Johann Bessler's Perpetual Motion Wheels Part IV

Bessler's "Principle of Movement"

In Maschinen Tractate, Bessler occasionally mentions a "principle of movement" and, more often, remarks that he is not always making full disclosures, e.g:—

No. 9  "... but nothing is to be accomplished with any device unless my principle of movement is activated..."

No. 11  "... but there is more in it than meets the eye, as will be seen when I pull back the curtain and disclose the correct principle..."

No. 15  "... From this drawing alone, however, nothing of the prime mover's source can be seen or deduced..."

No. 24  "This invention should not be scorned. ... There is, however, more to explain about it before you will grasp and correctly understand its good qualities."

No. 25  "... There is more to this than one might think. Mark my words."

No. 26  "... There is more to be sought in this problem."

No. 38  "... There is more to this invention than there is to the previous one, but here the correct application of the stork's bills is not shown."

No. 44  "... This proposed model looks good, but as sketched it does nothing special as long as nothing else is applied..."

No. 48  "... The principle is good, but the figure as it is will not give birth to any motion until completely different structures bless this marriage."

Simple harmonic motion?

My first thought, with regard to the "principle of movement" that Bessler talks about for Nos. 9 and 11, and hints at for No. 44 at least, was that this principle could perhaps be simple harmonic motion, as a result of mass-spring resonance. It would be possible to apply mass-spring resonant simple harmonic motion, in one way or another, to each of these three examples (and others).

Looking in particular at Nos. 44 and 45, we see that there are two wheels geared together, with weights being transferred between the wheels; rising in one and falling in the other.

Maschinen Tractate No 45, redrawn

Oscillating wheels

As Bessler points out in his comments to No. 44, the gearing ratio shown is wrong "as long as nothing else is applied..." But, assuming a correct gearing ratio, what if either of these wheels were to undergo rotary oscillation as it turned, with weights still being transferred at the same heights as before? That is, more weights on an oscillating wheel carrying the falling weights, and/or fewer weights on an oscillating wheel carrying the rising weights.

My simplified oscillating-wheel silux model

I decided to simplify this idea down to a single 180º stack of weights as shown below. Weights 1 and 5 start on the horizontal centerline.

The five 4kg weights are all attached at 0.4m radius to a light 0.01kg disc (red) which has a central torsion link to a wheel (black, with small circular black marker to show its angle). The wheel is forced to turn at an absolutely constant clockwise speed.

180º stack of weights, at start of simulation

180º stack after overswing forward

The stack of weights starts clockwise at a certain initial velocity, and falls, exerting forward torque on the wheel. It "overswings" forward, reaching its lowest position, as shown above, at the same velocity at which it started. Weight 1 is very quickly brought to rest, detached, and held to Earth. The remaining four weights have their velocities reversed in direction, (with magnitude, hence energy, left unchanged). Then they "backswing" to the position shown below, again exerting forward torque as the wheel turns further, completing a cycle of operation. Weight 1 is then brought back up to speed, and rejoined to the stack, whose velocity is changed back to a forward direction, for the next cycle. 

180º stack at end of cycle

I found I could "tune" this model (at least for the stack falling) with the following values:—

Wheel rotational speed: 1.4303 rad/s (about 13.7 rpm).

Weight-disc starting and finishing its fall, starting its rise, and ideally finishing its rise, at ±10 rad/s, with weight velocities to suit.

Torsion-link: constant-torque at 48 N-m, active between weights 2 and 4 crossing the horizontal centerline when falling, and again at 48 N-m over the same net torsion-link angle for the weights rising. (I know, a constant-torque spring like this is a bit artificial — along with some other aspects of this model — but it's OK in theory, and was easier to model in this case).

At the end of the cycle of operation the wheel has advanced by 45º, as it must do.

Only forward torque, with fewer weights rising than falling

So it would seem that:—

- There is clockwise torque on the wheel at times, but never any anti-clockwise torque.

- While five weights always fall as a group, only four weights ever rise as a group.

The flaw

It really doesn't require any analysis to spot the flaw in this model, which is obvious enough just from visual inspection. The five falling weights can never deliver any more energy than is required to reset the four weights for the next cycle. (This can be confirmed if necessary by center of gravity calculations). That objection remains valid no matter what number of weights comprise the 180º stack.

So, any energy delivered to the wheel during the overswing downwards becomes unavailable to cause the weights to rise as they should during the backswing.

I realise there are many more variations of the oscillating-wheel idea that could be analysed, but I don't think now that Bessler's "principle of movement" was this kind of rotational simple harmonic motion.