Absolute Speed
At EVGM 11, elements of figure EVGM 03 of above section Basic mechanics are shown once more. Here, steady turning of rotor-arm (RT) of each 30 degrees is assumed. Representative for this motion, each position of the rotor-bearing (RL, blue circles, part of rotor-arm) are marked. Resulting of this motion will be, the excenter-sickle (ES) same time will make different segments turnings, differing from 25 to about 37 degrees (red numbers below). Representative for the excenter-sickle, positions of radius of a mass point (MP) are marked.

If the cylinder (ZY) will keep its position, this mass point will move around the excenter-axis (small black circle) at a concentric track. Above it was noted, by acceleration and deceleration of excentric masses, a turning momentum will result, which will make the cylinder co-turning aorund the system-axis (small blue circle). Motions thus must be looked at, in relation to the system-axis.

This circle track around the excenter-axis, related to the system-axis, will mark an outward- and inward-bended spiral track. As a mass point always will be at a radius from sytem-axis towards rotor-bearing (but with different distance to the system-axis), angles-speed of mass point will be nearby same than angles-speed of rotor-arm. While the rotor-arm here will turn constant 30 degrees within a time-unit, the mass point will turn between some 31 to 28 degrees same time (grey numbers upside).

So, if the cylinder will also turn, a mass point will show much less acceleration resp. deceleration - concerning its angles-spped (but these 28 to 31 degrees instead of 25 to 37 degrees, by an average of 30 degrees at one time unit). Minimum angles-speed then won´t be any more at the inner most track point, but (here) right-angle of the line between system-axis and (each) position of excenter-axis. Angles-speed of mass point, then will show two phases of acceleration and two phases of deceleration.

However, decisive for inertia-power not (only) angles-speed will be, but absolute speed. Even more important than these small differences of angles-speed, radius of motions will be. At the drawing (probably not exactly at the screen), excentrity (distance between system- and excenter-axis) 6 mm will be, radius of rotor-bearing and mass point as well are 30 mm. Thus, a mass point at its inner-most track point will move with a distance to the system-axis of but 24 mm, at its outmost track point however of 36 mm.

So, by absolute speed, a mass point still will move by maximum speed at its outmost track point and by minimum speed at its inner-most track point.

Co-turning cylinder
At EVGM 12, now the track curve of a mass point (MP) is shown, where it´s assumed, each 30-degrees-turning of the rotor-arm (resp. rotor-bearing, RL), the cylinder (ZY) will turn same time each 10 degrees, same direction. The mass point then will move at an outward- and inward-bended spiral track. A cyclus (from outer to inner and back to outmost track point), thus will take 540-degrees-turning of rotor-arm.

Above by static view, the track was circle-like, now here that track is stretched to a long loop-like track. As a result of geometrical investigations at Swivel-arm-maschine was noted, the cylinder probably will turn 1/10 speed of rotor-arm´s speed (thus a cyclus would take 400 degrees). By investigations at Sling-effect geometrically was found, the ideal sling-curve does fit to a relation Felix Würth called ideal: ´a quater back´. This would mean, each rotor-arm´s 360-degrees-turning, the cylinder could co-turn by 270 degrees (thus a cyclus would take four full turnings of rotor-arm). The relation here shown, ´a third co-turning´ thus could be realistic.

Closing and opening curves
The grey curve here does show deceleration-phase of mass point. At a road, one would say: this curve does ´close´ - and it will make sence to change from gas- to brake-pedal. Red curve will show the track of acceleration-phase. This curve will ´open´ - by some gas, the car automatically will find correct way.

Braking a car into a curve, will ´destroy´ kinetic energy, and same amount of power it will ´cost´ accelerating out of that curve, to achieve original speed resp. kinetic energy. Tracks here are symmetrical, thus can be assumed, all other forces too. Cause it´s common sence, energy neither can got lost nore will be won. By common ´logical law´ of science´, all is balanced, especially with regard to energy. So why thinking about. But, perhaps, anyway, even more logical could be:

Asymmetry of forces
By these procedures, not at all symmetry will exist. At the inward-curve, the car will effect remarkable pressure towards the ground, by braking (in direction of cars motion) and by inertia-power (tangential to the motion´s curve). At the outward-curve, the car will make much less pressure to the ground. Direction of driving more and more will be nearby inertia-direction (thus there will be less thrust sidewards to the ground). The car not at all must make all additional speed by drive-power (thus thrust backwards to the ground). Cause that falling-outwards of the car, as a power-component will add to final speed (see that diagonal resulting line at section above).

Racers do search for ideal-line. This won´t be the shortest nore the ´straightest´ track. Ideal however will be, at the outmost track to brake most late, then driving a relative narrow curve, in order to accelerate at a most long, opening spiral track - thus to take a maximum of centrifugal force into final speed.

Every normal driver well knows that ´easyness´ of acceleration, out of a narrow into an opening curve, comparable with accelerating from a horizontal road down into a valley. At both cases, ´let-it-fall´ is an essential component to achieve speed. At second case however: the car can´t accelerate well - cause it´s too ´light´ - gliding over the down-hill, see above.

So, driving a car through a curve, neither with regard of subsystem car (forces of deceleration and acceleration) nore concerning subsystem road (amount and direction of thrust), demanded or effective forces will compensate. Thus, there must be a remaining resulting component of forces.

Different to these road-examples, at here discussed systems, the track will be an excentric wall (mass will move ´up and down´) and the ´ground´ (in shape of the cylinder) will be movable. So, that remaining resulting power component, by motion of subsystem cylinder, shall be used as output.

Symmetric track but one-sided pressure
At EVGM 13, both phases of loop-track above once more are shown, upside deceleration phase and below the acceleration phase. These black points (in the middle) do mark co-turning of excenter-axis (and thus excentric wall resp. cylinder too). From excenter-axis (at each position) to mass point (at corresponding position) a radius is marked. In order to make comparable, by dotted line a circle is shown, around the starting position of excenter-axis.

At deceleration phase one can see, by co-turning of cylinder, the mass may move longer at an outer track section. As the excenter-axis is backward (in realtion to actual motions direction), the mass will pull the excenter-axis ahead. Afterward, mass will come into a strongly inward bended section, practically slinging around the excenter-axis. While this sling-motion, still a turning momentum towards the excenter-axis will exist. Lastly system-axis will be support-point of the motion.

Opposite to this, outward phase at the beginning will show a track within comparable circle. This realtive flat track at the begin of outward-slinging is very valuable (see conciderations at Sling-effect). Even better than at earlier drawings here one may see, the rotor-arm not at all has to do whole acceleration-work. Angles-speed of rotor-arm and mass as well, here are relative constant. The mass moves outside to a larger radius, but by centrifugal forces. Remaining acceleration-work, as the rotor-arm will pull the mass ahead, same time will reduce pressure towards the backside of excentric wall.

Ball-experiment
That one-side-pressure may be demonstrated by simple experiments, as e.g. Felix Würth did. A pipe will be bended in shape of an inward-turning spiral, corresponding to the track at deceleration phase above. At the outer end of the pipe, a ball will be brought in with defined speed.

Experts easyly may calculate, by which angles-speed and absolute speed the ball will leave the pipe at the inner end, which momentums resp. kinetic energy will exist at start and end of the experiment. This experiment can be done by fixed ´Pirouette-pipe´ and should be done, the pipe turnable around a central axis. Some experts did recognize, something might not be ok with common physical laws.

Double-sling-experiment
At a patent-description, Dr. Pavel Imris did discuss this experiment (EVGM 41): a mass (MP) will rotate at a lever arm around system-axis (SA). By angles-speed and radius, momentum resp. energy (E1) are defined. The lever arm is build by two parts, connected by a bearing. At first, this bearing is blocked, so the mass will rotate at fix lever arm and large radius (R1).

Then, a barrier (H, German Hindernis) will be inserted to the system, which abruptly will stopp the inner part of lever arm and same time de-block the bearing. Mass now will rotate around new center (H), at short radius (R2). By tests and formulas as well, this inventor did approve, not all physical laws can be valid. Every expert may check these simple formulas.

Question of systems
I can´t share this view of world as an assembly of formulas, won´t trust (nearby) any, can´t and won´t judge. Often however, I got the impression, borders of systems are fixed too narrow, at closed systems is thought too much. Here for an example at this Piroutte-pipe, whether effects towards nore from the pipe´s inner walls may be neglected and also forces towards or from that barrier above. Both by counter-pressure will bring energy into the system resp. will take energy, thus are parts of the system. Looking but at the masses - too blinded view will be. Just these ´side-effects´, at my designs here, will make possible to ´earn´ energy.

At the concept discussed here, angles-speeds are relatively constant while absolute speeds of mass will vary. Energy will be present or available at rotor-arm or cylinder. There might be energy losses, at maximum linear to turning speed.

Decisive however will be, centrifugal forces will contribute to acceleration of mass. Opposite, excentric wall has to centripedal piston-stroke-work. By this, inevitable, thrust-components in direction of system´s turning will exist. Inertia-power will rise by square with turning speed (if this formula will be true). Thus also differences of power-effects here will rise.

Let´s fall and press
In connection with experiments above and concerning concepts here presented, I want to make this essential suggestion. At EVGM 16, a mass will turn around system-axis (SA), from A to B. At continuous circle track, after same time-unit the mass will achieve point C. Tangential inertia-power will show from B to D. For redirection of inertia-direction, power must be brought in (grey curve, D-C), at a wheel done by spokes. Also one may think, a wedge with circle-shaped surface, this pressure into centripedal direction could effect. Pressure demanded, exactly will correspond to centrifugal force.

If now, given inertia would not be re-directed and still angles-speed should be same, an acceleration from D to E should be done. Absolut speed, e.g. here should rise by some 10 percent. However, kinetic energy then will be available at a radius 15 percent longer.

On the other hand, re-direction could be organized that kind, versus given centrifugal force but half counter-pressure would be used. A flat wedge then would guide the mass at the light-green track. If again, angles-speed should be constant, again an accelerationn would be neccessary (short blue line towards F). Absolute speed thus would rise e.g. by 3 percent. Kinetic energy however, would be available at a radius stretched by 6 percent.

Third, versus centrifugal force a higher counter-pressure could be used, e.g. by a wedge with inward-bended spiral-shaped surface. So inertia would be redirected further inward (than circle track). It might not be expected, absolute speed should be reduced by this measures. However, same time-unit mass will run larger angles, e.g. to G. So, the mass would show higher angles-speed, but be positioned at smaller radius. If now, that system wouldn´t allow higher angles-speeds or even will reduce angles-speed, a corresponding thurst-component will exist (towards the rotor-arm).

Using a wedge, this will not only effect pressure towards the mass, but same time inertia of mass will effect pressure towards the wedge correspondingly (or at a wedge more flat/steep correspondingly less/higher pressure). Analog to this wedge, the excentric wall will be. Pressure-surplus towards this wall, by cylinder will be output-power of the system. It´s up to experts, to design corresponding formulas and to calculate these effects.

Lenght of resulting line
Vectorial addition of forces, by circle-arcs or bended curves can´t be shown well. So, three theoretical steps are neccessary. At first, e.g. motion at a circle track must be unrolled to straight line. Thus length of that line will show speed within that time-unit resp. actual inertia (T, German Trägheit), like at EVGM 17 upside left.

Right-angles towards that circle track (also this track is unrolled to a straight line), centrifugal force (F, left side) will effect. If mass abruptly may leave its circle track, for example releasing a discus, centrifugal force will escape instantly. Then, this line T will show new direction of motion, by steady absolute speed, thus also will be represative for steady kinetic energy.

At a fix wheel, versus this centrifugal force a counter-force of same amount will exist, for example a spoke will do this work (A, German Arbeit) of redirection. Centrifugal force and pulling force will compensate to null, so no force-triangle or force-parallelogram will be, amount of inertia, speed and kinetic energy are unchanged. A line T, now again back-rolled to circle track (F, right side), situation will be unchanged (but direction of motion did change).

At both cases, mass will still move with same absolute speed, thus kinetic energy is unchanged. However, at continuing track circle (centrifugal) force on and on will be destroyed. On the other hand, releasing this missile off its circle track, centrifugal power immediately will disappear. Wouldn´t it make more sence, whether to destroy nore let escape this power?

When mass is moved alongside an opening spiral track, counter-force towards inside (here pressure of excentric wall) no longer will show radial towards circle center, but will show an obtuse (>90) angles towards each inertia-direction. It´s obvious, resulting line of both forces will be longer than original inertia. At EVGM 17, middle, this situatio is shown:

First theoretical step again will be, within last time-unit done track (circle track or bended track) to un-roll to a straight line. Right-angles towards this line, again corresponding centrigual force will show. As the track-curve now will open, counter-pressure (B) will be less than centrifugal power. Thus, as second theoretical step, a forces-triangle will exist with an resulting line (C), longer than the centrifugal-line, thus representing higher speed resp. kinetic energy. Third step now will be, to roll back this new diagonal line to a curved track (G), corresponding to these power-relations, will say less bended than circle-track or bended-track before.

Whenever counter-pressure will be less than centrifugal force (but not null), remaining radial power-component (centrifugal minus counter-force) vectorially will add to tangential inertia-power. Conclusive evidence, higher absolute speed will result. Angles-speed, thereby will be reduced but few, while radius of motion will become decisive larger. So in sum, momentum will be higher resp. mass will show remarkable inforced kinetic energy.

On the other hand, this counter-pressure (D) also can be stronger than centrifugal force, e.g. at inward-bended section of excentric wall. Naturally also here, a larger resulting line (E) will exist, thus higher absolute speed. When this diagonale line will be rolled back to corresponding (harder) bended curve (H), higher angles-speed will result. Mass however, then will be positioned at smaller radius. So but within a small range, turning momentum resp. kinetic energy might be increased too.

Essential statements of general importance
Above this, that gear of concept discussed here, at the inward-phase will sometimes show reduces angles-speed. Absolute speed at this phase will be reduced essentially (e.g. by one third). Corresponding to this, pressure-components are much higher than discussed above, first towards the rotor-arm (like acceleration-force at outward-phase), second towards excentric wall (which will be available as output energy).

So, following essential statements of general importance will be valid: at a fix wheel work will be done (by pulling of the spoke). The power invested corresponds by amount and direction exactly to centrifugal power, both will compensate each other. Thus (centrifugal) power will be destroyed. A fix wheel or in general, moving mass steady at circle tracks, will be a ´dead´ system, even a system ´killing´ energy.

Opposite, if mass is moved at spiral tracks, amount and direction of forces are differing, thus all times an effective resulting power component will be produced, in-avoidable. This will effect higher turning momentums resp. higher kinetic energy of masses, or higher momentum at the rotor-arm and excentric wall as well. Thus, centrifugal-power no longer will be un-effective ´fictive´ force, but really usable energy. When moving masses at spiral tracks (that special kind here discussed), inertia will produce surplus of energy.

So it´s clear, why in nature no circles exist, but spirals wherever you look. Experts easily could calculate optimum of bended curves, speeds etc. As nobody did by now, I suppose, optimale relations at crop circle picture are shown.

Two mass points
Here now, an other point of view with essential importance shall be discussed. Above mass of excenter-sickle was thought, theoretically to be concentrated within one point. This point of view, relations of power won´t show completely, cause mass-parts of excenter-sickle will move by different speeds and different directions. So, representative for these different motions, at the following at least two mass points shall be looked at. In direction of turning, then one mass-point will be in front (MV, German vorn), the other backside (MH, German hinten).

Boomerang-flight
This problem already was discussed at workouts to Würth-Schwungsysteme (available but as download in German, see German pages), there at a description to the flight of boomerang. By boomerangs, a transformation of turning-motions in motion-ahead will occure. One special characteristic for example will be, a mass-point for moments will stand still in space and around that relative fix mass, other masses will sling around. Analog to this situation, here motions do look like. Moving-ahead, here analogly will mean turning in general direction of system´s turning.

Excenter-ring and sickle-shape
Sickle-shape discussed here, in principal is similar to boomerang-shape. On the other hand, that sickle-shape does show an extreme kind of excentric rings, here also used. Already above at discussion to Threefold-crank-concept that ring was shown, existing of diverse mass-points. There was noted, why this kind of shape relatively easy will move also through critical phases. This point of view, at the following once more will be detailed.

Right-angles towards radius
At EVGM 14, the excenter-sickle (ES) is show in a position crossing from acceleration phase (red curve, at backside mass point) to deceleration phase (at front mass point, grey inward showing spiral). Marked are two mass points, a backside mass point (MH) and a front mass point (MV).

At both mass points, direction and amount of inertia are shown (green arrows), simply from last position to actual position drawn ahead. Inertia of backside mass point does show towards outside, and this mass may go on falling towards outside, while turning of some more 30 degrees. Inertia of front mass point, aready does show further towards inside. This mass point did come from its outmost track point by highest speed, thus amount of inertia there is some higher than that of backside mass point.

So, an lever-effect will exist (with turning point right side at the excentric wall), where the backside mass will push inside the front mass point. Each mass in rotation wants to stay at its outmost position, won´t like to move towards inside. By that sickle-shape however (and similar to this excentric-ring-shape), transition of outward- to inward-motion will be smooth.

Secondly, both inertia-components will have effect towards the rotor-bearing (RL, blue circle) resp. rotor-arm (blue line). At the rotor-bearing, both forces will be combined to a resulting component. It´s easy to recognize, these differing directions mentioned above, in sum will mostly add to right-angles direction. Above this, mass-points at a whole will always be inside from the rotor-bearing (even more clear at longer sickles or at excentric rings). Resulting power as a whole, thus will be nearby right-angles towards the rotor-arm. As expected, between outward- and inward-phase, at the rotor-arm nearby null forces towards the rotor-arm will exist.

Resulting line of both inertia-parts, also will have effect towards excentric wall (und thus the cylinder). Center of excentric wall, the excenter-axis (EA) will be, which turnable around the system-axis (SA) is. At the position shown here, this resulting inertia-power thus will also show nearby right-angles towards the radius of cylinder. As the cylinder will move much slower than the excenter-sickle, these relative high inertia-forces will effect acceleration of cylinder-turning.

Pressure-point at minimum angles-speed
At EVGM 15, once more two positions of excenter-sickle are shown, however: each marked but by front (MV) and backside mass point (MH), their related radius (red lines) to excenter-axis (EA), related rotor-bearing (RL) and their radius (blue lines) to system-axis (SA). Upside left, situation is shown, where the front mass point will show minimum angles-speed.

As both inertia-forces will effect at rotor-bearing, resulting power-direction again will be nearby right-angles towards the rotor-arm. Absolut speed of mass will be decelerated there, corresponding kinetic energy will be transfered to rotor-arm as a turning momentum. This deceleration will be done by reduction of radius towards the system-axis (the rotor-bearing will be more and more outside the mass-points), by pressure of the excentric wall. Radius from excenter-axis to mass points (red lines), will show direction of centrifugal force towards the excentric wall. Inertia-power (green lines) will show direction, into which excenter-axis will be pulled around system-axis, thus showing turning momentum of cylinder.

Turning center at minimum absolut speed
At EVGM 15 below, situation is shown, where the front mass point will show minimum speed. At whole phase of deceleration, and here discussed as an example, the boomerang-effect will be valid: transforming rotation into straight motion (here in direction of general turning of system). Based at design of this gear, at deceleration phase each front mass will show lower speed than each mass behind. Thus each mass ahead will work like ´traffic-jam´ towards each mass following.

Relatively, masses ahead stand still in space, so each following mass has to swing outside around this turning center. Their inertia-forces, indeed does show into this direction. Related to the system-axis, again a turning momentum towards the cylinder will result.

Sickle-effect
Boomerangs by their special shape, do show special characteristics of flight. So high rotation speed at the beginning, will be transformed into translation-speed while flying (like some other flying toys do achieve). Also sickle-shape of excentric masses do show this characteristics, whereby here this translation will mean turning of cylinder. Similar shaped excentric rings do show analog function.

This surplus of thrust (here cylinder turning) is achieved while speed of effective mass is reduced. This deceleration naturally will same time mean a reduction of kinetic energy. ´Fill up´ of kinetic energy of effective mass (thus re-acceleration of speed, at relatively constant angles-speed, however at larger radius) by the rotor-arm has to be done. However this will demand not same amount of input-power by the system, cause by ´let-it-fall-outside´ of mass at its outmost track, centrifugal power will bring this surplus by itself.

Within that acceleration phase, inertia all times will show less steep towards the excentric wall, than at deceleration phase. Power input of rotor-arm at the acceleration phase, will effect pulling the mass off the backside wall. Front mass points in that phase, all times do show higher speed and towards further ahead, than each follow mass point. Thus front mass points by their inertia, following mass points will also pull off the excentric wall.

Thus that sickle-shape does show positive effects at outward-phase, transmision from outward- to inward-phase and at the inward-phase too. Excentric-sickles - and analog excentric-rings - thus fulfill essential functions by earning energy.

Results
Already by looking at but one mass point above, asymmetry of power-relations at this movements procedure was deduced. By sickle-shape (here discussed by looking at two mass points), further reasons for co-turning of cylinder are detected.

Once more was approved, input-power is but demanded for achieving and maintaining turning of effective masses (here of excentrtic sickle). By this input, but existance of inertia-power of moved masses will be started resp. maintained. Inertia-power will help accelerating masses, when movement in this direction will not be hindered (resp. completely blocked, like spokes of normal wheels do). On the other hand, inertia-power will effect turning momentum towards the cylinder, whenever this separated element will push mass back towards inside.

There is a decisive difference, between moving concentric mass at circle tracks, and accelerating/decelerating excentric masses at spiral tracks. The one kind of motion does kill mass-inherent-energy, the other does produce a surplus of energy resp. will allow to earn this over-unit-energy.

Evert / 05.04.2000