GB2215048A - Linear force from rotating system - Google Patents

Abstract

A pair of flywheels (30) acting as gyroscopes are rotatably mounted on shafts (32) spun by motors (44) and flexible drives (46, 48). The shafts (32) are journalled in arms (38) pivoted to a central shaft (42) driven by a motor (52) via a worm drive (54, 56) which constrains the central shaft (42) to a constant rotational speed. The natural tendency of the flywheels (30) to precess upwardly is controlled by a cam (58) which allows the flywheels to rise slowly and then forces them downwardly. In another embodiment the flywheels are constrained to precess in a plane, and a mechanism is provided for forcing variations in their precessional speed. In both instances, a net linear thrust is produced. <IMAGE>

Description

PRODUCING LINEAR FORCE FROM ROTATING SYSTEM This invention relates to a method and apparatus for producing linear force from a rotating system, in an apparently unbalanced action-reaction manner.

To explain the principles underlying the invention, there will first be discussed the behaviour of a mass spinning in a plane (i.e. a gyro) and undergoing precession.

Referring to Fig. 1, consider a flywheel 1 secured to one end of a shaft 2 which is itself mounted on a second shaft 3 by means of a gimbal 4 such that the first shaft 2 may pivot in a plane in line with the second shaft 3, and the second shaft 3 can rotate about its axis. The behaviour of a flywheel mounted such that its precession and spin planes are about the same point is well known. The behaviour of a system of the type shown in Fig. 1, where the spin plane of the flywheel and the precession plane are separate, has given rise to a number of interesting observations, some of which (it has been claimed) would 'make Newton turn in his grave'. It will be shown that these phenomena can in fact be explained without any detraction in substance from Newton's laws, as a result of a more rigorous definition of mass than was hitherto thought necessary.

The problem of finding a mathematical expression for the behaviour of the precessing system of Fig. 1 is one of defining a consistent frame of reference from which the forces and velocities can be measured. In the following, the axis and spin plane of the flywheel are chosen as the origin of measurement of force and velocity. (Note:.the following analysis is not a replacement for conventional calculations, but simply expresses the physical phenomena in an alternative or additional manner).

Thus the spin speed of the flywheel is expressed in the conventional 13 (radians/s)but the velocity of the flywheel through space is expressed in metres/s. The importance of this becomes clear when it is realised that the radius of precession measured to a point on the rim of the flywheel is greater than the radius of precession at the axis of the flywheel. Reference is now made to Fig. 2, which is a schematic plan view of the system of Fig. 1. In Fig. 2, R is the radius of the flywheel 1, ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ P is the radius of precession at the axis (= length of shaft 2), L is the radius of precession at the rim of the flywheel, Z is the velocity in the direction of precession of a point on the rim of the flywheel, and V is the like velocity of a point on the axis of the flywheel.Thus in terms of these velocities a point on the rim can be said to accelerate at a rate defined by Z-V 1t(R/2 3 ) This acceleration is in the direction of precession as the point moves from a vertical position in line with the precession axis to a horizontal position in line with the precession plane. It is counter to the direction of precession as the point moves from the horizontal to the vertical position.

It is emphasised that the velocity of the point relative to the precession axis is greater at both sides of the flywheel in the precession plane than at the vertical position. If the rotation of the flywheel is subtracted, this is perfectly valid since we are considering only the acceleration defined by the precession velocity.

Effectively, the acceleration between the precession plane and the precession axis plane can be considered as an addition and subtraction to the centripetal force acting on the mass points on the rim of the flywheel as defined by v M R Since we are considering only acceleration, M can be ignored for the present.There is no actual displacement of mass with respect to the axis of the flywheel and we are dealing only with the apparent acceleration caused by V2 R + a Thus the resultant velocity at right angles to a, Vr, is defined by 2 - 2 + axR R and from this the vertical component of a, at, is #v a# #t where #v = vr - v From the above it can be seen that af is directly proportional to V at the precession plane rim of the flywheel minus V at the axis of the flywheel, provided that the velocities are measured as a vector through the plane of the flywheel.It can be seen therefore that at is proportional to the angular velocity of the precession and the spin velocity of the flywheel which defines the At of the acceleration between V at a point on the rim of the flywheel vertical to the axis of precession to V at a point horizontal to the plane of precession. Using the terms defined above, it can be seen that (cos(arctan R/P)) equals the vector of AV through the flywheel plane. Thus at = (cos(arctan R/P)) x (Z - V) T 2 Note that t2R = At for 90 rotation of the flywheel.

The force required to produce at is defined by F-+ = M x (cos(arctan R/P)) x (Z - V) R where F-E is the resultant vector of force in the flywheel plane. This vector is used to change the # of the flywheel and increases the resistance to motion of the flywheel precession.

It should also be noted that the conventional rotation of the flywheel plane about its axis at right angles to an induced rotation about its axis still takes place, and this results in any movement of the flywheel following a path rotating about the axis of precession which, as can be seen from the above equations, results in a constant angular velocity in a plane at right angles to the applied force.

Note that when the flywheel is under an acceleration equal to F-E = M x (cos(arctan R/P) x (Z - V) = M x R 2'o it need not displcae vertically for the force to balance, but if at is greater than any vertical acceleration (such as gravity) then it will displace in the apth described. If such displacement is prevented, then the force applied results in a direct acceleration of the flywheel with the force F = Ma modified by F-+ as defined above, the difference between F and F-E being absorbed in the rotation of the flywheel just as before.

It should also be apparent that if R is less than P then the conventional precession rotation will result in a net side force on the axis of precession which, if restricted, returns us to the losses described in the discussion on restricted displacement above. If R is greater than P, a net downward force on the axis of precession results. No change in the rotation speed 13 occurs unless the vertical force does work, i.e. displaces mass, in which case (3 reduces. If a displacement occurs which is greater than that defined by the vertical force, o would increase.

Use of these equations can predict the behaviour of all of the observed phenomena described in Professor Laithwaite's Engineer through the Looking Glass and reveal a number of useful methods of exploiting the results.

It should, of course, be pointed out that the above equations deal with an idealised flywheel where all mass is on the rim, and that for the real world the acceleration is an integration between Z and V. A simplification is to define the effective mass radius and calculate Z from the effective R.

For instance, for a flat disc flywheel the effective R would equal

being the radius of the effedtive centre of mass at the effective rim of the flywheel. Obviously for a very good flywheel where most of the mass is on the rim the basic equations are quite adequate and will give results within a few percent of the measured values.

Working systems Having thus outlined the principles underlying the invention1 two practical embodiments of the invention will now be described, by way of example only, with reference to the remainder of the drawings, in which: Fig. 3 is a schematic side view of an apparatus embodying the invention; and Fig. 4 is a schematic perspective view of an alternative embodiment.

The apparatus of Fig. 3 comprises a pair of flywheels 30a, 30b ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ each rigidly mounted on a respective shaft 32a, 32b so as to be pivotably movable in a vertical plane about a central point 34. It is preferred that the distance D between the centre of the flywheel 30 and the central point 34 be equal to the radius R of the flywheel. The shafts 32a, 32b are each journalled in bearings 36a, 36b fixed to arms 38a, 38b mounted by pivot bearings 40 to a central tubular shaft 42.

The tubular shaft 42 is journalled in bearings 41 in a base frame 43. A stationary central shaft 45 is secured to the base frame 43, and bearings 47 are provided between it and the tubular shaft 42.

Means are provided for driving the flywheels in rotation. In this embodiment, each flywheel 30a, 30b is driven by a respective electric motor 44a, 44b via pulleys 46 and flexible (e.g. rubber) bands 48. The motors 44 are secured to a beam 49 fixed to the tubular shaft 42 to rotate therewith.

Means are provided to rotate the central pivot bearings 42 so that the flywheels 30 may be forcibly precessed. A critical aspect of the invention is that these means for forcibly precessing the flywheels must be capable of rotating the assembly at a fixed speed irrespective of the forces acting upon it, and most particularly it must not be possible to appreciably accelerate the forced precession.

One suitable method for achieving this is shown in the present embodiment, in which the tubular shaft 42 is driven in rotation by a motor 52 via a substantial worm and pinion reduction transmission 54, 56 which prevents back transmission of force.

Further, means are provided for rapidly displacing the flywheels 30 downwards against their precession resultant at at least one position in the precession path.

Such means may be, as shown in the present embodiment, a cylindrical cam 58 acting on cam followers 60 on the arms 38, the cam 58 being mounted on the stationary central shaft 45.

Preferably, the cam 58 has a profile 58a which forces the flywheels 30 down twice in each precession revolution at 0 and 1800 positions, and allows them to rise to a maximum height at 900 and 2700 positions. Alternatively, solenoids or other linear actuators may be used for this purpose.

The precession resultant will hereinafter be referred to as the precession l-ift. Since the precession lift does not result in an equal and opposite down force on the pivot 40, the cam 58 which accelerates the flywheels 30 downwards experiences a reaction upwards. At the bottom of the cam form 58a, the flywheels 30 are again swept upwards, with the precession reduced reaction lift resulting in a net linear force. This action depends on the precession not being allowed to accelerate as the flywheels are forced downwards.

The energy for the work done comes from the flywheel spin inertia, and thus from the motors 44 or other means driving the flywheels. It is necessary for this drive to be delivered in & manner which does not restrict the vertical motion of the flywheels. The use of the rubber bands 48 has been found to impose an acceptably small restriction on this motion in a small scale system. Other possible means of delivering drive would include flexible shafts, and forming the flywheels with blades driven by gas jets, and bevel gear systeins.

It is believed that the efficiency of the system (i.e. linear force]/[power supplied] x 100%) is approximately 40%, disregarding mechanical losses in the drive.

In a development (not shown) of the above embodiment, a second, similar, pair of flywheels and cam are provided, the flywheels being arranged for precession about the same axis but in the opposite direction.

It will thus be understood that the embodiment of Fig. 3 operates by forcing the flywheels downwardly (i.e.

in the direction of the precession axis) at selected points of the precession. Fig. 4 illustrates another embodiment in which, in contrast, the vertical movement is limited and the horizontal rate of precessionis forcibly altered.

Referring to Fig. 4, the apparatus is basically as described with reference to Figs. 1 and 2. A column 70 carries a gimbal 72 to which flywheel 74 is secured by shaft 76. Means are provided for spinning the flywheel, such as motor 78 operating through pulley-and-belt drive 80. In this embodiment, however, vertical movement of the flywheel is restrained, as by rail 82, and means are provided to impart a horizontal acceleration to the flywheel over 90" of the precessional rotation. In the example shown, said means comprises a motor 8 rotating a series of spokes 84 set in a plane at an angle to the plane of the shaft 76, the spokes 84 being driven at a greater speed then the speed of precession.

The reaction resulting from the driving of the precession while constraining vertical movement of the flywheel moves the system in the direction X, opposite to the direction of the flywheel, during the driven part of the cycle. The system thus moves horizontally in a stepwise manner. The force required to drive through the 900 is of course Ma + F-E using the same notation as above. F- > is always through the plane of the flywheel so that this force acts as friction to the motor. The displaced mass of the flywheel is, however, decelerated by the internal force (see pages 3 and 4 above) giving the effect of the disappearance of the inertia of the flywheel as soon as the 900 forward precession period is over.

Thus the system axis A continues at the velocity attained in each pulse as a reaction to the mass of the flywheel until the next pulse.

It should be noted that in this system R should equal P, otherwise the precession axis would tend to wobble and losses would begreatly increased.

The duty cycle of the system of Fig. 4 is very poor.

Also, the transmission of F-t directly to the motor rahter than to a worm or ratchet mechanism reduces practical efficiency. The system is however useful since the forces are well defined and directly measurable.

Claims (7)

1. Apparatus for producing linear thrust, comprising: at least one flywheel mounted for rotation about its centre, and for precessional movement about a point aligned with but spaced from its centre; flywheel rotation drive means for driving the flywheel in rotation; precession drive means for imparting a predetermined precessionary movement, other than the natural movement of precession, to the flywheel; and displacement defining means for modifying the natural displacement of the flywheel in the direction parallel to the axis of precession.

2. The apparatus of claim 1, in which the precession drive means is arranged to constrain the precession to a constant angular velocity, and the displacement defining means acts to forcibly displace the flywheel in said direction at at least one point in the precessory motion.

3. The apparatus of claim 2, in which there are two flywheels mounted for pivotal movement about a common point.

4. The apparatus of claim 3, in which said precession drive means comprises a motor connected to a precession shaft via a transmission which does not permit reverse transfer of force.

5. The apparatus of claim 4, in which said transmission is a worm and pinion.

6. The apparatus of any of claims 2 to 5, in which said displacement defining means comprises a cam with respect to which said precessory motion occurs.

7. The apparatus of claim 1, in which the displace defining means acts to set a limit to movement of the flywheel in the direction parallel to the precession axis, and the precession drive means is arranged to impart a driving force in the direction of precession to the flywheel over 90" of the precession path.