Objectives
Basic principles of solutions of chapters above, here shall be described as a comprehensive summary. This workout and drawings may be basis for experts, in order to check ideas presented here. Thus, formulars could be defined, to approve over-unit-effect of these engines.

Experimental arrangement
At EVGM 01 upside, both first elements are shown shematically by cross-sectional view. Whole system will turn around the system-axis (SA). Here in general, turning counter-clockwise is assumed. Within the housing (here not shown), a round cylinder (ZY) is mounted, turnable around the system-axis. This cylinder will have a round drilling hole, the center of will be excentric to system-axis. This center-point is called excenter-axis (EA). The wall of this empty space resp. drilling hole is called excentric wall (EW). The distance between system-axis and excenter-axis is called excentrity.

Alongside the excentric wall, effective mass will move. This mass can be thought (theoretically) to be concentrated at a mass-point (MP). As the mass should glide alongside resp. within the excentric wall, here however mass is arranged like a sickle-shaped body. This excenter sickle (ES) should take some more than half of a circle.

That sickle-shape, special qualities does show concerning transmision at critical phases within motions approach, as described for example at Threefold-crank-concept. Thus, theoretical conciderations at least should look at a front mass point (MV, front = German vorn) and a backward mass point (MH, backward = German hinten), here however detailed later on.

At EVGM 01 below, these elements shematically are shown by longitudinal cross-section view. The cylinder is fix installed at a shaft (around the system-axis), which will be the output (AB, German Abtrieb) of the system. This shaft is mounted turnable within the housing (here not shown). The input (AN, German Antrieb) is organized analog, also by a shaft around the system-axis, here e.g. arranged upside.

At the input-shaft fix installed a rotor-arm (RT, German Rotor-Träger) will be. Outside at the rotor-arm, a pin (resp. short shaft) will be fix installed, which here is called rotor-bearing (RL, German Lager). These three constructional elements, practically a crank-shaft will be. This pin will reach into a drilling hole of the excenter-sickel (ES), which here is called excenter-bearing (EL). This drilling hole is long-stretched, so the pin (rotor-bearing RL) may glide within that slot in radial direction, inwards and outwards.

At EVGM 01 middle, this input-rotor-shaft around the system-axis is marked (by blue circle), the rotor-arm (RT) as well, also that pin of the rotor-bearing (RL). Within the excenter-sickle (ES), the long-stretched excenter-bearing (EL) is marked. When the crank-shaft will turn, the excenter-sickle will turn within the excentric wall. Rotor-bearing thereby will glide within the excenter-bearing-slot, from an inner to an outer position and vice versa. Left side, by thin lines, the position of the excenter-sickle is marked, after 180 degrees turning form starting postion right side.

So, by this crank-shaft plus glide-bearings, the input will maintain turning of the system. Thereby the excenter-sickle also will turn within the excentric wall. Resulting of this, diverse motions and power-effects will exist, which are discussed next. At first will be assumed, the cylinder to remain steady at its position.

Stationary cylinder, constant motion of mass
At EVGM 02, the cylinder (ZY) is assumed to keep its position. The excenter-sickle (ES) is assumed to turn steady (but here assumed at first, in order to analyse motions). Here, positions of a mass point (MP) of the excenter-sickle are marked after each 30 degrees turning. Motions of mass points will be concentric around the excenter-axis (small black circle), thus around the center-point of excentric wall.

The input of turning will be done by the rotor-arm, which will turn around the system-axis (small blue circle). Postions of rotor-arm here are marked by blue lines. At the outer end of the rotor-arm, rotor-bearing will glide within the excenter-bearing (here not shown). Here for example, the mass-point sometimes will be outside the rotor-bearing, and vice versa.

If a steady turning of excenter-sickle like here should be achieved, the rotor-arm should have to turn with different speeds around the system axis. When like here, the mass point should turn 30 degrees each time-unit, so same time the rotor-arm, e.g. should turn right side some 25 degrees, left side however some 37 degrees.

Losses by friction
At steady turning of masses at concentric circle tracks, like here around the excenter-axis, all inertia-power components will be symmetric and will compensate each other. So no effect towards outside will exist. Maintaining of motions like this, theoretically no energy will cost. Practically however, energy loss by friction will exist. Friction will be at shaft-bearings within the housing, between excenter-sickle and excentric wall, within the rotor- and excenter-glide-bearing. Losses by friction are un-avoidable (but can be reduced by good glide-oils), these energy-losses here (as normally) are ignored.

Drive by rotor-bearing here, not all times will be in tangential direction towards mass point. So, within this bearing, also pressure-components will show in radial direction. Such components mostly are decisive reason, why perpetuum mobile constructs in reality won´t work. In spite of this, these power-components here at first are ignored, cause other kind of bearings (see next section) only normal friction-losses will show, respectively this energy won´t be lost for the system as a whole (as discussed later in detail).

Steady turning input
So it can be noted, steady turning of mass point within this system will demand no energy (besides friction, as usual). This will also be valid, if now the rotor-arm shall turn steady speed, so mass points of excenter-sickle will have to move by different speeds.

At EVGM 03 this is shown, where now the rotor-bearing (RL, blue points) are marked after each 30 degrees turning within one time-unit. Corresponding to this, now the mass points will move different degrees same time. Red lines here will mark the position of each radius around the excenter-axis. Nearby the system-axis (left), a mass point will show but some 25 degrees of angles-speed, far away of the system-axis (right) however these some 37 degrees at a time-unit.

Depending at the relation of excentrity and radius, these relative differences of speed will be. At conciderations to Sling-effect and also at the Swivel-arm-maschine, maximum was some third above, minimum some quater below average speed.

Energy-costs for maintaining these turning motions, like conciderations above, will but be demanded to compensate friction losses. Opposite to conciderations above, now based at these different speeds of masses, inertia-power components will show essential effects towards outside.

Effective inertia-power
EVGM 04 once more does show positions of radius, at un-steady motions of mass points (by segements of about 25 to 37 degrees). In addition, inertia-components of mass points are marked at each point, green lines tangentially to excenter-axis, center of contentric turning. The value of each inertia is marked by the length of each green line. Now, these inertia forces not at all are symmetrical, won´t compensate each other, but a resulting line will exist.

The mass will turn around the excenter-axis, which is center of the excentric wall (EW). Excentric wall by itself is a part of the cylinder (ZY). Up to now was assumed, the cylinder would keep its position. This restriction now will be canceled. Thus, the excenter-axis (small black circle) may turn around the system-axis (small blue circle), as discussed above at experimental arrangement.

Inertia forces upside and downside theoretically will compensate each other. However, it must be pointed out, a mass point downside (here at this picture) will take along with itself inertia from low speed, which will be accelerated. Opposite, mass point upside, does show inertia from (earlier) higher speed and will there be decelerated. Strictly speaking, thus theoretically a mass point at no moment will show a certain (constant) speed, but accelerating or decelerating speed. Consequently, mass points at opposite positions no symmetric inertia forces may show. However these differences but marginal will be, nevertheless would be worth to think about seriously.

Co-turning
Difference of inertia forces of mass points, left versus right side (here at this picture) however obviously is. It´s no question, at the excenter-axis a resulting power-component towards upside will exist. Thus, the excenter-axis will start to turn also in turning-direction of rotor-arm (turning-center of the excenter-axis is the system-axis, so all inertia-power-components indeed are related to the system-axis). Well noted: this co-turning will not result of input power at the rotor-arm, cause this in sum will be null (besides friction). This co-turning solely will result of different inertia forces of mass points. These different forces by itself, are based on different speed of mass points at opposite positions.

Pull and push
In order to accelerate masses, the rotor-arm will have to transfer power towards the excenter-sickle. The amount of force demanded, corresponds to each acceleration of angles-speed. From inside-left towards downside, here the speed must be accelerated by nearby one degree each time-unit (25-26-27). From downside to outside-right however, each time about three degrees acceleration will be neccessary (31-34-37). Corresponding power demanded, by blue lines are marked, each right-angle towards position of rotor-arm.

Here one may notice, direction of these forces do show towards inside, in relation to each direction of inertia-forces. That´s valuable especially at the phase of essential acceleration. Thus, the rotor-arm while accelerating masses, same time will pull these masses off the excentric wall. So, the pressure of mass towards the excentric wall by centrifugal force, will be reduced (here again, resulting power-component will not be right-angles towards mass-point nore rotor-arm, however see following sections).

Opposite the situation will be, after maximum speed will be achieved (outside-right). Masses there will be essentially faster than the rotor-arm. So now, mass of excenter-sickle by rotor/excenter-bearing, will push the rotor-arm ahead. These thrust-forces are marked by black lines correspondingly (upside). Here again, power-components won´t show same direction: besides a power-component right-angles towards each position of rotor-arm (accelerating the rotor-arm resp. resulting a turning momentum), a power-component towards outside will remain. Especially at that phase of essential deceleration (outside-right to upside), thus a pressure towards the excentric wall will exist.

Thus, towards the backside half (downside, counter direction of turning) of excentric wall, in sum will exist far less pressure than at the frontside half (upside, showing into direction of turning) of the excentric wall. This difference of pressures will result a turning-momentum at the excenter-axis, will reinforce its turning around the system axis, thus also co-turning of cylinder.

This turning-momentum is based on that power-input for acceleration of mass. Corresponding to this power-input by the rotor-arm, same amount of power the rotor-arm will accfept by thrust at the deceleration-phase. So again has to be noticed, maintenance of turning of mass within a round wall won´t cost energy, whether by constant speed nore when mass is accelerated / decelerated same kind. So again: that remaining turning-momentur towards the cylinder, solely at the existance of different inertia-forces-components is based.

Turning momentums
So there are two kinds of momentums, which will bring co-turning of cylinder: on the one hand there is a momentum, based but at different speed of mass. On the other hand a momentum does result of that ´active´ input of power for acceleration of mass, and by deceleration that ´passive´ feed-back towards input-unit correspondingly.

At EVGM 05, source of the additional power is shown. Left side, a (dotted, vertical) line is drawn from system-axis (SA) to excenter-axis (EA), further down to an inner (R1) and outer (R2) track-position of mass. Instead of a circle track, the track is marked by a straight line towards right side.

Mass at the inner track point does show a relative low angles-speed (WG, red, German Winkel-Geschwindigkeit), e.g. of 24 degrees at a time-unit. Its inertia while six time-units will be able, to run 144 degrees. If however, after these six time-units, 180 degrees should be done, angles-speed must be accelerated (WG, blue, 36 degrees) by power-input of rotor-arm. Above this, this angles-speed must be achieved at an outer radius. This outwards motion will be achieved by centrifugal power (F, German Fliehkraft). The diagonal line (representing the spiral track) will be done by total speed (GT, German Geschwindigkeit-total). That resulting, diagonale line is longer than the original inertia-power plus input-acceleration-power!

Power by centrifugal forces
At EVGM 05 upside-right, this situation once more is shown, now with circle tracks. At the inner track point basic angles-speed (G) exists. Corresponding inertia power will take the mass at the outer track, e.g. but 96 degrees ahead (same distance as 144 degrees at the inner track would be). One the other hand, the rotor-arm has to bring remaining degrees of angles-speed (B). These are marked, related to excenter-axis (like segments above), at the inner track. This acceleration however must finally be done at the outer track, with these 36 degrees above. Missing distance resp. remaining speed-acceleration will result of centrifugal force (F).

By analysing Sling-effect it was noted, that slinging will lastly bring a third higher speed than speed of rotor-arm does show. Above this, this high kinetic energy will cost but low input-energy, cause input forces has to work at relative small lever-arm. This surplus of energy, there was concidered to be based at this Addition of power. Naturally this addition of inertia- and acceleration-power will exist at any acceleration-process, e.g. at straight accelerated movement too. At circle-shaped tracks however, normally centrifugal forces on and on will be ´destroyed´, e.g. by ´pulling-work´ of spokes at a normal wheel. Opposite here, space is available for centrifugal forces to have its effect, produce motion, thus producing diagonal resulting line above.

Above was ignored these differing directions of forces (cause this can be eliminated by better gears than this simple one here). However, these power-components do reinforce motion in direction of inertia, thus anyway won´t be lost for the system as a whole. How to use all these power-components inclusive that surplus of energy, next will be discussed, analog to conciderations at Tricks of Six-Day-Drivers.

Gliding over the slope
At EVGM 06, circumference of the cylinder is shown as a straight line. When the excentric wall (EW) same way is ´unrolled´, a ´wave-like´ track will result. This track no sinus-curve will be, the ´top of the hill´ will be relatively sharp, the ´hill-side´ stretched and the ´valley´ rather flat. Inner track point here will be at level R1, the outer track point at level R2. Movement of mass, from left to right is assumed.

Starting from inner track point, minimum speed (G, German Grundbeschwindigkeit) is given, to which acceleration (B, German Beschleunigung) will be added. Next, mass now may fall towards outside (here correspondingly downwards), by inertia- resp. centrifugal-force (F, German Fliehkraft). Thus by this triangle, a resulting line will exist, which is longer than given speed plus acceleration. This diagonal line is representative for kinetic energy (KE) achieved.

Same time this diagonal line (KE) does show, the mass while acceleration practically will fly parallel to that downward- hillside (at the following simply called ´down-hill´). Correspondingly this will say, mass will glide alongside excentric wall. Normally e.g., as a ball will roll down a slope, there will be a pressure towards that slope. Here however, cause the mass is accelerated within that phase, this pressure towards the down-hill (here towards excentric wall in direction to left side) at least will be reduced.

This static view can´t show situation completely. Viewed from the mass point while this acceleration phase, the down-hill seams to get steeper and steeper. In other words: the mass looks like falling slower and slower. Thus but reduced pressure may be effected towards that down-hill-side.

Acceleration- like deceleration-power
Oposite situation will be, after maximum speed is achieved, when the mass got to its outmost track point (here does run through the valley). Here it´s obvious e.g., how this high kinetic energy is directed counter next upward-hillside (at the following simply called ´up-hill´). Corresponding to mass-view above: by that high speed, also this up-hill seams more steep than this static picture may tell.

It´s clear, at the end of ´climbing´ upward (moving back to the inner track point), the mass again will show its basic speed (G). Analog to (active) acceleration, the rotor-arm by the bearings will (passive) decelerate the mass again. Corresponding to input-power for acceleration, the rotor-arm here will get a thrust-momentum of same amount, based at deceleration (V, German Verzögerung). Thus in sum, input-force at a whole will still be null (besides fristion).

Crash towards the counter-hillside
So, acceleration and deceleration of mass will be power-neutral. However, the system now has to ´work´, must bring back mass from the outer to the inner track (from level R2 to R1). At a fix (solid, normal) wheel, this work is done by spokes, on and on pulling mass towards inside, continuously redirecting inertia-direction towards inside. Here, for some moments, this work will not be done, while the mass will be allowed to fly towards outside. Next phase, now that (remaining) redirection must be made up.

It´s clear: if now this work would be done by any kind of pulling, demanded energy would exactly be same like spokes do resp. like that surplus of kinetic energy, falling-outside of mass did achieve. Thus, to avoid this balance of forces, a decisive criterium of these maschines here will be, centripedal movement of masses exclusively will be done by pressure from outside towards inside.

Thrust at the wedge
Practically, that up-hill to impacting mass like a wedge will work. Mass must be moved towards inside in radial direction, here at this picture upwards. This up-hill here, towards the impacting kinetic energy, but may show a counter-pressure right-angles towards its surface. By this counter-force, work (A, German Arbeit) will result in shape of the vertical motion upwards (resp. inwards). Same time, a horizontal power-component will result, practically a thust-force (S, German Schubkraft, here to right side).

This counter-hill-wedge, within the cylinder will correspond to the front half of excentric wall (in direction of turning). As the cylinder is free movable around the system-axis, this horicontal power-component will be like a thrust in tangential direction, thus will effect a turning momentum at the cylinder, in direction of systems general turning.

The more flat that wedge will be (the less excentrity will be chosen), the smaller that thrust will be (excentrity null will correspond to rolling of mass within a round track, where null thurst towards the track will be). However, as soon as excentrity is given - or even motion with differing speed (see discussion above at EVGM 03/04), a turning momentum towards the track will exist. Here for example, this thrust-component (S) will correspond to that length of diagonal line, kinetic energy (KE) is longer than starting speed (G) plus acceleration (B). That´s the procedure, surplus of kinetic energy (based on centrifugal forces), will be transformed into free output-power.

Input-power constant
This system must have an input of power, in order to compensate friction. There might be also losses by differing directions of power-components, as mentioned above (and reducable by better design of bearings, see later sections). The system also will need power for accelerating masses. This input however will be totally compensated by power-recovery at deceleration-phase. Also here, differing directions of power-components will occure, which however totally will be available at the output.

This input-power must exist resp. these energy-losses will be given at any turning speed, however won´t rise proportionally with turning speeds. Cause basicly, masses are but moved around circle tracks resp. outward- and inward-bended spiral tracks, accelerated and decelerated same kind, thus a no-win-no-loss-motion-game. Concerning energy-input demanded, it won´t bother decisively, whether 100 or 200 or 4.000 rpm shall be maintained.

Inertia-power by square
Output of the system will be taken at the cylinder, by a shaft around the system-axis. Output totally independant from input will be that kind, there is no direct coupling between: mass may turn completely free within the excentric wall of the cylinder. So far, input-power won´t result any output-power on direct manner.

The output-momentum, exclusively is based at inertia-power (while the input-power but will produce resp. maintain movement, in order to make inertia-power existent). Concerning centrifugal forces however, it´s an huge, really enormous difference, whether this engine will drive 100 or 200 or 4.00 or even more rpm. So, the output-momentum at least (really pessimistic view) will rise proportionally with turning speed. So above mentioned losses, at higher speeds will be without any importance. Above a critical speed, over-unit-effect will exist, no doubt.

Results
By this workout, decisive characteristics of this rotor-system in compact form once more are described. A (theoretical) experimental arrangement was introduced, approaches of motions discussed, power-effects deduced. The claim is, thus theoretical basis of a perpetuum mobile is defined. Reasons were named, why energy surplus can be achieved. Now it would be find, if experts would seriously check these texts and drawings, per formulas or simulations could confirm these claims.

At following sections, the energy-balance once more will be detailed, later on some new gears will be introduced, lastly a maschine presented, totally conform to crop circle picture.

Evert / 29.03.2000