Abstract:
The invention is a device that converts a linear input to a rotational output. The invention includes a system of one or more extendable and retractable members that actively change the radius of rotation of weights on the members. The members are connected to a rotatable member for rotation about a non-vertical axis. By actively changing the radius of rotation of a weight, a non-circular path is established for each weight to follow. This path is biased so that, while the weight has the greatest radius of rotation, it also is undergoing a downward stroke. While the weight is undergoing an upward stroke, the radius of rotation is at its minimum. The system thereby utilizes the force of gravity during transitions between maximum and minimum radii to produce a rotational output.

Description:
FIELD OF THE INVENTION  
       [0001]     The present invention relates generally to rotational machines and devices and more particularly to a gravity operated or assisted machine for supplying, conserving, and/or recovering energy, for example for the purpose of rotating a shaft.  
       BACKGROUND  
       [0002]     A variety of different devices utilizing gravity to produce a rotary output have been invented. Typically, such devices include one or more weights arranged on movable members and coupled for rotation with a rotating shaft. For example, in U.S. Pat. No. 6,694,844 to Love (“Love”) an apparatus to recover energy through gravitational force is disclosed having a wheel-like, connected, encircling surface, including an axially horizontal track which has an interior surface which weighted objects contact and are carried around the interior surface. The interior surface is a connected, encircling, wheel-like surface, is not a round circle or a cylinder, but has an offset center of rotation closest to a side which approaches perpendicular, the weighted objects are carried by spokes attached to a support hub through the offset center of rotation. A plurality of spokes extend diametrally of the track in axially and circumferentially spaced array. Weighted objects are mounted on opposite ends of each spoke. The offset center causes the spokes to move axially diametrally of the track and extend the weights to rise and lower as the weights traverse the path of the interior surface.  
         [0003]     Similarly, U.S. Pat. No. 6,237,342 to Hurford (“Hurford”) discloses a gravity motor formed of at least one motor unit which has at least one motor member fixed to an output shaft. The output shaft is rotationally mounted on a housing. The housing includes a guide surface. The motor member is low frictionally longitudinally movable relative to an output shaft. Each end of the motor member includes a weighted follower which is low frictionally movable relative to a guide surface. The rotation of the motor unit will cause one weighted follower to be moved toward the output shaft by the guide surface with the opposite weighted follower of the motor member being moved away from the output shaft.  
         [0004]     Existing devices, such as those described above, generally tend to require a significant amount of energy to operate due to the substantial frictional resistance inherent in such designs. Further, such devices do not operate in a manner that results in efficient utilization of gravity to produce a rotational output.  
       SUMMARY OF THE INVENTION  
       [0005]     A machine for converting a linear input to a rotary output is provided comprising: a rotatable member, an extendable and retractable member coupled to the rotatable member for rotation therewith, and a control that extends and retracts the extendable and retractable member during rotation of the rotatable member generally in relation to the angular position of the extendable and retractable member while tending to maintain the potential energy of the extendable and retractable member during at least part of extension and retraction.  
         [0006]     A method for converting a linear input to a rotary output is also provided comprising: radially extending and retracting an extendable and retractable member coupled to a rotatable member as it rotates about an axis of rotation that has a vector component which extends perpendicularly to the direction of a gravitational field;  
         [0007]     wherein the extending includes extending the extendable and retractable member generally in relation to the angular position of the extendable and retractable member with respect to such axis while tending to maintain the potential energy of the extendable and retractable member during at least part of extension.  
         [0008]     Another method for converting a linear input to a rotary output is also provided comprising: radially extending and retracting an extendable and retractable member coupled to a rotatable member as it rotates about an axis of rotation that has a vector component which extends perpendicularly to the direction of a gravitational field;  
         [0009]     wherein the retracting includes retracting the extendable and retractable member generally in relation to the angular position of the extendable and retractable member with respect to such axis while tending to maintain the potential energy of the extendable and retractable member during at least part of retraction.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0010]     Many aspects of the invention can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present invention. Likewise, elements and features depicted in one drawing may be combined with elements and features depicted in additional drawings. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views.  
         [0011]      FIG. 1  is an oblique view of an embodiment of the invention.  
         [0012]      FIG. 2  is an end view looking down the axis of rotation Z of the embodiment of the invention shown in  FIG. 1 .  
         [0013]      FIG. 3  is an end view looking down the axis of rotation Z of the embodiment of the invention shown in  FIG. 1  showing the position of the extendable and retractable member at six circumferential locations.  
         [0014]      FIGS. 4A-4L  are schematic diagrams showing the radial position of the extendable and retractable member at twelve circumferential positions, looking down the axis of rotation Z.  
         [0015]      FIG. 5  is a diagram of the path traveled by a moveable weight during a complete revolution of an extendable and retractable member.  
         [0016]      FIG. 6  is an oblique view of a machine having three extendable and retractable members.  
         [0017]      FIG. 7  is a cross-sectional view of a machine having three extendable and retractable members.  
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0018]     For the sake of facilitating this detailed description of the invention the approximate rotational positions are described relative to the typical twelve hours shown on the face of a clock. Six o&#39;clock is oriented in the downward direction and twelve o&#39;clock is oriented in the upward direction. Therefore, it will be appreciated that with this orientation, the six o&#39;clock direction is the direction of the force of gravity.  
         [0019]     Further, as used herein the term “upward sweep” refers to rotational movement in a direction opposed to the direction of the force of gravity. Similarly, with this orientation, 0 degrees corresponds to the 12 o&#39;clock position and 180 degrees corresponds to the 6 o&#39;clock position The term “downward sweep” refers to rotational movement in a direction coincidental to the direction of the force of gravity. Rotational movement from twelve o&#39;clock to six o&#39;clock, clockwise or counterclockwise is a downward sweep. Rotational movement from six o&#39;clock to twelve o&#39;clock, clockwise or counterclockwise, is an upward sweep.  
         [0020]     It will also be appreciated that the actual rotational positions and paths traveled the components described herein are approximate. This is because in operation of the machine one or more components of the machine may be in the process of moving over a radial path while also undergoing rotation about a central axis. Thus, it is to be understood that the rotational positions set forth in the following description are merely illustrative and that in practice the rotational positions may differ.  
         [0021]     The following description is exemplary in nature and is in no way intended to limit the scope of the invention as defined by the claims appended hereto. Referring to  FIGS. 1 and 2 , a machine  10  is shown for converting a linear input to a rotary output. The machine includes a rotatable member  20  rotating about an axis of rotation Z and coupled to an output  26 . An extendable and retractable member  30  is shown coupled to the rotatable member  20  for rotation therewith. The extendable and retractable member  30  is shown in  FIGS. 1 and 2  coupled perpendicularly to the rotatable member  20  and extending through the rotatable member  20 . However, other configurations are possible including extendable and retractable members that do not extend through the rotatable member  20  and are not perpendicular to the axis of rotation Z. The extendable and retractable member  30  includes a shaft  32 , a movable weight  34  configured on the shaft  32  for radial movement, and a counterweight  36 . A control  40  is configured to adjust the radial position of the movable weight  34  in response to the circumferential position of the movable weight  34  relative to the axis of rotation Z. The control  40  may operate a power or work input device  42  such as an electric, hydraulic, pneumatic, or magnetic motor that provides a work input to move the movable weight  34  along the shaft  32 , e.g., as may be needed to overcome losses or the like in the machine  10  due to friction, air resistance, or other resistance to rotation of the rotatable member  20 .  
         [0022]     Turning to  FIGS. 3-5 , the operation of the machine  10  will be described. In  FIG. 3 , a diagram depicts the machine  10  in six positions. The machine  10  for converting a linear input to a rotary output is shown having a single extendable and retractable member  30 . Six different circumferential positions, A, B, C, D, E, and F, of the extendable and retractable member  30  are indicated in  FIG. 3 . The radial position of the movable weight  34  in each of the circumferential positions is also shown. In this embodiment, the machine  10  for converting a linear input to a rotary output rotates in the clockwise direction.  
         [0023]     Beginning at circumferential position A, the extendable and retractable member  30  is in the twelve o&#39;clock position and the movable weight  34  is spaced radially from the axis of rotation Z a distance R 1 . As the extendable and retractable member  30  rotates from twelve o&#39;clock at circumferential position A to two o&#39;clock at circumferential position B (a downward sweep), the movable weight  34  is extended radially outward away from the axis of rotation Z to a distance R 3 . As the movable weight  34  is extended radially outward, it tends to maintain its potential energy by traveling along the horizontal path T 1 . T 1  is a line tangent to the arc of rotation at twelve o&#39;clock of the moveable weight  34  at a distance R 1  from the axis of rotation Z. It will be appreciated that during the transition in radius from R 1  to R 3 , the potential energy of the movable weight  34  is maintained while gravity inputs work to the system tending to rotate the extendable and retractable member  30 , that in turn rotates the rotatable member  20 . In an exemplary embodiment, the potential energy of the moveable weight  34  is maintained generally constant during the transition in radius from R 1  to R 3 .  
         [0024]     At circumferential position C, the extendable and retractable member  30  is in the four o&#39;clock position. The movable weight  34  is spaced from the axis of rotation Z a distance R 3 . Thus, as the extendable and retractable member  30  rotates from two o&#39;clock at circumferential position B to four o&#39;clock at circumferential position C (a downward sweep), the movable weight  34  remains at a maximum distance R 3  from the axis of rotation Z.  
         [0025]     As the extendable and retractable member  30  rotates from four o&#39;clock at circumferential position C to 6 o&#39;clock at circumferential position D (a downward sweep), the movable weight  34  is retracted radially inward towards the axis of rotation Z such that the distance between the movable weight  34  and the axis of rotation Z, or radius, is returned to R 1  when the extendable and retractable member  30  reaches six o&#39;clock at circumferential position D. Thus, from circumferential position C to circumferential position D, the movable weight  34  tends to follow the horizontal line T 2 . T 2  is a line tangent to the arc of rotation at six o&#39;clock of the movable weight  34  at a distance R 1  from the axis of rotation Z. Again, it will be appreciated that during the transition in radius from R 3  to R 1 , the potential energy of the movable weight  34  is maintained while gravity inputs work to the system tending to rotate the extendable and retractable member  30 , which in turn rotates the rotatable member  20 . In an exemplary embodiment the potential energy of the moveable weight  34  is maintained generally constant during the transition in radius from R 3  to R 1 .  
         [0026]     As the extendable and retractable member  30  is rotated from six o&#39;clock at circumferential position D through circumferential positions E and F and back to twelve o&#39;clock at circumferential position A (an upward sweep), the radius remains R 1 . During this time, the moveable weight  34  is elevated from line T 2  to line T 1  and therefore must act against the force of gravity.  
         [0027]     In the illustrated embodiment, R 1  is approximately one-half the distance R 3 . For the sake of this description, it will be appreciated that the distance R 1  is less than the distance R 3 . In addition, R 1  and R 3  may represent the respective minimum and maximum distances that the movable weight  34  is spaced from the axis of rotation Z at any point during a revolution. However, it will be appreciated that in some embodiments, R 1  and R 3  may not be the respective minimum and maximum distances that the movable weight  34  is spaced from the axis of rotation Z. For example, in some applications it may be desirable to further increase or decrease the radius of the movable weight  34  at the circumferential locations A, B, C, D, E, and F, or at other intermediate circumferential locations.  
         [0028]     In general, the spacing between the movable weight  34  and the axis of rotation Z is greater during the downward sweep than during the upward sweep. That is, the radius of the movable weight  34  from the axis of rotation Z is generally greater on average when rotating from the twelve o&#39;clock position A to the six o&#39;clock position D than when rotating from the six o&#39;clock position D to the twelve o&#39;clock position A.  
         [0029]     It will be appreciated that, by maintaining the potential energy of the movable weight  34  during segments of a revolution as described above, gravity can be utilized to produce a rotational output from a linear input.  
         [0030]     Turning to  FIGS. 4A-4L , a more simplified illustration of an embodiment of the machine  10  of the present invention will be described. In  FIGS. 4A-4L , the radial position of the movable weight  34  is shown at each of the twelve hour positions beginning with the twelve o&#39;clock position  4 A and rotating clockwise through the hours to the 11 o&#39;clock position  4 L. It will be appreciated that the center of the rotatable member  20  in each of the  FIGS. 4A-4L  is in the same relative position and the difference between the drawings is the relative position of the extendable and retractable member  30  and the relative position of the moveable weight  34 .  
         [0031]     Beginning in the twelve o&#39;clock position as shown in  4 A, the movable weight  34  is at radius R 1 . In  FIG. 4B , the extendable and retractable member  30  is at one o&#39;clock rotating clockwise (a downward sweep) while the movable weight  34  is extending radially outward. The radius of the movable weight  34  at this position is R 2 . It will be appreciated that R 2  is an intermediate radius greater than R 1  but less than R 3 . The position of the movable weight  34  is generally along a line T 1  tangent to the arc of rotation at twelve o&#39;clock of the movable weight  34  at a radius R 1 . Thus, the movable weight  34  in  FIG. 4B  has generally the same potential energy as when at twelve o&#39;clock, as calculated by PE=mgh, wherein m is mass, g is the gravitational constant, and h is height. There is generally no loss of potential energy of the movable weight  34  while undergoing this movement even though the force of gravity is acting on the moveable weight  34  and the system through the extendable and retractable member  30 .  
         [0032]     In  FIG. 4C , the extendable and retractable member  30  is rotating clockwise at  2  o&#39;clock and the movable weight  34  is at radius R 3 . Again, the position of the movable weight  34  is generally along a line T 1  tangent to the arc of rotation at twelve o&#39;clock of the movable weight  34  at a radius R 1 . Thus, the movable weight  34  in  FIG. 4C  has generally the same potential energy as when it was at twelve and one o&#39;clock, as calculated by PE=mgh, and this is when the system is gaining energy.  
         [0033]     In  FIG. 4D , the extendable and retractable member  30  is rotating clockwise at 3 o&#39;clock and the movable weight  34  is at radius R 3 . Similarly, in  FIG. 4E , the extendable and retractable member  30  is rotating clockwise at 4 o&#39;clock and the movable weight  34  is at radius R 3 . In  FIG. 4E , the movable weight  34  is generally along a line T 2  tangent to the arc of rotation at six o&#39;clock of the movable weight  34  at a radius R 1 .  
         [0034]     In  FIG. 4F , the extendable and retractable member  30  is rotating clockwise at five o&#39;clock and the movable weight  34  is at radius R 2 . Again, the movable weight  34  is generally along a line T 2  tangent to the arc of rotation at six o&#39;clock of the movable weight  34  at a radius R 1 .  
         [0035]     In  FIG. 4G , the extendable and retractable member  30  is rotating clockwise at six o&#39;clock and the movable weight  34  is at radius R 1 . It will be appreciated that from four o&#39;clock to six o&#39;clock the movable weight  34  travels along the horizontal line T 2  tangent to the arc of rotation at six o&#39;clock of the movable weight  34  at a radius R 1 . Therefore, the potential energy of the movable weight  34  is essentially constant from the four o&#39;clock position seen in  FIG. 4E  to the six o&#39;clock position seen in  FIG. 4G , as calculated by PE=mgh.  
         [0036]     During the remaining portion of the revolution of the extendable and retractable member  30  from six o&#39;clock in  FIG. 4G  to 12 o&#39;clock in  FIG. 4L  (upward swing), the extendable and retractable member  30  is rotating clockwise and the movable weight  34  is at radius R 1 .  
         [0037]     Turning now to  FIG. 5 , a diagram is shown depicting the path P traveled by a moveable weight  34  during the clockwise revolution of an extendable and retractable member  30  in a typical embodiment of the present invention. It will be appreciated that the path P is equally applicable to the moveable weight  34  of a single extendable and retractable member machine  10  or a multiple extendable and retractable member machine  10 ′. A circle  100  divided into six equal portions is superimposed in phantom over the path P. Location A is at the twelve o&#39;clock position, location B is at the two o&#39;clock position, location C is at the four o&#39;clock position, and location D is at the six o&#39;clock position.  
         [0038]     Beginning at 12 o&#39;clock in location A as the extendable and retractable member  30  begins a downward sweep, the moveable weight  34  travels horizontally along the line A-B to two o&#39;clock in location B. This movement of the moveable weight  34  is indicative of an extension of the radius of the moveable weight  34  from R 1  to R 3  as shown. From two o&#39;clock in location B, the moveable weight  34  maintains radius R 3  as it rotates along the arc B-C to 4 o&#39;clock in location C. The moveable weight  34  then travels horizontally along line C-D to six o&#39;clock in location D, where it is at radius R 1 . From six o&#39;clock in location D to twelve o&#39;clock in location A the extendable and retractable member  30  is in an upward swing and the moveable weight  34  travels along the arc D-A thereby maintaining the radius R 1 . Collectively, lines A-B and C-D, and arcs B-C and D-A, form the path P.  
         [0039]     In  FIG. 6 , a machine  10 ′ (primed reference numerals designate elements that are similar to elements designated by the same non-primed numerals) having three extendable and retractable members  30 ′ space uniformly around a rotatable member  20 ′ is shown. In this embodiment, the three extendable and retractable members  30 ′ each function individually in a similar manner as described previously with respect to a single extendable and retractable member  30 ′ machine. That is, as each extendable and retractable member  30 ′ rotates about the axis of rotation Z′, the movable weight  34 ′ of each extendable and retractable member  30 ′ is extended or retracted radially by the control  40 ′ as a function of the circumferential position of each respective extendable and retractable member  30 ′. Due to the additional extendable and retractable members  30 ′, this embodiment may achieve a more balanced machine  10 ′ and may increase efficiency over a single extendable and retractable member machine  10  through energy exchanges arranged between the plurality of extendable and retractable members  30 ′.  
         [0040]     It will be appreciated that, in general, any suitable number of extendable and retractable members  30 ′ may be used to practice the present invention, the primary consideration being the extension and retraction of the members in the manner previously set forth. Further, the extendable and retractable members  30 ′ can be arranged along axis Z of the rotatable member  20 ′ such that one or more extendable and retractable members  30 ′ are in different axial planes (i.e., planes extending through the axis Z).  
         [0041]     In a machine  10 ′ having multiple extendable and retractable members  30 ′, it may be advantageous to provide a linkage that hydraulically, mechanically, or otherwise links the individual extendable and retractable members  30 ′ such that the extension of one moveable weight  34 ′ couples to the retraction of another moveable weight  34 ′. Such an interlink between two or more extendable and retractable members  30 ′ may provide additional increases in efficiency by facilitating energy transfer between the extendable and retractable members  30 ′ during extension and retraction, thereby preserving system energy, and increasing overall efficiency.  
         [0042]     For example, in  FIG. 7 a  machine  10 ′ having three extendable and retractable members  30   a ′,  30   b ′, and  30   c ′ is shown including a linkage device  50 . The linkage device  50  may be hydraulic, pneumatic, mechanical, magnetic, etc. Linkage members  52  link each extendable and retractable member  30   a ′,  30   b ′,  30   c ′ together via the linkage device  50 . The linkage device  50  can provide for the extendable and retractable members  30   a ′,  30   b ′,  30   c ′ to exchange energy during extension and retraction. Thus, as one extendable or retractable member  30   a ′,  30   b ′,  30   c ′ is extended, one or both of the other extendable and retractable members  30   a ′,  30   b ′,  30   c ′ may be retracted. It will be appreciated that the rotational kinetic energy of an extendable and retractable member  30   a ′,  30   b ′,  30   c ′ tends to decrease during extension and increase during retraction. The increase in rotational kinetic energy is supplied by the energy input required to retract the extendable and retractable member  30   a ′,  30   b ′,  30   c ′ inwardly. Therefore, by linking the extendable and retractable members  30   a ′,  30   b ′,  30   c ′, the linkage device  50  can transfer at least a portion of the energy input required to retract the extendable and retractable members  30   a ′,  30   b ′,  30   c ′ by providing for the transfer of rotational energy from an extending extendable and retractable member  30   a ′,  30   b ′,  30   c ′ to a retracting extendable and retractable member  30   a ′,  30   b ′,  30   c ′. For example, the linkage device  50  provides for the transfer of rotational energy from an extending extendable and retractable member  30   a ′ to a retracting extendable or retractable member  30   b ′. As the machine rotates, energy from extendable and retractable member  30   b ′ is then linked and exchanged with extendable and retractable member  30   c ′ and so on throughout the system, energy being progressively exchanged between typically adjacent extendable and retractable members. In this manner, the linkage device  50  may tend to further increase the efficiency of the machine  10 ′ by facilitating these transfers of energy. As previously mentioned, in a multiple extendable and retractable member machine  10 ′, the members  30   a ′,  30   b ′,  30   c ′ can be offset axially along the axis Z. Such and arrangement of the extendable and retractable members  30   a ′,  30   b ′,  30   c ′ can be advantageous when utilizing the linking device  50  to exchange energy between the extendable and retractable members  30   a ′,  30   b ′,  30   c′.    
         [0043]     The linkage device  50  described above with reference to a three extendable and retractable member machine  10 ′ can be incorporated into a machine having any number of extendable and retractable members  30 . Furthermore, when two or more extendable and retractable members  30  are linked to exchange energy, it may be sufficient or advantageous to maintain the potential energy of the linked extendable and retractable members  30  as a group, rather than the potential energy of each member  30  as the linked members  30  are exchanging energy and in the process of extension or retraction. In a single extendable and retractable member machine  10 , the linkage device  50  can link the extendable and retractable member  30  to a stationary counterweight capable of storing/restoring the energy of the extendable and retractable member  30  as it is extended and retracted, respectively. The energy may be stored in kinetic or non-kinetic form. As another example, a resilient member, such as a spring, may be used to store potential energy.  
         [0044]     The extendable and retractable members  30   a ′,  30   b ′, and  30   c ′, as described above, include a shaft  32 ′ and a moveable weight  34 ′ coupled thereto. However, the moveable weight  34 ′ may be integral with the extendable and retractable members  30   a ′,  30   b ′,  30   c ′ such that the extension or retraction of an extendable and retractable member  30   a ′,  30   b ,  30   c ′ functions the same as an extension or retraction of the moveable weight  34 ′ as described above.  
         [0045]     In general, the control system  40  in any of the above described embodiments may be a computer, electromechanical switching apparatus, or any other suitable control device. One or more electric or magnetic fields produced by devices such as solenoids and electromagnets can be used to effect retraction and extension of the extendable and retractable members  30 ,  30 ′. Certain mechanical devices, such as geneva gears, can also be configured to control extension and retraction. Hydraulic or pneumatic pressure also can be used to actuate the extendable and retractable members  30 ,  30 ′. Suitable pumps and/or check valves can be used to control the flow of a fluid in a hydraulicly or pneumatically operated system.  
         [0046]     For example, in a hydraulically linked system a first extendable and retractable member  30   a ′ can be extended, the energy released during extension thereof being transferred hydraulically via the linkage system and one or more pumps and/or check valves and utilized to retract a second extendable and retractable member  30   b ′. A check valve can be used to maintain the retracted extendable and retractable member  30   b ′ in the retracted position. As the second extendable and retractable member  30   b ′, rotates and begins to extend, the energy released from the second extendable and retractable member  30   b ′ can be transferred to the third extendable and retractable member  30   c ′. This process can be repeated thereby minimizing system energy losses.  
         [0047]     It will be appreciated that system energy will be lost or consumed during movement of the extendable and retractable members  30 ,  30 ′ in any of the above embodiments. As such, the pumps or other devices as described above can be utilized to provide energy to the system to offset such losses and thereby improve overall efficiency of the system.  
         [0048]     An extendable and retractable member  30 ,  30 ′ in any of the above embodiments can be configured with the rotatable member  20 ,  20 ′ such that the extendable and retractable member  30 ,  30 ′ can shift radially about the rotatable member  20 ,  20 ′ a predetermined amount. This radial “play” about the rotatable member  20 ,  20 ′ can be advantageous for maximizing the system efficiency, particularly in multiple extendable and retractable member  30 ,  30 ′ embodiments.  
         [0049]     It will be appreciated that the rotatable member  20 ,  20 ′ may be coupled to any suitable output device  26 ,  26 ′. The output device  26 ,  26 ′ may be any device that receives rotational input such as a generator, an alternator, a drive shaft, a direct drive, etc.  
         [0050]     It will further be appreciated that the axis Z is this description and the axis of rotation referred to in the claims can be any non-vertical axis, vertical being defined as the direction of a field of gravity. Therefore, it will be understood that the axis Z and/or axis of rotation of the rotatable member can extend in any direction relative to the direction of a field of gravity provided that axis has a vector component which extends perpendicularly to the direction of the gravitational field.  
         [0051]     Although the present invention has been described in the context of increasing the rotational efficiency of a rotatable member  20 ,  20 ′, the present invention is equally well suited to braking the rotation of a rotatable member  20 ,  20 ′ by operating the machine in a reverse mode. In such a configuration, for example with reference to  FIG. 4A-4L , the moveable weight  34 ,  34 ′ would be extended to the larger radius of rotation R 3  during the upward sweep and returned to the smaller radius of rotation R 1  prior to the downward sweep. In this manner, the effect of gravity on the system would be against the direction of rotation of the rotatable member  20 , and thereby tend to dampen energy from the machine  10 ,  10 ′. Configuring the machine  10 ,  10 ′ in such a reverse mode may be useful, for example, for braking and/or decreasing the rate of rotation of a rotatable member such as a drive shaft of a vehicle.  
         [0052]     It will be appreciated that the rotary output from the machine  10 ,  10 ′ of the present invention may be used for a wide variety of purposes that require power input or power braking, particularly in situations using rotary motion power.  
         [0053]     Although the invention has been shown and described with respect to certain preferred embodiments, other equivalents and modifications will occur to others skilled in the art upon the reading and understanding of the specification. The present invention includes all such equivalents and modifications, and is limited only by the scope of the following claims.