Strange and asymmetric swinging of pendulum masses, shown at end of previous chapter Swivel-Arm-Wheel, here at this chapter is described in details. In order to inforce asymmetry, here pendulums are used showing asymmetric shape by itself.
Starting basics
At picture EV PRM 01 schematically is shown cross-sectional view of basic design. A rotor arm (RT, German Rotorträger) is turnable around system axis (SA). This rotor arm is a round disc or is build by several spokes (in real machines resp. following model each disc or spoke are arranged double at central shaft, so weigths are supported symmetrically).
At this rotor arm are installed one or several (here e.g. eight) axis (RA, rotor-axis, small blue points at dotted blue circle). A rotor (RO) is mounted turnable around each of these rotor axis. The rotor, in principle is build by two lever arms (red lines), not straigt arranged but showing an angle between, here e.g. of some 135 degrees. At the end of each lever arm, effective masses are fixed. Relative light mass (ML) is installed at long lever arm, at short lever arm is installed a mass more heavy (MS, German schwerere Masse).
Symmetric weights
Based on gravity, all masses are pulled downwards corresponding to each weight. So here are effective vertical weights of light masses (GL, German Gewichtskraft leicht) and weights of more heavy masses (GS, German Gewichtskraft schwer). Lenghts of lever arms should be that kind, at resting system momentums are balanced and long lever arm generally should show in horicontal direction.
When system is turned slowly (here counter clock-wise is assumed in general), each rotor will keep that horicontal position. Both masses of rotor will move at circled tracks, however not concentric around system axis, but at tracks marked here by green dotted circles. Light masses move at circle around its turning point (DL, German Drehpunkt leicht), shifted some left of system axis. Heavy masses turn around a turning point (DS, Drehpunkt schwer) shifted some downside right of system axis.
By slow turning, all forces are balanced. Also moving masses downwards and upwards, in sum is balanced concerning forces (naturally losses by friction not regarded). If however that system turns faster, centrifugal forces will come up with ´strange´ consequences.
Asymmetric centrifugal forces
Situation above, once more is shown at picture EV PRM 02, here however centrifugal forces are marked. All masses moved, based on inertia, want to move further on, in straight direction by same speed, as well known. Here both masses are redirected into both circled tracks. So corresponding centrifugal forces will exist, radial to each turning point (DL resp. DS). Values and directions of centrifugal forces of light masses (ML) are marked by short green lines (FL, German Fliehkraft leicht). Centrifugal forces of heavy masses (MS) are marked by longer green lines (FS, German Fliehkraft schwer).
If rotor is positioned most upside or most downside, centrifugal forces will weight at lever arms of corresponding lengths, so forces are symmetric resp. balanced. If rotor however is at any other position, both different centrifugal forces of its masses will weight at different length of effective lever arms, so turning momentums around each rotor axis will exist. (Distance between masses and rotor axis, looked from system axis, here is called ´effective lever arm´).
At rotor position upside left e.g., centrifugal force of heavy mass will push in direction towards rotor axis and thus won´t have effect. Opposite, centrifugal force of light mass does work at effective lever arm and thus will turn rotor around rotor axis clock-wise.
Analogly, e.g. centrifugal force of light mass at position left outside will pull radially at rotor axis, so no turning effect exists. Centrifugal force of rotor´s heavy mass at this position however will effect turning momentum.
At position downside left, both centrifugal forces work at both sides of rotor axis. Based on different values and lengths of lever arms, still a momentum will exist turning rotor clock-wise.
Analog relations of forces are given at upward phase, right side of this picture. So, also at this system all centrifugal forces in sum are symmetric. However, as asymmetry at upside left position already will turn rotor clock-wise, masses no longer will move at concentric tracks with constant speed. Correspondingly, also centrifugal forces will show different values and differing directions. By this concept of mass arrangement, thus symmetry of forces is broken, opposite to all ´normal´ rotor-systems.
Unsteady turning
Picture EV PRM 03 does show existing turning momentums in principle and how rotor thus will have to turn. As neutral starting position, rotor upside (near H) will be looked at. For comparison, ´normal´ tracks of both mass points (at slowly turning system) are marked by dotted green circles.
Upside left, centrifugal force (FL) of light mass will effect turning of rotor clock-wise. Resulting of that movement, also centrifugal force (FS) of heavy mass now will work at effective lever arm. Upside at this section A, thus rotor will ´rise-up´: light mass (ML) will keep relative high level outside of its (normal) circled track, while heavy mass (MS) can fall down will accelerated speed.
Outside left, effect of centrifugal force of light mass will got lost, cause some times working radial to rotor axis. By ´straighten-up´ position of rotor, centrifugal force of heavy mass however can work at even longer effective lever arm (section B). Above this, heavy mass will show high value of inertia, based at its relative high speed at this phase.
Keeping this ´up-right´ position, rotor can fall further downwards. Light masse there will move relative far inside, heavy mass rather far outside of corresponding circled tracks. At section C, both centrifugal forces will (partly) compensate each other. At least quite downside at section D, heavy mass will hang vertically below rotor axis, while weight of light mass will work at effective lever arm. Down there, thus rotor will swing back to horicontal position, based on weights of masses.
Downside right at section E, rotor again will show balanced position concerning weights of both masses. Centrifugal force of light mass however will effect further on in given direction (so now turning rotor counter clock-wise). Outside right, both centrifugal forces do work same turning sense. At section F, thus light mass will be positioned relative deep below rotor axis, while same time heavy mass is positioned at relative high level.
Weight of light mass thus does work at relativ short effective lever arm, while heavy mass weights at relativ long effective lever arm. This un-balancy of weight-momentums and (partly) compensation of centrifugal forces will effect back-swinging of rotor at section G. Thus rotor there will turn clock-wise around its axis and does swing back to its starting position of section H. This swinging movement will go on by ´straighten-up´ at section A as described above.
This animation visualizes process of movements in principle. Instead of circled tracks, masses here move at tracks somehow eliptic. Light mass swings out upside-left and downside-right. Heavy mass swings out rather far downside-left and a little bit upside-right.
Turning momentums
At picture EV PRM 05 tracks of both masses are marked. Track of light mass (ML) is marked by green thin curve, track of heavy mass (MS) is marked by grey thick curve. By dotted lines also are marked ´main-axis´ of both tracks, which look somekind like elipses. Both main-axis show an angle between, some half of 135-degree-angle between rotor-arms.
A rotor (RO) is drawn at position downside left. Weight and centrifugal forces of masses are beared by rotor axis (RA). From there, practically by a spoke (SP) of rotor arm, these forces are beared resp. supported by system axis (SA).
At position of rotor shown here, light mass is moving at a track rather flat. Light mass here also moves rather slow. So at this position, light mass will show rather small centrifugal forces.
Opposite, from section above, heavy mass was allowed to fall downwards at nearby parabel-shaped track, so at position downside-left heavy mass does show rather high speed. Corresponding high centrifugal forces now will come up at following phase of redirection into circled track. These relative strong forces of heavy mass, lastly are supported by system axis. So distance between SA and MS will be stretched.
Angle-shaped design of rotor does allow that stretching movement demanded. By stretching movement, rotor axis is accelerated into turning sense of system. Same time, light mass is strongly accelerated towards right side. So demanded redirection is ´cushened´ resp. transformed into relative soft transition. Above this, at rotor arm (here represented by that spoke) will result turning momentum in turning sense of system. As an other positive aspect, light mass will achieve high speed without loosing correspondingly its potential energy of high level.
This system is characterized by its special arrangement of masses. Effective mass is not installed directly at rotor arm, but at a two-arm (and in addition asymmetric) pendulum, turnably beared by rotor axis. In principle, each mass tries to stretch distance between mass and system axis. Mass behind (in turning sense of system) rotor axis thereby will pull back rotor arm, mass ahead of rotor axis (like heavy mass at position marked here) will pull rotor arm ahead. Thus this pendulum-rotor shows negative and positive turning momentum same time, at every position of rotor.
Shifted phases
At picture EV PRM 06 once more these tracks above are drawn, track of light mass (ML, green thin curve) and track of heavy mass (MS, grey thick curve). For comparison, each circled track (dotted green resp. grey circle) around each turning point are marked (tracks of masses at slow turning system). Again there is drawn rotor at position downside left, in addition now also opposite rotor upside right.
Light mass is behind (in turning sense of system) its rotor axis at section of track from A to B. At this phase, light mass will produce negative turning momentum, e.g. if rotor is at position downside left. Light mass at this section however is far inside of corresponding circled track. So light mass moves relativly slow and at this rather flat section will show only small centrifugal forces.
Opposite, at section from B to A, light mass does move rather near to circled track. Corresponding to longer distance, mass will do this section by higher speed. Based on steady redirection will exist correspondingly higher centrifugal forces. So light mass at this upside section does show higher turning momentum. As light mass there is positioned before its rotor axis (e.g. light mass of rotor here upside right), this momentum will work positive in turning sense.
Totally different is situation and effect of heavy mass. At its track section from C to D, heavy mass is positioned before its rotor axis (with generally positive momentum). Mass there moves rather outside of corresponding circled track (with correspondingly high speed). Mass from upside left can fall down rather free, so correspondingly high kinetic energy is build-up. Finally downside left, these strong forces are redirected elastically and thereby transformed into positive turning momentum.
Heavy mass is behind its rotor axis at track section from D to C. Mass there moves at a track rather near to corresponding circled track, so there does move relative slowly. Resulting negative turning momentum of this upper section thus is far smaller than positive momentum of heavy mass at its downside section of track.
Building-up oscillation
In principle, this picture shows two oscillating circuits. Both ´eliptic-shaped´ tracks are phase-shifted. Just these shifted phases, at previous chapters were recogniced to be essential prerequisite for building-up of mechanical oscillating circuits.
Mutual building-up is essentially based on stretching movement of lever arm system, when heavy mass downside left has to be redirected strongly. Same time, light mass does move at rather flat track. At the following however, downside right, light mass must be redirected rather sharp. Thereby, heavy mass is slinged upwards at rather straight track. Also at this upward-phase thus stretching movement exists, here however between light mass and system axis.
Both masses swing at tracks with variing radius and move with differing speeds. Each rotor in principle is build by two different lever arms, like two asymmetric but coupled pendulums. Based only at this skillful arrangement of pure mechanical parts, both mechanical oscillating systems do build-up each other.
Turning speed of system is self-accelerating, however only up to certain speed, cause weight does work as regulator. If that system would move mass faster downwards than mass would fall free, mass at downward movement won´t weight on spokes any more (while at upward phase masses weight even more at spokes). Up to this maximum turning speed however do exist accelerating forces, which partly are available for free usage outside of system.
Design
Amount of usable energy depends on effective masses at rotors, lengths of lever arms of these pendulums, angle between these pendulum arms, but also on relation of these lenghts to length of spokes resp. diameter of rotor arm. Optimum can be found by experiments or by simulation programs with corresponding calculations.
Different number of rotors can be installed at one axial level. Above, processes of movements were demonstrated by eight rotors, previous animation shows three rotors as an example. Even only one rotor could be installed (and rotor arm practically would be just a crank-shaft). Also number of rotors at each axial level is to find by experiments or calculations.
Picture EV PRM 07 schematically shows basic design of that machine, upside by longitudinal cross-sectional view, downside as cross-sectional view. There must be a housing (GE, German Gehäuse), within which a shaft at system axis (SA) must be mounted turnable. Fix connected with that shaft must be a rotor arm (RT, German Rotorträger) with its bearings (RA), by which turnably beared are rotors (RO, here e.g. three). At each rotor, light mass (ML) and heavy mass (MS) must be installed by principles mentioned above.
Model
In order to approve these claims and to test this system, I installed two boards parallel to each other, turnable around system axis. At each end of that rotor arm, two rotors are installed, also turnable around their rotor axis. Each rotor is build by two boards, between which light and heavy mass is fixed. Boards are simple laminated boards from hobby market, masses are dumbbells from sports shop, bearings are simple bolts and nuts. Supporting block of previous model is used once more.
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Foto left side shows construction of rotor with both different masses. Foto at the middle shows rotor arm with both pendulum-rotors while turning. For some phases, process of movements were exactly as theoretically descirbed above. If however rotor downside left did produce turning momentum, rotor arm is accelerated and thus has influence to swinging movement of rotor opposite.
So, damned, again phases came up with unsteady and much too short swinging and system did kill its beautiful movements by itself. So, I removed one rotor and balanced rotor arm by masses directly at rotor axis (foto right side). However, unfortunately, I couldn´t manage to make this system steady turning.
Sychronous swinging
Advantage of this concept is usage of pure mechanical parts, instead of elastic spring elements of previous model. However it still seems to be essential fact to coordinate pendulum swinging with system turning speed. Only if pendulums make one oscillating movement while one turning of system, building-up of these mechanical oscillating circuits is possible - and automatically will be a self-accelerating system.
Thus again, all distances and weights must be coordinated well. Probably should be used freewheel bearings (turnable only one direction), so relative back turning is eliminated. Probably this system can work only with one rotor and unsteady speed of turnings. On the other hand it could make sense to drive this system with more than these two rotors, and supported by flywheel with constant turning speed. It also might be, this system does work only with workload (more than only friction-losses of this model).
All these experimental variations I can´t do with my small workshop and poor equipment. However, if ever it should be possible to build-up mechanical oscillating circuits by pure mechanical tools, concept here described will be good theoretical basis. Probably these conciderations are interesting enough for someone to achieve better results by better resources.
I did well know about my poor mechanical skills, so I shouldn´t have to approve this matter of fact once more with constructing models by myself. So at the future, I will return to pure (might be poor) theoretical conciderations. I am glad I can do this, cause just at this very moment, a colleague and inventor with much better skills did succeed really. So Bessler-Problem is solved practically - and I am allowed to write about theoretical aspects of that solution at next chapter. At further chapters I will work out theory for solutions in general and also will show some applications.
Evert / 08.04.2002
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