so that was you
how you analysed it's dynamics?
can it work reverse?
Yes, it can work in reverse (rotary to oscillating rotary). Also, if you hold what would be the rotary shaft still and rotate the housing, the other shaft rotates one direction with a momentary dwell, smoothly accelerating and decelerating to and from dwell.
First, analyzing was mental while it was just concept. Then I spent much time making a model in Google Sketchup with Sketchyphysics to show dynamics. I was satisfied enough with the results to have the prototype made, besides doing patent applications. I have the Solid Works files which should allow motion studies, and I think they could have included those studies so I could view them in e-drawings, but I haven't been able to find them with e-drawings.
So my next study of the dynamics was handling the prototype. I can see that it acts as I expected. There is what could be compared to a top and bottom dead center where force applied to the oscillating shaft doesn't have much effect to rotary shaft, but that is momentary. As soon as you get past that momentary spot, force applied has good effect to turning the rotary. It is what I expect by watching the simulation. The oscillating shaft quickly gets up to speed and is fairly constant through the oscillation. The torque that I feel with the prototype seems to relate to that. Torque is high at the points of changing direction but quickly becomes near constant until close to changing direction again. The closer to the same size the two gear sets, the quicker the oscillating shaft will change direction and the more steady the torque in/torque out. The pulley on the rotary shaft acts somewhat as a flywheel to help it go past the dead spot and its kinetic energy is reintroduced into the other direction.
The animation I used in the video starting this thread was made with the Phun simulator, a free download. With it I can display the critical values which include the forces and velocities of the various parts. Those values change so fast, it is hard to read them. I though of making a screen recording and slowing it down, but I was satisfied that what I was seeing was what I would expect.
I wish I had the motion studies that should go along with the Solid Works assembly file, but again, I feel it would only confirm things. I put in a submission to a university to ask them to do a study on it, but so far they haven't responded. If an engineer or university would validate the dynamics and feasibility, it could make it easier to find interest in taking it to market.