Please see
https://ibb.co/mHPKmRK for details. If the mechanism does not generate energy then there should be physics which can clearly show that without it being assumed in the method of analysis used. Included in the analysis should be clearly shown details of a torque opposing the rod's rotation since the absence of such a torque would seem to mean that the mechanism continues to operate indefinitely and in doing so it seemingly continues to power the motion of m2 indefinitely.
If it does produce energy then energy is not conserved.
More could be said about this interesting mechanism e.g. acceleration of m1 in the x direction without a force being applied to it in that direction, the force on m2 in the x direction without there being a reaction force, how rotation produces inertia, implications for Newton's laws of motion and so on. I would be grateful if someone can clarify how it works and the (presumed) significant error(s) in my analysis. In case your analysis comes to the same main conclusion as mine then please be careful how you present your response in this forum as a moderator may censor it if it shows that you support anything that is overunity. Thanks for your interest.