Abstract:
A horizontal axis wind turbine with a ball-and-socket hub is disclosed. The hub provides for a second vertical axis, the hub axis, intersecting the center of the hub that enables a change in orientation of the rotor axis without changing the orientation of the main shaft axis. The cause for the rotation around the hub axis is an imbalance in torque applied by the blades across a wind shear axis due to a gradient in wind velocity. Rotation around the hub axis will continue until back-and-forth rotation of the blades is such that the torque is balanced across a wind shear axis and the rotor axis is set at an optimal angle. As changes in wind direction occur, the torque will become imbalanced, and the hub will rotate until a new optimal angle is achieved. The present turbine design allows for the hub to freely rotate ±20° around the hub axis and continuously maintain orientation of the rotor axis at an optimal angle. When a control limit is reached, a computer signals the yaw axis motor to rotate the main shaft axis until it is aligned with the rotor axis. Laser measuring devices and linear actuators located in the front of the nacelle provide for monitoring and control of the hub movement.

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to the field of wind turbine generators, and more particularly to the field of horizontal-axis wind turbines. One of the principal problems involved in designing horizontal axis wind turbines is wind shear, which is the variation of wind velocity with height above ground level. Wind velocities tend to increase with altitude due to aerodynamic surface drag and the viscosity of air. As a result, turbine blades at the top of the rotation experience higher wind velocities than blades at the bottom of the rotation. If not compensated for in the design of the wind turbine, this vertical wind velocity gradient will both degrade the performance and efficiency of the wind turbine and subject it to damaging stresses. 
     In addition to wind shear due to natural differences in wind velocity with altitude, wind shear can also be induced by improper alignment of the main shaft axis, i.e., not facing the axis at the optimal angle with respect to the wind direction. Most often, improper alignment results from changes in wind direction. If there is no wind shear, the rotor axis (the axis around which the blades are rotating) should face directly into the wind so that all blades will experience the same wind speed. If however, the main shaft axis is aligned obliquely to the wind in one direction, blades at the top of the rotation will move into the wind, and blades at the bottom of the rotation will move with the wind. This will cause blades at the top of the rotation to experience a greater effective wind speed than blades at the bottom. Conversely, if the orientation of the main shaft is oblique to the wind in the opposite direction, blades at the bottom of the rotation will experience a greater effective wind speed than those at the top. 
     Of vital importance in the design of wind turbine generators is operation of the turbine blades at the optimum tip speed ratio to extract as much power as possible out of the wind. Tip speed ratio is defined as the speed at the tips of the turbine blades divided by the speed of the wind. For example, if the wind is blowing at 20 mph and the blade tips are rotating at 100 mph, then the tip speed ratio is 5. If however, there is a wind velocity difference of 10 mph between the lowest and highest blade positions, the tip speed ratio will vary from 4 to about 7, thereby diverging from the optimum design point with consequent loss of efficiency. Variations in tip speed ratio due to wind shear also cause changes in the angle of attack of the turbine blades, which depends on the speed of the blades relative to the wind speed. The effect is to increase the angle of attack at the top of the blade&#39;s path and decrease it at the bottom. In the above example, the angle of attack will be increased by almost 3 degrees at the top and decreased by almost 3 degrees at the bottom. This can result in stall at the top and reduced lift power at the bottom. 
     The lift generated by turbine blades during rotation is applied both in the direction of rotation and in a backward direction. Forces applied in the direction of rotation are also designated as in-plane forces and forces applied in a backward direction are also designated as out-of-plant forces. These backward forces are usually substantially greater than the forces applied in the direction of rotation. Because of this, wind shear will cause more backward force to be applied to blades experiencing the greater effective wind speed. The stress produced by this unbalance in backward forces is augmented by the concomitant changes in the angle of attack of the blades. This cyclical stress on the blades and bearings can cause excessive wear, maintenance problems, and shorten the useful life of the wind turbine generator. 
     The prior art in this field has responded to the problems presented by wind shear through the use of a “teeter pin” that is part of the hub. A teeter pin provides for an additional degree of freedom by enabling the turbine rotor to pivot back-and-forth like a playground seesaw. The addition of the teeter pin causes a backward force to be converted to backward torque. This back-and-forth rotation results in a balancing of the torque on the blades around the teeter axis because blades experiencing the higher wind velocity move with the wind and blades experiencing the lower wind velocity move into the wind. Such teeter pins are useful as applied to two-bladed wind turbines, as they allow the upper blade to tilt backward while the lower blade tilts forward. Thus, the teetering motion of a two-bladed wind turbine tends to equalize the effective wind speeds for both blades, thereby maintaining a constant tip speed ratio. Teetering also tends to equalize the backward torque on both blades, thereby reducing shear stresses. 
     The limited seesaw pivoting enabled by teeter pins is, however, inadequate to compensate for wind shear in turbines having three or more blades. This is because teetering is limited to one blade moving forward and the other moving backward in an equal and opposite manner. The concept of the present invention is to provide a ball-and-socket hub that enables back-and-forth rotation of blades for turbines having two or more blades. The center of the ball-and-socket hub is defined as the origin of x, y and z axes. As shown in  FIG. 2A , the y-axis is parallel to the yaw axis, through which the nacelle rotates about the tower to change the orientation of the rotor with respect to the wind. The z-axis is aligned with the main shaft axis and generally with the direction of the wind, and the x-axis is aligned horizontally and roughly parallel to the ground. 
     The hub has a series of dynamic rotational couplers between the ball and socket that rotationally couples the ball and socket around the z-axis so that rotational torque generated by the turbine blades is transferred from the socket to the ball. In addition the dynamic rotational couplers enable the socket to move back-and-forth with respect to the ball in response to the back-and-forth rotation of the blades. This back-and-forth rotation provides an additional degree of freedom. 
     The back-and-forth rotation of the blades exhibits a cyclic pattern that is dependent upon the gradient in wind speed. For example, again referring to  FIG. 2A , if blades are rotating clockwise around the rotor axis (as viewed from the front), and there is a vertical gradient in wind velocity, blades will start to rotate backward around the x-axis due to higher wind speed starting at the 180° position and continue rotating backward a until reaching the maximum backward position at 0°. Then the blades will begin to rotate forward due to lower wind velocity until the maximum forward position is reached at 180°. The term “wind shear axis” is used to describe an axis which is perpendicular to the gradient in wind shear, such that the maximum forward and maximum backward rotation positions occur along the wind shear axis. In the above example, the x-axis is the wind shear axis. This rotation of the blades around the wind shear axis causes a rotation of the hub socket around the hub axis, which is perpendicular to the wind shear axis. In the above example, the hub axis is the y-axis. The hub axis is not a physical axis such as the teetering axis, but rather a virtual axis created by rotation of the socket around the ball. The hub axis is perpendicular to the rotor axis and to the wind shear axis, and can be any axis in the x-y plane that intersects the origin of the x, y, and z axes. The rotation of the hub socket around the hub axis is not a separate degree of freedom, but rather a necessary outcome imposed by the geometry of the ball-and-socket. The extent of rotation around the hub axis is determined by the extent of back-and-forth rotation of the blades. 
       FIGS. 2B and 2C  show the relationship between the back-and-forth rotation of the blades around the wind shear axis  233  and the resulting rotation of the rotor axis  222  around the tub axis  235 . 
     As with teetering, the back-and-forth rotation of the blades occurs in order to balance torque on the blades. This balance occurs across the wind shear axis, e.g., the x-axis. Each blade applies a torque around the wind shear axis based upon the backward force multiplied by the distance from the wind shear axis. When the back-and-forth rotations are such that the torque contributions above and below the wind shear axis are balanced, the back-and-forth rotations will reach a steady state. At this time, the rotation of the hub socket around the hub axis will stop and the angle where it stops becomes the optimal hub angle (the angle between the rotor axis and the main shaft axis). In cases where there is no wind shear, the rotor axis will point directly into the wind. Otherwise, the rotation of the hub socket around the hub axis will orient the rotor axis obliquely into the wind and create rotations that largely offset the wind shear. As changes in wind direction occur, the blade torque above and below the wind shear axis will become unbalanced and cause the extent of the back-and-forth rotations to change. This change will in turn cause the hub socket to rotate around the hub axis until a new optimal hub angle is achieved. 
     Since the hub axis is perpendicular to the rotor axis, rotation of the hub socket around the hub axis will cause a change in orientation of the rotor axis. This change in orientation of the rotor axis, however, does not affect the orientation of the main shaft axis which remains fixed along the z-axis. An essential consequence of this change in orientation of the rotor axis is that the blades retain rotational symmetry and thus balance the forces of the rotor with respect to both the rotor axis and the main shaft axis. The central feature of the present invention, the ball-and-socket hub, will now be described in further detail. 
     SUMMARY OF THE INVENTION 
     Definition of Axes used in Summary 
     Main Shaft Axis: the axis of rotation of the main shaft and main shaft ball. The main shaft axis is the z-axis. 
     Rotor Axis: the axis of rotation of the hub socket, outer hub, and blades which comprise the rotor. The rotor axis is perpendicular to the hub axis and determines the orientation of the rotor. 
     Wind Shear Axis: an axis in the x-y plane where blades rotate forward on one side of the axis and backward on the other side. The axis is determined by connecting the two angles where there is a reversal in the direction of rotation. The wind shear axis is generally the x-axis. 
     Hub Axis: an axis in the x-y plane that is perpendicular to the wind shear axis and the rotor axis. The orientation of the rotor axis is changed by rotating around the hub axis. The hub axis is generally the y-axis. 
     As depicted in  FIG. 1 , a typical horizontal wind turbine generator comprises a vertical cylindrical tower  102 , a horizontal cylindroidal nacelle  104  and a rotor  106 . The rotor  106  comprises a rotor hub  108 , from which extend two or more blades  110 . The rotor hub  108  is axially connected to a main shaft  112 , which transmissively connects through a gear box  114  to a generator  116  in the nacelle  104 . The nacelle  104  is rotatably attached to the tower  102 , such that the nacelle  104  and rotor  106  can be rotated about a yaw axis  118 , which axially extends vertically through the tower  102 . The rotation about the yaw axis  118  is used to keep the rotor  106  pointed into the wind, i.e., to keep the z-axis aligned with the wind direction  120 . This yaw rotation is actuated by a yaw drive  122  and yaw motor  124  in the top of the tower  102 , which in turn is controlled by a microprocessor controller  126  in the nacelle  104 , based on readings from an anemometer  128  and a wind vane  130 . 
     The typical wind turbine generator as shown if  FIG. 1  is modified by replacing the rotor hub  108  with a ball-and-socket hub  200  as depicted in  FIG. 2A . As shown in  FIG. 2A , the ball-and-socket hub  200  of the present invention comprises a main shaft ball  202 , a hub socket  204  and outer hub  205  that surrounds the main shaft  112 . This change in the design of the hub applies to all embodiments of the present invention. 
       FIGS. 2B and 2C  show a 20° back-and-forth rotation of a blade  110  during one rotation cycle around the main shaft  112  and the resulting 20° change in orientation of the rotor axis  222  for all embodiments of the present invention.  FIG. 2B , which is a side view, shows blade  110  rotates around the z-axis and also rotates back-and-forth around the x-axis (perpendicular to plane of paper). Blade  110  is at the maximum forward position at 180° ( 110   a ). During clockwise rotation, blade  110  continues to rotate backward due to higher wind speed past the top of the rotation until it is at the maximum backward position at 0°  110   e . The blade then rotates forward due to lower wind speed to the bottom of the rotation and continues to do so until reaching the 180° position  110   a  where the rotation cycle is completed. 
     Reversals in the direction of rotation occur at 180°  110   a  and 0°  110   e , indicating that the x-axis is the wind shear axis  233 . Since the wind shear axis  233  is the x-axis, the hub axis  235  is the y-axis, or the axis perpendicular to the wind shear axis  233  in the x-y plane.  FIG. 2C , which is a top view of  FIG. 2B , shows the wind shear axis  233 .  FIG. 2C  shows the blade at the 180° position  110   a  and at the 135° position  110   b  have a forward rotation angle of 20°, as indicated by the angle formed by the wind shear axis  233  and the radial lines  231  drawn through the center of the blades  110 . The blade at the 45° position  110   d  and at the 0° position  110   e  show a backward rotation angle of 20° with respect to the wind shear axis  233 .  FIG. 2C  shows all blades align along this 20° rotation with respect to the wind shear axis  233 . This alignment of all blades indicates that the plane of blade rotation is rotated 20° with respect to the x-y plane. The rotor axis  222  is at the center of blade rotation and perpendicular to the plane of blade rotation.  FIG. 2C  shows the orientation of the rotor axis  222  is rotated 20° around the hub axis  235  ( FIG. 2B ) with respect to the z-axis. In a typical horizontal wind turbine generator as depicted in  FIG. 1 , an equivalent change in orientation of the rotor axis would require a 20° rotation of the wind turbine around the yaw axis  118 . In general, a back-and-forth rotation by the blades by a given angle leads to a rotation in orientation of the rotor axis  222  around the hub axis  235  by the same angle. In cases where the wind speed is greater at the bottom of the rotation than at the top, the angle is negative, so that back-and-forth rotation of the blades  110  and rotation of the rotor axis  222  around the hub axis  235  would be in the opposite direction. 
     The present invention is based on a transfer of rotation around the z-axis from the hub socket  204  to the main shaft ball  202  by multiple rotational transfer means, which can operate mechanically or magnetically.  FIG. 3  illustrates the configuration the main shaft ball  202  and the main shaft  112 . The main shaft  112  is inserted through the center of a main shaft ball  202 . The main shaft ball  202  contains multiple round ball magnets  206  that fit into recesses in the main shaft ball  202 . The round ball magnets  206  are uniformly equatorially distributed, which means that they are centered on and uniformly distributed around an equator of the main shaft ball  202  that is perpendicular to the z-axis, or main shaft axis. The round ball magnets  206  are magnetized such that the entire outer surface of each has a uniform magnetic strength and polarity, e.g., north. The center of the main shaft ball  202  defines the origin of the x-axis, y-axis and z-axis as shown in  FIG. 2A . 
       FIG. 4  illustrates the preferred configuration of the hub socket  204  and outer hub  205 . The hub socket  204  comprises an inner socket surface  208  and an outer socket surface  210 . The inner socket surface  208  is a portion of the surface of a sphere having a slightly greater diameter than that of the main shaft ball  202  ( FIG. 3 ), which it slidably surrounds. Embedded in the inner socket surface  208 , are a series of longitudinal socket magnets  212 , indicating that they have the same curvature and orientation as the longitudinal lines of earth. The longitudinal socket magnets  212  are spherical shell segments that conform to the contours of the inner socket surface  208 . The longitudinal socket magnets  212  are uniformly equatorially distributed, which means that they are centered on and uniformly distributed around an equator of the main shaft ball  202  ( FIG. 3 ) that is perpendicular to the rotor axis  222 . The longitudinal socket magnets  212  are elongated in the direction of the rotor axis  222 . The inner surface of each of the longitudinal socket magnets  212  has a uniform magnetic strength and polarity, which is opposite to the polarity of the outer surface of the corresponding round ball magnet  206  ( FIG. 3 ), such that there is a strong magnetic attraction between the longitudinal socket magnets  212  and the round ball magnets  206  ( FIG. 3 ). The longitudinal socket magnets  212  align over the round ball magnets  206  ( FIG. 3 ) so as together to form a series of cooperating pairs of dynamic rotational couplers  214 . The dynamic rotational couplers couple the hub socket  204  with the main shaft ball  202  ( FIG. 3 ) during rotation of the rotor  106 , while at the same time enabling back-and-forth rotation of the hub socket  204  with respect to the main shaft ball  202  ( FIG. 3 ). The outer hub  205 , which is positioned on the outer socket surface  210 , is comprised of multiple annular cylindrical socket extensions  216 , multiple pitch adjustment rings  218  that can be rotated to change the pitch of the blades  110  ( FIG. 2A ), and multiple blade connectors  220 . 
       FIG. 5  shows a front view of the arrangement dynamic rotational couplers  214  and turbine blades  110  surrounding a main shaft  112  for a typical three bladed turbine, with remaining parts of the ball-and-socket hub are removed for clarity.  FIG. 5  shows the alignment of three dynamic rotational couplers  214  with three blades  110 . This alignment is indicated by radial lines  231  intersecting the center of the dynamic rotational couplers  214  and the blades  110 .  FIG. 5  also shows three other dynamic rotational couplers  214 .  FIG. 5  also shows the center of the main shaft  112  has a pitch control wire opening  246  that allows for passage of wires to control the pitch of the blades  110 . 
       FIG. 6A  shows a top view of the dynamic rotational couplers  214 , turbine blades  110 , and main shaft  112  described in  FIG. 5 .  FIG. 6A  shows that the blades  110  and dynamic rotational couplers  214  are all perpendicular to the main shaft  112 .  FIG. 6B  shows a top view of the dynamic rotational couplers  214 , turbine blades  110  and main shaft  112  after the hub socket  204  ( FIG. 4 ) has been rotated around the y-axis by 20°. Comparison of  FIG. 6B  with  FIG. 6A  shows the only changes are that blade  110   a  and longitudinal socket magnet  212   a  rotate forward together as indicated by radial line  231   a  intersecting the center of each, and blade  110   c  and longitudinal socket magnet  212   c  rotate backward together as indicated by radial line  231   c  intersecting the center of each. The round ball magnets  206   a  and  206   c  do not rotate about the wind shear axis.  FIGS. 6A and 6B  demonstrate that the back-and-forth rotations of the blades  110  result in a corresponding back-and-forth rotation of the longitudinal socket magnets  212  across the round ball magnets  206 .  FIG. 6B  also shows that the rotor axis  222  is no longer aligned with the main shaft  112 , since the rotor axis  222  is now oblique to the main shaft axis (or z-axis) at an angle of 20°. 
       FIGS. 7A and 7B  are isometric drawings that show the movement of a longitudinal socket magnet  212  across a round ball magnet  206  during one rotation cycle.  FIGS. 7A and 7B  show the longitudinal socket magnet  212  does not move across the round ball magnet  206  for positions at the y-axis, which indicates that the hub axis is aligned with the y-axis.  FIGS. 7A and 7B  show maximum forward and backward rotation of the longitudinal socket magnet  212  for positions along the x-axis, indicating that the wind shear axis is the x-axis. The back-and-forth rotations depicted in  FIG. 7A  lead to a 10° rotation of the hub socket  204  ( FIG. 4 ) around the y-axis, which is the hub axis. As the vertical gradient in wind speed increases, the back-and-forth rotations of the hub socket  204  ( FIG. 4 ) also increase. This increase is shown in  FIG. 7B  where the back-and-forth rotations lead to a 20° rotation of the hub socket  204  ( FIG. 4 ) around the y-axis (hub axis). The rotations are best observed at the intersection of the x-axis with the longitudinal socket magnet  212 . Examination of one rotation cycle for the movements of the longitudinal socket magnets  212  in  FIGS. 7A and 7B  shows a rotation around the x-axis in addition to the rotation around the z-axis.  FIGS. 7A and 7B  demonstrate that back-and-forth rotation around the x-axis (wind shear axis) causes a rotation of the hub socket  204  ( FIG. 4 ) around the y-axis (hub axis) and that the extent of rotation around the y-axis is determined by the extent of back-and-forth rotation of the blades. Although  FIGS. 5 ,  6 A,  6 B and  7 A are depicted with dynamic rotational couplers  214  comprised of longitudinal socket magnets  212  and round ball magnets  206 , any dynamic rotational couplers  214 , including mechanical couplers, could be substituted in the drawings. Dynamic rotational couplers  214  based upon magnetic rotational coupling, however have the advantage of avoiding frictional forces inherent in mechanical coupling, thereby reducing wear-and-tear on the mechanism. 
     Another approach to the design of dynamic rotational couplers  214  is depicted in  FIGS. 8 and 9 . In this exemplary configuration, the rotational transfer means operate by mechanical coupling.  FIG. 8  illustrates the preferred configuration of the main shaft ball  202  and the main shaft  112 . This configuration is identical to that of the magnetic version depicted in  FIG. 3 , except that the round ball magnets  206  have been replaced by coupling rods  224  in the outer surface of the main shaft ball  202 . The coupling rods  224  are uniformly equatorially distributed in relation to the z-axis.  FIG. 9  depicts the preferred configuration of the hub socket  204 , which is identical to that of the magnetic version shown in  FIG. 4 , except that the longitudinal socket magnets  212  have been replaced by longitudinal socket grooves  226 , and the number of blades has been decreased from three to two. The longitudinal socket grooves  226  are uniformly equatorially distributed in relation to the z-axis. The coupling rods  224  ( FIG. 8 ) fit within the longitudinal socket grooves  226  in hub socket  204 . The longitudinal socket grooves  226  and the coupling rods  224  ( FIG. 8 ) cooperate to function as mechanical rotational transfer means—transmitting the rotational motion from the hub socket  204  to the main shaft ball  202 —in the same way that the longitudinal socket magnets  212  and the round ball magnets  206  cooperate to function as magnetic rotational transfer means. Together a coupling rod  224  ( FIG. 8 ) and a longitudinal socket groove  226  comprise a dynamic rotational coupler  214 . 
     The most significant advantage of the ball-and-socket hub is that the rotor axis is continuously maintained at an optimal hub angle by wind forces without changing the orientation of the main shaft axis. Because effective wind speeds on the blades are largely balanced at the optimal hub angle, there will be less cyclic stress placed on the blades and other moving parts of the wind turbine. Also, for a conventional wind turbine, realignment of the rotor axis requires rotation about the yaw axis and considerable torque is needed to overcome the gyroscopic forces that resist changes to the rotor axis. When a rotation about the yaw axis is necessary in the present invention, the rotor axis is already oriented at the optimal angle, and the yaw drive merely rotates the nacelle to align the main shaft axis with the rotor axis. Furthermore, by enabling more rapid response to shifts in wind direction, the y-axis rotation of the present invention&#39;s rotor axis enhances the efficiency of the wind turbine by reducing power output losses associated with non-optimal yaw angle. 
     Other advantages of the present invention have been shown by computer modeling. A ball-and-socket hub on a three-bladed turbine is predicted to significantly reduce stress forces applied to the blades, shaft, yaw bearing, and tower when compared to a three-bladed turbine with a fixed hub. Additionally, a ball-and-socket hub on a three-bladed turbine is predicted to significantly reduce stress forces applied to the blades and tower when compared to a teetering two-bladed turbine. This reduction in stress forces will reduce both cost of manufacture and/or lifecycle time of the wind turbine. 
     Two additional advantages enabled by the present invention apply specifically to ball-and-socket hubs with magnetic coupling. Firstly, by having a small gap between the ball and socket magnets, magnetic coupling allows for back-and-forth movement of the socket magnets over the ball magnets while transferring significant torque without any physical contact between the magnets. Secondly, the strength of the magnetic coupling can be set to a value that limits the amount of torque that can be transferred from the socket to the ball. When the torque exceeds this limit, the coupling between each magnet pair breaks and the ball and socket magnets form new pairs. This allows the turbine blades to spin faster than the main shaft in cases where there are sudden strong gusts of wind that could possibly damage the generator. If the blades do rotate faster than the shaft, it would be absolutely necessary to rapidly apply wind brakes in order to slow rotation and avoid damage to the blades. 
     The foregoing summarizes the general design features of the present invention. In the following sections, specific embodiments of the present invention will be described in some detail. These specific embodiments are intended to demonstrate the feasibility of implementing the present invention in accordance with the general design features discussed above. Therefore, the detailed descriptions of these embodiments are offered for illustrative and exemplary purposes only, and they are not intended to limit the scope either of the foregoing summary description or of the claims which follow. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a perspective view of a typical horizontal-axis wind turbine generator, depicting the principal components thereof; 
         FIG. 2A  is a perspective view of a horizontal-axis wind turbine generator, where a ball-and-socket hub has replaced the rotor hub, as well as orientations of the x, y and z axes; 
         FIG. 2B  is a side view of eight positions of a single blade during one rotation cycle around the main shaft after the blade has been rotated 20° around the y-axis; 
         FIG. 2C  is a top view of  FIG. 2B  showing the alignment of all blades and the 20° rotation of the rotor axis with respect to the wind shear axis; 
         FIG. 3  is a side detail view of the main ball shaft and main shaft of the present invention based on magnetic rotational coupling; 
         FIG. 4  is a detail view of a portion of the inner socket sphere of the present invention based on magnetic rotational coupling; 
         FIG. 5  is a front detail view of the dynamic rotational couplers and turbine blades surrounding the main shaft of the present invention based on magnetic rotational coupling; 
         FIG. 6A  is a top detail view of  FIG. 5  showing the dynamic rotational couplers and turbine blades surrounding the main shaft of the present invention based upon magnetic rotation coupling; 
         FIG. 6B  is a top detail view of the dynamic rotational couplers and turbine blades surrounding the main shaft of the present invention based upon magnetic rotation coupling; depicting the movement of the blades and longitudinal socket magnets relative to round ball magnets; 
         FIG. 7A  is a detailed isometric view of a 10° rotation around the y-axis caused by movement of longitudinal socket magnets across round ball magnets during one rotation cycle of the present invention; 
         FIG. 7B  is a detailed isometric view of a 20° rotation around the y-axis caused by movement of longitudinal socket magnets across round ball magnets during one rotation cycle of the present invention; 
         FIG. 8  is a side detail view of the main shaft ball and main shaft of an exemplary embodiment of the present invention based on mechanical rotational coupling; 
         FIG. 9  is a detail view of a portion of the inner socket sphere of an exemplary embodiment of the present invention based on mechanical rotational coupling; 
         FIG. 10  is a side detail view of the main shaft ball and the main shaft of the first preferred embodiment of the present invention based upon magnetic rotational coupling; 
         FIG. 11  is a cutaway perspective detail view of the hub socket of the first preferred embodiment of the present invention based upon magnetic rotational coupling; 
         FIG. 12A  is a detail side view of the round socket magnets and the longitudinal ball magnets, with the main shaft ball and hub socket removed for clarity, of the first preferred embodiment of the present invention; 
         FIG. 12B  is a detail side view of round socket magnets and the longitudinal ball magnets of  FIG. 12A , where the socket magnets have been rotated 20° about the y-axis; 
         FIG. 13A  is a detail top view of round socket magnets and the longitudinal ball magnets, where the round socket magnets have been rotated 20° about the y-axis of the first preferred embodiment of the present invention; 
         FIG. 13B  is a detail top view of round socket magnets and the longitudinal ball magnets where the round socket magnets are first rotated 20° around the y-axis as in  FIG. 13A , and then the longitudinal ball magnets were rotated 180° around the z-axis and the round socket magnets rotated 180° around the rotor axis; 
         FIG. 14  is a side detail view of the main shaft ball and the main shaft of the second preferred embodiment of the present invention; 
         FIG. 15  is a cutaway perspective detail view of the hub socket of the second preferred embodiment of the present invention; 
         FIG. 16  is a detail side view of the main shaft ball of the second preferred embodiment of the present invention, where the coupling rods have been rotated 20° about the y-axis; 
         FIG. 17  is a side view of the optional nose cone and the inner hub protector with the hub removed for clarity; 
         FIG. 18  is a perspective view of the front of the nacelle with the back portion removed for clarity; 
         FIG. 19  is a side view of the rotor, the nacelle and the tower; 
         FIG. 20A  is a top view of the rotor and nacelle without rotation about the y-axis; and 
         FIG. 20B  is a top view of the rotor and nacelle with rotation about the y-axis. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The first preferred embodiment of the present invention is based on magnetic rotational coupling between the main shaft ball  202  and the hub socket  204 .  FIG. 10  illustrates the preferred configuration the main shaft ball  202  and the main shaft  112 . The main shaft  112  is inserted through the center of a main shaft ball  202 . The main shaft ball  202  contains multiple longitudinal ball magnets  228  that snuggly fit into recesses in the main shaft ball  202 . The longitudinal ball magnets  228  are oblong spherical shell segments conforming to the contours of the surface of the main shaft ball  202  and uniformly equatorially distributed in relation to the z-axis. The longitudinal ball magnets  228  are magnetized such that the entire outer surface of each has a uniform magnetic strength and polarity, e.g., north. The longitudinal ball magnets  228  are elongated in the direction of the z-axis.  FIG. 11  illustrates the preferred configuration of the hub socket  204 , comprising an inner socket surface  208  and an outer socket surface  210 . The inner socket surface  208  is a portion of the surface of a sphere having a slightly greater diameter than that of the main shaft ball  202 , which it slidably surrounds. Multiple round socket magnets  230  are embedded in the inner socket surface  208 . The round socket magnets  230  are round spherical shell segments that conform to the contours of the inner socket surface  208 . The round socket magnets  230  are uniformly equatorially distributed, which means that they are centered on and uniformly distributed around an equator of the inner socket surface  208  that is perpendicular to the rotor axis  222 . The outer surface of each of the round socket magnets  230  has a uniform magnetic strength and polarity, which is opposite to the polarity of the outer surface of the corresponding ball magnet  228  ( FIG. 10 ), such that there is a strong magnetic attraction between the round socket magnets  230  and the longitudinal ball magnets  228  ( FIG. 4 ). This magnetic attraction causes the round socket magnets  230  to align over the longitudinal ball magnets  228  ( FIG. 4 ) and form a magnetic rotational coupling. Together, a round socket magnet  230  and a longitudinal ball magnet  228  ( FIG. 4 ) comprise a dynamic rotational coupler. On the outer socket surface  210  are multiple annular cylindrical socket extensions  216  that are used for mounting the rotor blades  110  ( FIG. 2A ). At the distal end of each socket is a pitch adjustment ring  218  that can be rotated to change the pitch of the blades  110  ( FIG. 2A ). The distal sides of the pitch adjustment rings  218  are, in turn, connected to the blade connectors  220 . 
       FIGS. 12A and 12B  are side views of a dynamic rotational coupler  214  showing the movement of a round socket magnet  230  across a longitudinal ball magnet  228  during one-half of a rotation cycle.  FIG. 12A  depicts the relative alignment of the round socket magnets  230  with the longitudinal ball magnets  228  when the axis of rotation of the hub socket  204  is aligned with the z-axis. Since the hub socket  204  and the rotor  106  move together, the axis of rotation of the hub socket  204  is identical to the rotor axis  222 . In this “90°” alignment, the round socket magnet  230  is positioned at the center of the longitudinal ball magnet  228  in all views of the dynamic rotational coupler  214 .  FIG. 12B  shows a side view of the positions of a dynamic rotational coupler  214  where the round socket magnets  230  are at various locations along the longitudinal ball magnets  228 . For example, a round socket magnet  230  at the 90° position is in the center of its corresponding ball magnet  228 , while at the 0° position the round socket magnet  230  is at one end of the ball magnet  228 . This movement of the round socket magnets  230  over the longitudinal ball magnets  228  is in response to the back-and-forth rotations of the blades  110 . 
     A ±20° rotation of the hub socket  204  around the hub axis is the preferred design limit for the apparatus. This allowable rotation determines the length of the longitudinal ball magnets  228 . For example, in  FIG. 12B  a round socket magnet  230  at the 180° position (with respect to the x-axis) is at one end of the longitudinal ball magnet  228 , while at the 0° position the round socket magnet  230  is at the other end of the longitudinal ball magnet  228 . The maximum rotation positions of the round socket magnet  230  at 180° and 0° indicate that the wind shear axis is the x-axis. As a consequence of these maximum rotation positions, the length of the longitudinal ball magnets  228  determines the allowable movement of the hub socket  204  with respect to the main shaft ball  202 . A smaller range of back-and-forth movement of the blades  110  will result in a correspondingly smaller range of back-and-forth movement of the round socket magnets  230  and less rotation of the hub socket  204  around the hub axis. 
     The magnetic attraction between each pair of socket and longitudinal ball magnets  230   228  provides the magnetic coupling that prevents the hub socket  204  from freely rotating around the z-axis. The overall magnetic attraction, however, remains constant as long as the round socket magnet  230  is positioned anywhere along the elongated longitudinal ball magnet  228 . This enables unconstrained back-and-forth movement of the round socket magnets  230  and the hub socket  204  with respect to the longitudinal ball magnets  228  and the main shaft ball  202 , as long as the round socket magnet  230  does go past the end of the longitudinal ball magnet  228 . Preferably, there should be a small gap between the round socket magnets  230  and the longitudinal ball magnets  228  to minimize friction. 
       FIGS. 13A and 13B  are top views of a dynamic rotational coupler  214  showing the movement of a round socket magnet  230  across a longitudinal ball magnet  228  during one-half of a rotation cycle. In both figures, there is a 20° rotation of the hub socket  204  around the hub axis.  FIG. 13A  shows movement of the round socket magnet  230  with respect to the longitudinal ball magnet  228  with  FIG. 12B , with maximum forward movement at 180° and maximum backward movement at 0°, indicating that the wind shear axis is the x-axis.  FIGS. 13A and 13B  also demonstrate that the longitudinal ball magnet  228  and round socket magnet  230  maintain integrity after rotating the two around different axes. In  FIG. 13A , a notch was placed in a longitudinal ball magnet  228   n  and a round socket magnet  230   n  for marking purposes. Then a CAD program used to rotate all longitudinal ball magnets  228  around the z-axis by 180°, and rotate all round socket magnets  230  around the rotor axis  222  by 180°. In this example, the orientations of the z-axis and rotor axis  222  differ by 20°.  FIG. 13B  shows that after rotation around different axes, all dynamic rotational couplers  214  maintain integrity.  FIG. 13B  shows that in this 180° rotation, the round socket magnet  230   n  slides across the entire length of the longitudinal ball magnet  230   n.    
     The second preferred embodiment of the present invention is based on mechanical rotational coupling between the main shaft ball  202  and the hub socket  204 .  FIG. 14  illustrates the preferred configuration the main shaft ball  202  and the main shaft  112 . This configuration is identical to that of the magnetic version depicted in  FIG. 10 , except that the longitudinal ball magnets  228  have been replaced by multiple longitudinal ball grooves  232  in the outer surface of the main shaft ball  202  and the number of longitudinal ball grooves has been increased from six to eight. The longitudinal ball grooves  232  are uniformly equatorially distributed in relation to the z-axis.  FIG. 15  depicts the preferred configuration of the hub socket  204 , which is similar to that of the magnetic version shown in  FIG. 11 , except that the round socket magnets  230  have been replaced by coupling rods  234  and the number of blades has been increased from three to four. Together a longitudinal ball groove  232  and a coupling rod  234  comprise a dynamic rotational coupler. The coupling rods  234  are uniformly equatorially distributed in relation to the rotor axis  222 , and they fit within the longitudinal ball grooves  232  ( FIG. 14 ) of the main shaft ball  202  ( FIG. 14 ). The longitudinal ball grooves  232  ( FIG. 14 ) and the coupling rods  234  cooperate to function as mechanical rotational transfer means—transmitting the rotational motion from the hub socket  204  to the main shaft ball  202  (FIG.  14 )—in the same way that the longitudinal ball magnets  228  and the round socket magnets  230  cooperate to function as magnetic rotational transfer means. 
     In the mechanical embodiment, freedom of the hub socket  204  to have an axis of rotation that differs from the axis of rotation of the main shaft is accomplished in a similar manner to that of the magnetic embodiment.  FIG. 16  shows a side view of the coupling rods  234  of the hub socket  204  positioned within the longitudinal ball grooves  232  of the main shaft ball  202 . In this view, the coupling rods  234  have been rotated 20° about the y-axis. This is the mechanical equivalent of the magnetic rotation depicted in  FIG. 12B . Optionally, either the mechanical or the magnetic coupling embodiment can include one or more pitch control wires to control the pitch of the rotor blades  110  ( FIG. 2A ). 
     Optional features of either of the preferred embodiments can also include a nose cone  248  and an inner hub protector  250 .  FIG. 17  shows a side view of the nose cone  248  and the inner hub protector  250  with the ball-and-socket hub  200  removed for clarity. The nose cone  248  attaches to the front surface of the hub socket  204  ( FIG. 2A ). The inner hub protector  250  fits over the main shaft  112  at the center and is attached to the back surface of the hub  200  at the outer perimeter. The nose cone  248  and inner hub protector  250  together create a seal that protects the ball and socket from the environment. Connection of the nose cone  248  and the inner hub protector is shown in  FIG. 19 . The inner hub protector  250  is constructed of a flexible material (e.g., rubber) that allows for movement of the hub socket  204  with respect to the main shaft  112 , as shown in  FIGS. 20A and 20B . A seal that protects the ball-and-socket hub  200  ( FIG. 2A ) from the environment would most likely be used in dusty and/or damp environments. 
     For any of the preferred embodiments,  FIG. 18  shows the front of the nacelle  104  with the back portion removed for clarity. The figure shows the main shaft  112  extending forward. The figure shows the ends of two horizontal linear actuators  236   a  and  236   b  that are positioned along the x-axis within the nacelle  104 . A horizontal wheel is located at the end of each horizontal linear actuator,  238   a  and  238   b . The figure also shows the ends of two vertical linear actuators  240   a  and  240   b  that are positioned along the y-axis within the nacelle  104  with a vertical wheel located at the end of each vertical linear actuator,  242   a  and  242   b .  FIG. 18  also shows the end of a vertical laser measuring device  244   a  positioned along the y-axis and the end of a horizontal laser measuring device  244   b  positioned along the x-axis. The laser measuring devices  244   a    244   b  read the distances to the back of the hub  200  and relay these measurements into a microprocessor  126  to determine the plane of rotation of the hub  200 . Based upon this information, the microprocessor  126  can change the plane of rotation by sending a signal to extend one or more of the linear actuators  236   a    236   b    240   a    240   b  so as to push the back of the hub  200  with the wheels  238   a    238   b    242   a    242   b  until the desired plane of rotation is achieved. 
     The linear actuators  236   a    236   b    240   a    240   b  also provide a stop for the movement of the hub socket  204  within the desired range of motion. In the present invention, the rotation limits around the y-axis are ±20°. The linear actuators  236   a    236   b    240   a    240   b  are also used during start up and shut down in order to assure that the blades  110  do not strike the tower  102  or nacelle  104 . In this case, all linear actuators  236   a    236   b    240   a    240   b  would be extended fully to position the hub socket  204  perpendicular to the main shaft  112 . After startup, the linear actuators  236   a    236   b    240   a    240   b  can be moved back to avoid unnecessary contact of the wheels  238   a    238   b    242   a    242   b  with the back surface of the hub  200 . 
       FIG. 19 , which is a side view of either of the preferred embodiments, shows the vertical cylindrical tower  102 , a horizontal cylindroidal nacelle  104  and a rotor  106 . The rotor  106  comprises a ball-and-socket hub  200 , from which extend two or more blades  110 , a nose cone  248 , and a flexible inner hub protector  250 . The nacelle  104  is mounted on a tower  102  that can be rotated around the yaw axis  118  using yaw drive  122 .  FIG. 19  shows the y-axis which is parallel to the yaw axis  118 . 
       FIGS. 20A and 20B  show two views of the top of the apparatus along with the x-axis and the z-axis.  FIG. 20A  shows an alignment of the rotor  106  with the z-axis. In this configuration, the magnetic coupling would be aligned as shown in  FIG. 12A .  FIG. 20B  shows a view where the rotor axis  222  is rotated 20° around the y-axis. In this configuration, the magnetic coupling would be aligned as shown in  FIG. 12B , and the mechanical coupling aligned as shown in  FIG. 16 .  FIGS. 20A and 20B  show front of the nacelle  104  is angled with respect to the z-axis in order to accommodate rotation of the hub socket  204  around the y-axis.  FIG. 20B  shows contact with the hub socket  204  with the horizontal wheel  238   b  of the horizontal linear actuator  236   b . The actuator  236   b  stops the hub  204  from rotating further in order to avoid damage to the nacelle  104 .  FIG. 20B  shows the rotor  106  maintains symmetry with respect to the rotor axis  222  after rotating 20° that axis around the y-axis. The rotor  106  also maintains symmetry with respect to the z-axis because the z-axis and the rotor axis  222  intersect at the y-axis. 
     Although the preferred embodiments of the present invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that many additions, modifications and substitutions are possible, without departing from the scope and spirit of the present invention as defined by the accompanying claims.