Johann Bessler's Perpetual Motion Wheels Part II

A silux model of MT-18.

One of Johann Bessler's more interesting examples in the book named (by John Collins) as "Maschinen Tractate" is number 18. In his notes on this example, Bessler says "...the principle is not to be scorned or disregarded, for it tells more than it shows."

I decided to make a silux model of this, just to see what would happen.

A silux model of Maschinen Tractate No. 18, as first prepared

Here is a screenshot of my model as I first prepared it, corresponding to the configuration as originally drawn by Bessler. See p23 of Maschinen Tractate as edited and published by John Collins.

The wheel is 1 meter diameter, with a large mass of 2000kg, which gives it a rotational inertia of 242kg-m². (A lighter wheel risks failing to complete a cycle of operation).
The four weights are 15kg each.

Each of the cantilever springs is fabricated from 13 segments, with each 1.5 milligram segment connected to its neighbour with a torsion link of 100N-m/rad. Torsion links of 250N-m/rad connect the springs to the wheel hub.

The model is turned to this configuration to start the simulation

Simulation results

I suspected, correctly, that the original configuration (or anything much like it) would not occur during continuous running of the simulation. Instead, I turned the wheel to the configuration shown, which does occur during continuous running, and so is a suitable starting point. 

The wheel is started at 1.05 rad/sec. The start is "smooth" with all components moving at their correct velocities — having been run up from a zero-velocity start. This includes, of course, the highest weight, which has begun its "flip" over to the descending side.

Even such a heavy wheel drops its rotational speed to 0.89 rad/sec just before the highest weight hits its wheel-rest on the descending side. Even with impacts set to a realistic elastic/plastic ratio of 10%/90%, the weight bounces at least 25 times against the wheel-rest, wasting energy with each bounce.

The simulation is finished after one cycle, i.e. after the wheel has turned through exactly 90 degrees, and so is once again approximately at its starting configuration. By then, its rotational speed has dropped to 0.655 rad/sec, and it has lost rotational energy (½Iω²) of 133.4 - 51.9 = 81.5J, a very large amount.

I suspect that not all of the "lost" energy is lost from the device as a whole — a fair amount of it has probably gone into greater deformation of the springs. (The wheel's already-reducing speed could easily cause a further significant energy exchange from the wheel to the springs). If I thought it was worthwhile, I would integrate a full torque vs angle graph for a wheel forced to turn at a constant speed, which had been settled down as far as possible to steady-state operation. I would also do that for various combinations of weight magnitudes and spring strengths. But I have already done enough work on this model to be fully convinced that it cannot deliver any net energy.

Even if the wheel is started from rest at the unrealistic original configuration, it doesn't turn far enough for the first weight to entirely "flip" over. The wheel accelerates at first, but then decelerates to rest again, and starts to turn back before the weight is able to reach the point of unstable equilibrium where it could complete its flip.