)/√2 the sum of energy can't be at 0

[EOW]

I calculated with a program and I find a difference. With quadmath it's the same difference.

[EOW]

I found my error it was in the equation of the distance from the center.

Maybe with friction and forces from the ground with 2 wheels

[EOW]

Maybe a wheel and a spike full of water under gravity. I can adjust the contact wall/water like I want. The trajectory of the point is in red. I named the wall of the wheel elastic but maybe it is more dynamic, it is possible to imagine a wall theoretical  that can move like the wheel. I just want to benefit the pressure on the wall A for example.

Image m4p7: it's possible to rotate the spike in the same time the wheel rotates and moves. The spike needs a lower energy to rotate than the wheel won.