Abstract:
A two-wheeled vehicle, with the wheels mounted in an in-line fashion, that maintains the point of contact of the wheels in an optimal controllability area during both straight and turning operations, thereby expanding the controllable operating envelope of the vehicle to be substantially coincident with the overall operating envelope of the vehicle. Preferably, this is accomplished with position regulator, such as a dynamically-variable linkage (DVL), connecting one or more of the wheels to the chassis of the vehicle. The position regulator permits a rider to reliably and easily control and maneuver throughout the operating envelope of the vehicle simply by tilting the vehicle. As a result, stable, hands-free maneuvering of the vehicle is possible simply by tilting the base in the direction of a desired turn, even over rough terrain, and without a user requiring excessive corrective force or unusually special balancing skills. A plurality of such position regulators can be installed on the vehicle to further enhance stability and performance of the vehicle. Also, the vehicle may be powered or de-powered, and can include additional suspension systems aimed at smoothing the vehicle&#39;s ride.

Description:
TECHNICAL FIELD 
     The invention is an improved two-wheeled vehicle. In particular, the invention concerns a two-wheeled vehicle that maintains the area of contact of the steering wheel near an optimal plane during both straight and turning operations, thereby improving stability and maneuverability. Preferably, this is accomplished with a dynamically-variable linkage connecting one or more of the wheels to the chassis of the vehicle. Forces acting on the linkage during operation of the vehicle actuate the linkage to bias the wheels into the optimal plane. 
     BACKGROUND OF THE INVENTION 
     Historically, wheeled vehicles and especially in-line, two-wheeled vehicles such as bicycles, motorcycles, scooters, and the like, have been popular forms of transportation, exercise, and sport. More recently, such vehicles are being used in particularly rugged environments including unimproved roads and rough terrain. For example, similar to a conventional snowboard operating over a snow-covered hill, it is desirable to use an in-line wheeled vehicle to travel downhill over rough terrain. 
     In general, a rider balances on an elongated frame of the vehicle while it is either being propelled by gravity, the rider or self-propelled, and steers the vehicle either by tilting the vehicle, as with a skateboard, or rotating a steering mechanism, such as the handle bar of a conventional bicycle, to turn at least one of the wheels on a fixed axis of rotation. In virtually all uses of such vehicles, it is desirable for the vehicle to travel smoothly, steer easily and responsively, and remain stable during both steady-state and dynamic operation. 
     The rider on a two-wheeled vehicle is a critical element in the dynamic balancing of the system, which must be stable for successful operation of the vehicle. In particular, similar to a person balancing a stick on his finger, the rider of a two-wheeled vehicle is the active element maintaining stability of the system. The rider develops particular skill to use his or her senses (i.e., eyes, ears, sense of balance, etc.) to detect if there is a need for corrective balancing action, and the degree and type of corrective force needed. 
     Preferably, stable operation includes the steering wheel remaining in its commanded position (i.e., either aligned straight or at a commanded turn angle) when no dynamic input or other disturbances are acting on the steering mechanism. Such stable operation is particularly desirable, but especially difficult to maintain, when the vehicle is operated over rough terrain. 
     As children first attempting to ride a bicycle learn, maintaining dynamic balance on a two-wheeled bicycle requires experience and skill. Numerous forces act on a two-wheeled vehicle to keep it dynamically balanced during operation. These forces include gravity, inertia, friction, and gyroscopic forces generated by the spinning wheels. A rider typically manipulates the vehicle by leaning and turning the handlebar to maintain dynamic balance and thereby maneuver the vehicle. 
     Particularly skilled riders can maintain stable, dynamic balance of traditional bicycles traveling straight without holding the handlebars. In such case, they may even be able to turn their bicycles left or right simply by leaning their body and tilting the vehicle. However, minor transient disturbances, such as those associated with riding on an uneven or rough road surface, or the rider needing to change speed or steering directions, quickly destabilize the vehicle. 
     In more technical terms, for any given two-wheeled vehicle, there is an overall operating envelope of speeds and turn radii for a given terrain in which the vehicle is expected to operate effectively. Similarly, for any given two-wheeled vehicle there is a controllable operating envelope of speeds and turn radii for a given terrain in which the riders&#39; ability to simply tilt the vehicle in one direction or the other is sufficient to correct dynamic instabilities arising during operation of the vehicle, while still maintaining controllability of the vehicle (e.g. also maintaining tilting commanding the vehicle to turn). Unfortunately, with conventional two-wheeled vehicles, the controllable operating envelope Is much smaller than the desired operating envelope of the vehicle. Accordingly, traditional two-wheeled vehicles are hand-steered to maintain controllability and stability of the vehicle throughout the entire operating envelope of the vehicle. 
     Previously, the key elements leading to two-wheeled vehicle stability have not been fully understood. This has limited the size of the controllable operating envelope of traditional two-wheeled vehicles. A typical bicycle or scooter will have a pair of in-line wheels operably secured to a base. Both wheels are typically rotatably secured to the base, such that they rotate freely about their axles to carry the vehicle on a substantially planar running surface. In addition, the front wheel is usually pivotally secured to the base along an axis, commonly known as a steering axis, which is substantially orthogonal to the surface such that the front wheel turns from side-to-side with respect to the base along this axis. 
     In general, and as discussed more fully in U.S. Pat. No. 5,160,155 to Barachet, the front wheel&#39;s point of contact with the planar running surface of the conventional two-wheeled vehicle is behind the point at which a line extended from the steering axis contacts the same surface. The distance between these two points is commonly referred to as the vehicle&#39;s “trail.” This orientation allows the front wheel to operate like a conventional caster. Namely, because of a moment arm defined by the trail, the front wheel will turn in the direction of the bases&#39; tilt. Accordingly, to some extent, a rider can steer the vehicle simply by tilting the base to one side. 
     Conventional two-wheeled vehicle dynamic stability analyses focus on determining the optimal length of the trail for a given design. This process has typically been a trial-and-error approach for a given commercial product. For example, as documented in an article titled “A Fresh Look At Steering Geometry” of the February 1981 issue of Cycling USA, Mathematics professor John Corbet experimented with trail lengths ranging from ⅞ of an inch to 4{fraction (5/16)} inches. He found that with the trail set at approximately 1⅝ inches the bicycle felt “nervous.” With a trail of 1{fraction (3/16)} inches, it had “the sort of hands-off stability which seems desirable yet still turns easily,” and with the trail of 2{fraction (15/16)} inches, “it was very heavy feeling.” 
     These conventional stability studies of hand-steered two-wheeled vehicles focus on the dynamic stability of the vehicle during straight, steady-state operation. Accordingly, experimentation has found that the larger the trail, the greater the straight, steady-state stability of the vehicle. However, such stability usually comes at the expense of vehicle controllability and dynamic stability of the vehicle during a turn. These studies of hand-steered two-wheeled vehicles are characterized by their qualitative nature and subjective results. Moreover, the studies focus virtually exclusively on the vehicle&#39;s trail, and they do not explicitly define the qualities that determine the operational desirability of a vehicle. Instead, they concentrate on “hands-off stability” without defining or evaluating controllability. 
     Barachet shows two-wheeled vehicles having different caster angles (also referred to as the “rake angle” which is defined as the angle between the steering axis and vertical). Arguably, these figures could be interpreted to suggest that caster angle is another important factor in two-wheeled vehicle stability (i.e. the ability of the vehicle to remain in a state in the presence of disturbances and with no rider input) and control (i.e., the ability of the board to respond in a predictable and desirable manner to rider commanded inputs.) Barachet struggles with finding an optimal design that provides desirable performance over the envelope of operations while having a fixed trail and caster angle. He acknowledges the limitations with his designs by showing several approaches aimed at biasing the steering wheel to a neutral position, and by depending upon unusual athletic techniques of the rider to control and maintain stability of the vehicle. 
     Another example of the limitations found with conventional analysis of two-wheeled vehicle stability and control can be found in the book  Bicycling Science  (2nd edition 1995), written by Massachusetts Institute of Technology engineering instructor David Wilson and Frank Whitt. This book summarizes the state-of-the-art of bicycle engineering, and is grounded in solid mathematical-based technical discussions that reflect the support and involvement of a broad spectrum of experts in the field. 
     A chapter in this book, entitled “Balancing and Steering,” discusses the current state of understanding of in-line, two-wheel vehicle dynamics and the handling qualities of bicycles, It ultimately concludes that “the balancing and steering of bicycles is an extremely complex subject on which there is a great deal of experience and rather little science.” This situation exists despite the attention of several famous mathematicians and analytical engineers attempting to quantitatively understand these concepts. They conclude that caster angle and trail are important factors in the handling of a two-wheeled vehicle, but they acknowledge that there is no consensus or understanding as to why these elements are important, or if there are other elements that are equally important in understanding the concepts. Accordingly, as with professor John Corbet&#39;s work previously described, their work has focused on empirical efforts to quantify the ranges and combinations of these two dimensions as to their relation to “good” handling of a bicycle. This has led to a good understanding of which values and combinations of caster angle and trail produce acceptable handling performance, but not much insight as to why. 
     Some inventors have attempted to improve a wheeled-vehicles&#39; ability to operate over rough terrain. However, such improvements have typically been in the form of introducing improved suspension systems between the wheels and the base of the vehicles. For example, U.S. Pat. No. 5,868,408 to Miller teaches mounting two pair of wheels to a board. One pair of wheels is mounted toward the front of the board and the other pair of wheels is mounted toward the rear of the board. Each pair of wheels is pivotally secured to the board, such that the wheels rotate about respective steering axes. Each wheel is linked to the steering axis through a dynamic linkage that is spring-biased to a neutral position. As one of the wheels hits an obstacle, the spring is compressed, and the wheel is deflected upward to allow the obstacle to pass. 
     The quality that determines a vehicle&#39;s desirability with regards to riding over irregular or rough surfaces is its ability to absorb the influence of the terrain or isolate the rider from the influence of the terrain without diminishing the rider&#39;s ability to control the vehicle. As described above, much effort has been expended designing and implementing suspensions that will absorb the dynamics of the terrain by putting springs and dampers between the wheels and the base of the vehicle. Although this approach offers some benefits, it does not change the inherent characteristics of the vehicle that determine the susceptibility to the roughness of the terrain. 
     There are two axes associated with a vehicle that are pertinent to the dynamics that are induced by the terrain. These are the vehicle&#39;s roll axis (which runs longitudinally through the vehicle and is nominally horizontal) and the pitch axis (which is perpendicular to the roll axis and is nominally horizontal). A four-wheeled vehicle is influenced by terrain roughness about both axes while an in-line two-wheeled vehicle is influenced only about the pitch axis. Therefore, the in-line two-wheeled vehicle is much more accommodating of irregular or rough riding surfaces by its inherent characteristics. This is evidenced by a motorcycle&#39;s ability to negotiate much rougher terrain than a four-wheeled vehicle such as a Sport Utility Vehicle. 
     While the suspension linkages in Miller offer a smoother ride, they do not teach or suggest a way for allowing a two-wheeled vehicle to remain dynamically stable, but still highly maneuverable, during both straight and turning operations. 
     Accordingly, despite the improvements of the conventional devices, there remains a need for an economical, two-wheeled vehicle that is highly stable, even over rough terrain, but still highly maneuverable simply by a user tilting the vehicle with their feet as is done with a snowboard, surfboard or skateboard. In addition to other benefits that will become apparent in the following disclosure, the present invention fulfills these needs. 
     SUMMARY OF THE INVENTION 
     This invention provides a two-wheeled vehicle, with the wheels mounted in an in-line fashion, that maintains the area of contact of the wheels in an optimal controllability area during both straight and turning operations, thereby expanding the controllable operating envelope of the vehicle to be substantially coincident with the overall operating envelope of the vehicle. Preferably, this is accomplished with a position regulator, such as a dynamically-variable linkage (DVL), connecting one or more of the wheels to the chassis of the vehicle. The position regulator permits a rider to reliably and easily control and maneuver throughout the operating envelope of the vehicle simply by tilting the vehicle. 
     A previously unrecognized, but major factor in two-wheeled vehicle stability is the un-stabilizing force associated with the point-of-contact of the steering wheel, which is pivotally secured to the vehicle along a steering axis, being spaced too far away from the vehicle plane, defined as the plane that includes the rear wheel&#39;s point-of-contact and the steering axis, when the steering wheel is turned. The optimal controllability area is defined as the maximum distance the point-of-contact of the steering wheel can be from the vehicle plane while still maintaining easy control and stability of the vehicle throughout a reasonable operating envelope of the vehicle, which is preferably the overall operating envelope of the vehicle. As a result, stable, hands-free maneuvering of the vehicle is possible simply by tilting the base in the direction of a desired turn, even over rough terrain, and without a user requiring excessive corrective force or unusually special balancing skills. 
     In a preferred embodiment, the rider of the invention stands on a substantially planar standing surface in the same manner as a rider of a surfboard, snowboard, or skateboard. 
     Once the steering wheel&#39;s point-of-contact is out of the vehicle plane, there are an infinite number of directions or paths the steering wheel&#39;s point-of-contact can take to return to the optimal controllability area. All of these can be characterized with respect to the plane of the steering wheel. If the return path of the steering wheel&#39;s point-of-contact is parallel to the wheel plane it is called “in-plane” movement. Where the return path of the steering wheel&#39;s point-of-contact is in a direction perpendicular to the front wheel plane, this is referred to as “out-of-plane” movement. Any path of the steering wheel&#39;s point-of-contact back to the neighborhood of the vehicle plane can be categorized as an “in-plane” or “out-of-plane” movement, or a combination of the two. Such movements can occur through axial, linear, or angular movement of the wheel with respect to its corresponding mounting frame. 
     The principles of this invention can be applied equally well to powered and de-powered vehicles, and with or without additional suspension systems aimed at smoothing the vehicle&#39;s ride. A plurality of such linkages can be installed on the vehicle to further enhance stability and performance of the vehicle. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1A is an isometric schematic view of a two-wheeled vehicle in accordance with a preferred embodiment of the present invention. 
     FIG. 1B is a side view of the two-wheeled vehicle of FIG.  1 A. 
     FIG. 1C is a top view of the two-wheeled vehicle of FIG.  1 A. 
     FIG. 1D is a rear view of the two-wheeled vehicle of FIG. 1A showing a possible side-ways&#39; tilting of the vehicle and its related orientation geometry. 
     FIG. 2 is a fragmentary, isometric, schematic view of the steering wheel portion of a conventional two-wheeled vehicle traveling straight and showing orientation of various components related to the steering wheel with respect to a substantially horizontal ground plane and a vertical plane. 
     FIG. 3 is the conventional two-wheeled vehicle of FIG. 2 with the steering wheel in a turned position and showing orientation of various components related to the steering wheel with respect to the ground and vertical planes. 
     FIG. 4 is the conventional two-wheeled vehicle of FIG. 2 with the steering wheel in the turned position of FIG.  3  and the vehicle tilted to one side and showing orientation of various components related to the steering wheel with respect to the ground and vertical planes. 
     FIG. 5 is a top, schematic view of the conventional two-wheeled vehicle of FIG. 2A showing the points-of-contact of the steering wheel with respect to controllability area  37  on a substantially horizontal ground plane at three points  36 ,  36 ′,  36 ″ during a turn. 
     FIG. 6 is a top, schematic view the two-wheeled vehicle of FIG. 1 showing the points-of-contact of the steering wheel with respect to controllability area  37  on a substantially horizontal ground plane at the same three points  36 ,  36 ′,  36 ″ of a turn shown in FIG.  5 . The point of contact of the steering wheel maintains alignment with the vehicle plane throughout the turn by moving the steering wheel out-of-plane from the steering wheel plane. 
     FIG. 7 is a top, schematic view of the two-wheeled vehicle of FIG. 1 showing the points-of-contact of the steering wheel on a substantially horizontal ground plan at the same three points  36 ,  36 ′,  36 ″ of a turn shown in FIG.  5 . The points-of-contact of the steering wheel maintain alignment with the vehicle plane throughout the turn by moving the steering wheel in-plane with the steering wheel plane. 
     FIG. 8 is an isometric view of the two-wheeled vehicle of FIG. 7 with the vehicle having an in-plane angular fork movement, dynamically-variable linkage. 
     FIG. 9 is a fragmentary side view of the two-wheeled vehicle of FIG. 7 with the vehicle having an in-plane, axial fork movement, dynamically-variable linkage. 
     FIG. 10 is a top view of the variable geometry cam taken along line  10 — 10  off FIG.  9 . 
     FIG. 11 is an exploded, fragmentary view of the cable linkage assembly taken along line  11 — 11  of FIG.  9 . 
     FIG. 12 is an exploded., fragmentary view of a lower portion of the cable linkage assembly taken along ling  12 — 12  of FIG.  9 . 
     FIG. 13 is a fragmentary, isometric view of the two-wheeled vehicle of FIG. 7 with the vehicle having an in-plane, linear fork movement, dynamically-variable linkage. 
     FIG. 14 is a fragmentary, side view of the two-wheeled vehicle of FIG. 6 with the vehicle having an out-of-plane, angular fork movement, dynamically-variable linkage. 
     FIG. 15 is an exploded, fragmentary view taken along line  15 — 15  of FIG.  14 . 
     FIG. 16 is a fragmentary, top view of the two-wheeled vehicle of FIG. 6 with the vehicle having a possible alternative out-of-plane, angular fork movement, dynamically-variable linkage. 
     FIG. 17 is a fragmentary, isometric view of the two-wheeled vehicle of FIG.  16 . 
     FIG. 18 is a fragmentary, front view of the two-wheeled vehicle of FIG. 6 with the vehicle having an out-of-plane, linear fork movement, dynamically-variable linkage. 
     FIG. 19 is a fragmentary, side view of the linkage of FIG.  18 . 
     FIG. 20 a fragmentary, top view of the two-wheeled vehicle of FIG. 6 with the vehicle having an out-of-plane, axial fork movement, dynamically-variable linkage. 
     FIG. 21 is a fragmentary, isometric view of the two-wheeled vehicle of FIG.  20 . 
     FIG. 22 is an isometric view of the two-wheeled vehicle of FIG. 7 with the vehicle having two dynamically-variable linkages in accordance with a preferred embodiment of the invention. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     Several preferred embodiments of a two-wheeled vehicle  30  that maintain the point-of-contact of the steering wheel  34   a  in an optimal controllability area  37  (FIGS. 6-7) during both straight and turning operations, thereby expanding the controllable operating envelope of the vehicle to be substantially coincident with the overall operating envelope of the vehicle are disclosed in FIGS. 1-20. This is preferably accomplished with at least one dynamically-variable linkage  32  (FIGS.  1  and  8 - 22 ) regulating the position of at least one steering wheel  34   a . The general concept of the invention is shown in schematic diagrams in FIGS. 1-7, with the physical characteristics leading to the instability of conventional two-wheeled vehicles shown in FIGS. 2-5. The solution provided by dynamically-variable linkages is shown schematically in FIGS. 6 and 7. Exemplar dynamically-variable linkages that follow the basic concept of the invention are disclosed in FIGS. 8-22. 
     A. Force Alignment Stabilization 
     One of the primary factors leading to two-wheeled vehicle instability is the fact that the forces leading to this instability and a rider&#39;s ability to detect and correct for those instabilities have been misunderstood. 
     In particular, and referring specifically to FIGS. 1A-D, which include many aspects of a conventional two-wheeled vehicle, a conventional two-wheeled vehicle includes the front steering wheel  34   a  and an in-line rear wheel  34   b  operably secured to a base. Both wheels  34   a ,  34   b  are typically rotatably secured to the base  48 , which preferably has a planar surface  49 , such that they rotate freely about their axles  50   a ,  50   b  to carry the vehicle  30  on the ground plane  38 . In addition, the steering wheel  34   a  is usually pivotally secured to the base  48 , preferably with a fork  52 , and aligned along an axis, commonly known as a steering axis  54 , which is substantially orthogonal to the surface (i.e., to within the caster angle  58 ) such that the front wheel  34   a  turns from side-to-side with respect to the base  48  along this axis  54 . The orientation of the steering wheel with respect to the steering axis is fixed in a conventional two-wheeled vehicle. 
     The geometry of these components define several relationships that are important to understanding the stability problems associated with the designs of conventional two-wheeled vehicles, and the solution offered by the force alignment stabilization of the present invention. These relationships include the ground plane  38  and the vehicle plane  40 , defined as the plane including the rear wheel&#39;s area of contact, which is preferably a point of contact  58 , and the steering axis  54 . The trail  60  is the distance between the steering wheel&#39;s point of contact  36  with the ground plane  38  and the point  39  at which a line extended from the steering axis contacts the ground plane  40 . The steering wheel offset  62  is the closest distance between the steering wheel&#39;s axis of rotation, or axle  50   a  and the steering axis  54 . 
     During operation of the vehicle  30 , the base  48  tilts side-to-side with respect to the ground plane  38  defining a roll angle  84  as the angle between the vehicle plane  40  and a vertical plane  66  perpendicular to the ground plane. 
     Unlike a car but like a bicycle or surfboard, the rider  70  (FIG. 1D) is a critical element in a dynamic system that must be stable for successful operation: The rider  70  of the invention is the active element maintaining stability. The rider himself has all the motion sensors (i.e., eyes, ears, sense of balance, etc . . . ) to tell him if there is a need for action and the degree of the need. Once the rider determines a correction is necessary, he must put a control input to the rest of the system by moving his feet in a tilting manner. For the overall vehicle system to operate successfully, the vehicle  30  must respond in a predictable and consistent manner for the rider  70  to realize the intended and expected results. The present invention provides a vehicle response to the rider&#39;s inputs that is desirable and amenable to stabilizing the vehicle system in a predictable and consistent fashion. 
     It is necessary that the design of this invention attain a level of robustness such that disturbances over Which the vehicle is moving do not impede the operation of the vehicle. These disturbances can be characterized as irregularities in the riding surface (i.e., bumps, depressions, or debris in the road). The present design provides a stabilized and controlled response through a reasonable envelope of operation, commonly referred to as an overall operating envelope herein. This overall operating envelope is defined by speed, maneuverability (i.e., radius of a turn), and riding surface irregularity. 
     As best shown in FIG. 1D, the rider  70  preferably commands the vehicle by manipulating the base  48 , which preferably has a planar surface  49  as shown. In particular, the rider  70  controls the orientation of the base  48  with respect to the ground plane  38  (i.e., tilt). During straight and upright operation of the vehicle  30 , the dynamic system consisting of the vehicle and rider (collectively referred to as the rider-vehicle system herein) is said to be at a point of unstable equilibrium. This means that if there are no control inputs (i.e., the rider  70  is not moving the board) or disturbances (i.e., irregularity in riding surface) the system will continue in this state. This situation is directly equivalent to the act of balancing. 
     The rider  70  on this vehicle, as on a bicycle or snowboard, is dynamically similar to the previously discussed balancing of a stick on a finger. Namely, the weight of the stick (i.e., gravity acting through the center-of-gravity of the stick), which is above the supporting force provided by the finger, is an inherently unstable system that must be stabilized by an active control element, such as the human. In balancing the stick, the finger is moved back and forth to continually align the supporting force with the weight force so that any destabilizing torque due to the misaligned forces will be maintained at zero: the stick will balance straight on the finger without moving. Likewise, in the present invention, as long as the force due to gravity  76  (FIG.  1 D), the dynamic forces associated with centripetal acceleration  78  (FIG. 1D) and the like, and the combined mass of the vehicle and rider Center-of-Gravity  72  (FIG. 1D) are perfectly aligned with the force exerted on the wheels  34   a ,  34   b  through their respective points-of-contact  36 ,  58 , the vehicle  30  and rider  70  will stay upright. 
     In particular and referring to FIG. 1D, the term specific force  74  refers to the resulting force which is the summation of the gravity force  76  and the force due to centripetal acceleration  78 . If support of the stick on a finger was in a state of acceleration, then the point of unstable equilibrium would move such that the specific force acting through the center-of-gravity of the stick would be aligned with the line that is between the center-of-gravity of the stick and the support point of the stick in the same fashion it was aligned in the stationary situation. Likewise, the rider-vehicle system will adjust its point of unstable equilibrium in the presence of acceleration such as in a constant radius turn. In a balanced system, the rider-vehicle system will lean into the turn such that the system plane  80 , which is defined as a plane that includes the points-of-contact  36 ,  58  of wheels  34   a ,  34   b , respectively, and the rider vehicle system&#39;s center-of-gravity  72 , contains the specific force  74 . 
     The degree of alignment of the specific force  74  with the system plane  80  determines the dynamic state of the system. If the specific force  74  is not in the system plane  80 , then the rider-vehicle system is either moving out of a turn or into a turn. The angle that the specific force makes with vertical, (as defined by gravity) is referred herein as the “bank angle”  82 . In a similar sense, the “system angle”  81  is the angle the system plane  80  makes with respect to the vertical plane  66  as defined by gravity. So the rider-vehicle system is in unstable equilibrium when the system angle  81  and the bank angle  82  are equal. 
     From the above discussion, it is now clear that for the rider-vehicle system to be stable or controllable, the system angle  81  and the bank angle  82  must be equal or close to equal. At times these two angles  81 ,  82  cannot be equal, for example, when a rider starts or ends a turn. Accordingly, the rider  70  will manage this angular difference by modulating centripetal acceleration, which occurs by controlling the orientation of the steerable wheel. If the wheel planes  88   a ,  88   b  (FIG. 1A) of the two wheels  34   a ,  34   b  are not coincident then the vehicle  30  is turning. When the vehicle  30  turns, centripetal acceleration  78  (FIG. 1D) is developed and the specific force  74  (FIG. 1D) is affected. 
     To stabilize the combined rider-vehicle system, the rider  70  must be able to steer at least the front wheel  34   a  (note: both wheels may turn but for clarity of this discussion it is assumed only the front wheel can turn). The only input to the vehicle  30  the rider  70  has is the position of the base, which is preferably a board having a substantially planar surface  49 , about the roll axis  90  (FIG.  1 ). The roll axis  90  is a line running through the points-of-contact  36 ,  58  of the two wheels  34   a ,  34   b.    
     As the rider  70  changes the orientation of the base  48  about the roll axis  90 , the front wheel  34   a  turns because of torque generated about the steering axis  54 . The steering axis  54 , which is not to be confused with the axle  50   a , is an axis about which the front wheel  34   a  turns and is fixed with respect to the base  48 . The wheel  34   a  is free to rotate about the steering axis  54  in response to torque generated about the steering axis  54 . This torque is generated by the force associated with steering wheel&#39;s  34   a  point-of-contact  36  being aligned with the specific force  74 . This force  74  will generate a torque about the steering axis  54  when it is not in a plane that contains the steering axis  54 , or in other words, is not pointing at the steering axis  54 . The vehicle plane  40  always contains the steering axis  54  and is defined by the plane containing the steering axis  54 , and the point-of-contact  58  of the rear wheel  34   b.    
     If the specific force  74 :associated with the steering wheel&#39;s  34   a  point-of-contact  36  is in the vehicle plane  40 , then no torque is generated about steering axis  54 . If the specific force  74  is not aligned with the vehicle plane  40 , then there may or may not be.torque about the steering axis  54  depending upon the particular geometry of the vehicle (i.e., the specific force  78  can still point at the steering axis  54  even if it is not in the vehicle plane  40 ). 
     As best shown in FIG. 1D, as the rider reorients the base  48  about the roll axis  90  the vehicle plane  40  angular displacement from the vertical plane  66  is changed (this angular distance is called the roll angle  84 ). This takes the vehicle plane  40  away from the specific force  74  and thereby causes a torque that results in the steering wheel  34   a  turning. As the wheel  34   a  is reoriented, the radius of the turn is changed which means that the centripetal acceleration  78  changes and the specific force  74  is reoriented. The specific force  74  is reoriented such that the roll angle  84  and the bank angle  82  are equal. The difference between the roll angle  84  and the bank angle  82  is called the control angle  86 . When the total rider-vehicle system is operating correctly, the rider  70  causes a control angle  86  by tilting the base  48  and the system will then nullify it. The control angle  86  induces torque. The torque turns the front wheel  34   a  about steering axis  54 . Turning the front wheel  34   a  changes the centripetal acceleration  78 . This reorients the specific force  74  which returns the rider-vehicle system to the point of unstable equilibrium and zeroes the control angle  86 . 
     Accordingly, the physical geometry of the steering wheel&#39;s  34   a  point-of-contact  36  with the ground plane  38  relative to the vehicle plane  40  is a significant factor in maintaining unstable equilibrium of a two-wheeled vehicle. If the point-of-contact  36  of the steering wheel  34   a  is positioned too far away from the vehicle plane  40 , the resulting torque is too great to be corrected or controlled by a rider  70  simply by tilting the base. Accordingly, the present inventor has determined that all two-wheeled vehicles have an optimal controllability area  37 , defined as the maximum distance from the vehicle plane  40  the point-of-contact  36  of the steering wheel  34   a  can be while still allowing a rider  70  to maintain easy control and stability of the vehicle  30  throughout a reasonable operating envelope of the vehicle, which is preferably the overall operating envelope of the vehicle  30 . 
     Optimally, the point-of-contact  36  of the steering wheel  34   a  is in the vehicle plane  40 . However, stability and controllable benefits may be obtained by maintaining the steering wheel&#39;s  34   a  point-of-contact  36  close enough to the vehicle plane  40  during turning operations such that the sum of the torque about the steering axis generate by friction of all the mechanical components that move with respect to one another, when forces on the wheel  34   a , forces due to irregularities of the riding surface, and gyroscopic effects, sum to a low enough value that the rider can quickly and easily maintain dynamic balance of the system simply by tilting the base  48 . Preferably this sum total of the torque about the steering axis is zero at point of unstable equilibrium. 
     B. Analysis of Conventional Two-Wheeled Vehicles 
     In light of the foregoing discussion, the reason conventional two-wheeled vehicles remain hands-free controllable only within a very limited controllable operating envelope can now be better understood. In particular, the front end of a conventional two-wheeled vehicle showing the relative geometry between the steering wheel&#39;s  34   a  point-of-contact  36  with the ground plane  38 , the steering axis  54 , the vehicle plane  40 , and an optimal controllability area  37  during various phases of operation is shown schematically and highly exaggerated for clarity in FIGS. 2-4. While the steering wheel of this conventional two-wheeled vehicle may turn about its steering axis, the relative position of the wheel axle  50   a  relative to the steering axis  54  remains fixed throughout the entire range of motion of the steering wheel  34   a.    
     When the conventional two-wheeled vehicle  30  is traveling straight along the ground plane  38  as shown in FIG. 2, the steering wheel  34   a  is aligned with the vehicle plane  40 , and the point-of-contact  36  of the steering wheel  34   a  is substantially on the vehicle plane  40 . Accordingly, since the point-of-contact  36  of the steering wheel  34   a  is within the optimal controllability area  37 , it is possible for a rider  70  to maintain dynamic balance of the vehicle  30  simply by tilting the base  48 . 
     However, when a turn is initiated as shown in FIG. 3, the point-of-contact  36 ′ of the steering wheel  34   a  moves out of the vehicle plane  40  in a first direction away from the vehicle plane  40 . If the commanded turn is sharp enough, the point-of-contact  36 ′ will move outside of the optimal controllability area  37 , thereby generating torque about the steering axis  54  that is too large to allow the rider  70  to maintain dynamic balance of the vehicle  30  and execute the turn at the same time simply by tilting the base. 
     Moreover, in addition to turning the steering wheel  34   a , the typical turn usually includes tilting the vehicle  30  to produce a roll angle  84  as shown in FIG.  4 . The simultaneous rolling of the vehicle  30  and turning of the steering wheel  34   a  about its steering axis  54  urges the steering wheel&#39;s  34   a  point-of-contact  36 ″ to initially move back toward the vehicle plane  40  (from its position in FIG. 3) and then in a second direction away from the vehicle plane  40  as shown in FIG.  4 . Again, this position of the point-of-contact  36 ″ outside of the optimal controllability area  37  generates a torque about the steering axis  54  that is too large to allow the rider  70  to maintain dynamic balance of the vehicle and execute the turn at the same time simply by tilting the base  48 . 
     FIG. 5 shows these relative points-of-contact  36 ,  36 ′,  36 ″ of the steering wheel  34   a  during a typical turn relative to the optimal controllability area  37  for a vehicle initially traveling in the direction of arrow  35 . For a typical turn, the fixed geometry of conventional two-wheeled vehicles make this point-of-contact move in and out of the optimal controllability area, thereby making the vehicle inherently unstable during turning operations. Accordingly, most two-wheeled vehicles require additional control features, such as handlebars and the like, to allow a rider to maintain control of the vehicle throughout its entire operating envelope. 
     C. Steering Wheel Position Regulator 
     To expand the operational envelope and to make the vehicle  30  inherently stable and controllable within this envelope, it is necessary to maintain the steering wheel&#39;s  34   a  point-of-contact  36  within the optimal controllability area  37  of the vehicle, and preferably in the vehicle plane  40  during both straight and turning operations. Referring to FIGS. 6-22, one known way to accomplish this is to include position regulator, which is preferably a dynamically-variable linkage  32  between the base  48  and the steering wheel  34   a . The dynamically-variable linkage  32  maintains the steering wheel&#39;s  34   a  point-of-contact  36  in or near the vehicle plane  40  so that the rider  70  can command a desired turn angle  92  on the steering wheel  34   a , and maintain control and stability of the vehicle  30  as previously described simply by tilting the base  48 . 
     In essence, the dynamically-variable linkage  32  moves the steering wheel  34   a  with respect to the base  48 , as a function of the turn angle  92 , so as to maintain the steering wheel&#39;s  34   a  point-of-contact  36  within the optimal controllability area  37 , and preferably within the vehicle plane  40 . The torque generated about the steering axis  54 , as described above, operates the dynamically-variable linkage  32  so that the steering wheel  34   a  turns in response to the rider&#39;s  70  inputs, and the point-of-contact  36  stays in, or close to, the vehicle plane  40 . The result is an in-line two-wheeled vehicle that a rider  70  may maneuver throughout its entire operating envelope in a fashion similar to a surfboard, snowboard, or skateboard. 
     Because no torque is generated about the steering axis  54  when the point-of-contact  36  of the steering wheel  34   a  is coincident with the steering axis  54 , the vehicle  30  becomes unstable and uncontrollable at this point. Accordingly, care must be taken in sizing the relative components of the dynamically-variable linkages to prevent this characteristic from arising throughout the entire range of motion of the linkages. However, by optimizing the lengths of the vehicle&#39;s trail  60  and offset  62 , this characteristic can be easily avoided. 
     The dynamically-variable linkage  32  can manipulate the steering wheel  34   a  in the manner described in several ways. One way includes moving the steering wheel  34   a  toward and away from the vehicle base  48 , generally in-plane with the steering wheel plane  88   a  when the vehicle  30  is traveling  110  straight in the direction of arrow  35 . This type of dynamic linkage is called “in-plane movement” herein and is shown schematically in FIG.  7 . Another way to move the linkage  32  to accomplish force alignment stabilization is to move the steering wheel  34   a  generally side-to-side with respect to the steering wheel plane  88   a . This type of dynamic linkage is called “out-of-plane movement” herein and shown schematically in FIG.  6 . Any path the steering wheel&#39;s  34   a  point-of-contact  36  takes to maintain itself within the optimal controllability area  37  of the vehicle  30  can be categorized as in-plane movement, out-of-plane movement, or a combination of the two. Accordingly, these two-types of movement and exemplar linkages of them are discussed in greater detail below: 
     1. In-Plane Movement 
     In-plane movement includes a dynamically-variable linkage  32  that moves the steering wheel  34   a  toward and away from the base  34   a  generally along the steering wheel&#39;s plane  88   a , such that it maintains the steering wheel&#39;s point-of-contact  36  within the optimal controllability area  37  throughout the entire range of motion of the steering wheel  34   a . FIG. 7 shows the same three points-of-contact  36 ,  36 ′,  36 ″ shown in FIG. 5, but with a dynamically-variable linkage that provides in-plane movement throughout the previously described turn. 
     In particular, when the steering wheel  34   a  is only turned (as in FIG.  3 ), the in-plane, dynamically-variable linkage  32  urges the steering wheel  34   a  forward in the direction of arrow  96  along the steering wheel plane  88   a  such that the point-of-contact  36 ′ is maintained in the controllability area  37 . Similarly, when the vehicle  30  is simultaneously tilted and the steering wheel  34   a  is turned (as in FIG.  4 ), the in-plane, dynamically-variable linkage  32  urges the steering wheel  34   a  backward in the direction of arrow  98  along the steering wheel plane  88   a  to maintain the point of contact  36 ″ within the controllability area  37 . 
     Exemplar structures for providing this type of movement are discussed in greater detail below. 
     a. In-Plane Angular Fork Movement 
     Referring specifically to FIG. 8, a two-wheeled vehicle  30  having a front steering wheel  34   a  that is operably secured to the base  48  with an in-plane, angular fork movement linkage  32   a  there between is disclosed. In particular, the vehicle  30  includes the front steering wheel  34   a  and an in-line rear wheel  34   b  operably secured to a base  48 . Both wheels  34   a ,  34   b  are typically rotatably secured to the base  48 , which preferably includes a substantially planar surface  49 , such that they rotate freely about their axles  50   a ,  50   b  to carry the vehicle  30  on the ground plane  38 . In addition, the steering wheel  34   a  is pivotally secured to the base  48 , preferably with a wheel mounting portion such as a fork  52 . The fork is preferably aligned substantially along an axis, commonly known as a steering axis  54 , which is substantially orthogonal but slightly tilted with respect to the surface such that the front wheel  34   a  turns from side-to-side with respect to the base  48  along this axis  54 . Preferably, a hand or foot brake  55  is operably secured to the rear wheel  34   b.    
     In particular, the in-plane, angular fork movement linkage  32   a  includes a base mounting portion, which is preferably a fork mounting portion  100  extending from the base  48  and defining an elongate channel  102  for pivotally receiving a steering shaft therein. A steering head  106  is rigidigly secured to the fork mounting portion  100 :and preferably extends forward from the fork mounting portion  100 , is substantially planar, is aligned substantially parallel with the planar surface  49 , and includes a guide cam engaging portion  108  as shown. 
     The steering shaft  104  is operably secured within the channel  102  such that it pivots freely about the steering axis  54 . The steering shaft  104  includes a fork engaging portion  110  for pivotally securing the fork  52 . Preferably, this fork engaging portion  110  includes at least one shaft  112  extending from the fork engaging portion  110  and aligned generally parallel with the planar surface  49 . 
     The fork  52  is operably secured to the fork engaging portion  110  of the sheering shaft  104 , preferably through openings  114  for receiving the shaft  112  as shown, such that the steering wheel  34   a  moves angularly about the shaft  112 , forward and backwards with respect to the base  48  along the steering wheel&#39;s plane  88   a . Preferably, the openings  114  in the fork  52  for receiving the shaft  112  are tapered as shown to permit the base  48  to tilt side-to-side while maintaining the front and rear wheel&#39;s  34   a ,  34   b  contact with the ground plane  38 . 
     The fork includes a guide cam portion  116  extending therefrom for operably engaging the guide cam engaging portion  108  of the steering head  106 . Preferably, the guide cam engaging portion  108  is an elongate curved opening  109  in the steering head  106 , and the guide cam portion  116  is elongate and slidably received within the curved opening  109 . 
     The guide cam engaging portion  108 , the guide cam portion  116 , the fork  52 , and other components are all sized and shaped such that the point of contact  36  of the steering wheel  34   a  is maintained within the controllability area  37  of the vehicle  30  through the entire range of motion of the steering shaft  104 . Preferably, the center  118  of the cam engaging portion  108  is the closest to the fork mounting portion  100  with the ends of the cam-engaging portion  108  extending away from the fork mounting portion  100 . More preferably, the guide cam portion  116  is aligned at the center of the cam-engaging portion  108  when the vehicle base  48  is substantially parallel to the ground plane  38  and the steering wheel  34   a  is aligned with the rear wheel  34   b  as shown in FIG.  8 . 
     b. In-Plane Axial Fork Movement 
     Referring specifically to FIGS. 9-12, a front steering wheel  34   a  that is operably secured to the vehicle base  48  with an in-plane axial fork movement linkage  32   b  is disclosed. This embodiment has substantially the same basic elements and construction of the previously described embodiment. Accordingly, in order to avoid undue repetition, unless specifically identified otherwise below, reference numerals refer to like numbered elements having a like orientation and configuration as those elements identified in the discussion of the first preferred embodiment. 
     In this embodiment the steering shaft  104  and fork  52  are a single monolithic structure  130 , and a wheel mounting portion  132  supporting the front wheel&#39;s axle  50   a  is slidably secured to the end of the fork  52  as shown to permit the steering wheel  34   a  to move forward and backward along the steering wheel&#39;s plane  88   a  relative to the base  48 . This movement is preferably regulated by mating sprockets  134   a ,  134   b . More preferably, an elongated substantially linear, or “rack,” sprocket  134   a  is secured to the wheel mounting portion  132 , and an axial, or “pinion,” sprocket  134   b  is secured to the fork  52  for operably engaging the linear sprocket  134   a  as shown. 
     A guide cam  136  is pivotally secured to the fork mounting portion  100  at pivot point  138  such that it pivots about pivot point  138  as the guide cam  136  moves along the cam-engaging portion  108  of the steering head  106 . Preferably, the steering head  106  is rigidly secured to the steering shaft  104  as shown, and the guide cam.  136  is pivotally secured to a mounting bracket  140  rigidly secured to the fork mounting portion  100 . 
     A control cable  142  having two ends  144   a ,  144   b  is secured to the guide cam  136  on opposite sides of the pivot point  138  such that movement of the guide cam  136  about its pivot point  138  pulls one end (For example  144   a ) of the cable  142  and loosens the other end (For example  144   b ). The cable  142  is operably secured to the axial sprocket  134   b  such that this movement causes the sprocket  134   b  to rotate about its pivot axis  146  in one direction or the other, thereby engaging the linear sprocket  134   a  forward or backward, and moving the point of contact  36  of the steering wheel  34   a  forward-or-backward as described. More preferably, a pair of mating sprockets  134   a ,  134   b  and related control cables  142 , one set on each side of the steering wheel  34   a , are used. 
     The guide cam  136 , the guide cam engaging portion  108 , fork  52 , mating sprockets  134   a ,  134   b , and cables  142  are all sized and shaped such that the point of contact  36  of the steering wheel  34   a  is maintained within the controllability area  37  of the vehicle  30  throughout the entire range of motion of the steering shaft  104 . 
     c. In-Plane Linear Fork Movement 
     Referring specifically to FIG. 13, a front steering wheel that is operably secured to the vehicle base with an in-plane linear fork movement linkage  32   c  is disclosed. This embodiment has substantially the same basic elements and construction of the first described embodiment. Accordingly, in order to avoid undue repetition, unless specifically identified otherwise below, reference numerals refer to like numbered elements having a like orientation and configuration as those elements identified in the discussion of the first preferred embodiment. 
     In this embodiment, the steering shaft  104  and fork  52  are separate structures that are slidably secured together as shown to permit the steering wheel  34   a  to move forward and backward in the direction of arrows  149  along the steering wheel&#39;s plane  88   a  relative to the base  48 . This movement is preferably regulated by a guide cam  136 , pivotally secured to the steering shaft  104  at pivot point  150 . One end  152  of the guide cam  136  is slidably received within the guide-cam engaging portion  108  of the steering head  106 . An opposite end  154  of the guide cam  136  is operably secured to the fork  52 . Preferably, the steering head  106  is rigidly secured to the fork mounting portion  100  of the base  48 . 
     Preferably, the fork  52  includes a substantially linear sliding portion  156 , and the guide cam  136  is secured toward one end of that portion  156  with a pin  158 . The pin  158  is received through an opening  160  in the guide cam  136 . Preferably, this opening  160  is elongated, and adequate tolerance is provided at pivot point  162  to permit the cam  136  to move as described throughout the entire range of motion of the steering shaft  104 . 
     The steering shaft  104 , fork  52 , guide cam  136 , guide cam engaging portion  108 , linear sliding portion  156  and related components are all sized and shaped such that the point of contact  36  of the steering wheel  34   a  is maintained within the controllability area  37  of the vehicle  30  throughout the entire range of motion of the steering shaft  104 . 
     2. Out-of-Plane Movement 
     Out-of-plane movement includes a dynamically-variable linkage  32  that moves the point of contact  36  of the steering wheel  34   a  side-to-side with respect to the steering wheel plane  88   a  (FIG.  1 A), such that it maintains the steering wheel&#39;s point-of-contact  36  within the optimal controllability area  37  throughout the entire range of motion of the steering wheel  34   a . FIG. 6 shows the same three points-of-contact  36 ,  36 ′,  36 ″ shown in FIG. 5, but with a dynamically-variable linkage that provides out-of-plane movement throughout the previously described turn. 
     In particular, when the steering wheel  34   a  is only turned (as in FIG.  3 ), the out-of-plane, dynamically-variable linkage  32  urges the steering wheel in the direction of arrow  100  away from the steering wheel plane  88   a  such that the point-of-contact  36 ′ is maintained in the controllability area  37 . Similarly, when the vehicle  30  is simultaeneously tilted and the steering wheel is turned (as in FIG.  4 ), the out-of-plane, dynamically-variable linkage  32  urges the steering wheel  34   a  away from the steering wheel plane in the direction of arrow  98  to maintain the point of contact  36 ″ within the controllability area  37 . 
     Exemplar structures for providing this type of movement are discussed in greater detail below. 
     a. Out-Of-Plane Angular Fork Movement 
     Referring specifically to FIGS. 14 and 15, a front steering wheel  34   a  that is operably secured to the vehicle base  48  with an out-of-plane angular fork movement linkage  32   d  is disclosed. This embodiment has substantially the same basic elements and construction of the first described embodiment. Accordingly, in order to avoid undue repetition, unless specifically identified otherwise below, reference numerals refer to like numbered elements having a like orientation and configuration as those elements identified in the discussion of the first preferred embodiment. 
     In this embodiment the steering shaft  104  and fork  52  are separate structures. The steering shaft  104  is pivotally secured to the fork mounting portion  100  and includes an outward extending portion  170  that preferably extends above and forward from the fork mounting portion  100 . An upper end  172  of the fork  52  is pivotally secured to the outward extending portion  170  of the steering shaft  104 , preferably at an opening  174  in the fork  52 . 
     A pivoting arm  176  extends from the fork mounting portion  100  of the base  48 . As best shown in FIG. 15, the fork  52  includes a pivoting arm engaging portion  178  that straddles the pivoting arm  176 . Preferably, wedge shaped portions  180  of the fork  52  operably engage the pivoting arm  176 , thereby allowing the fork  52  to turn substantially about an axis  182  that is substantially parallel to steering axis  54  as shown in dashed lines in FIG.  15 . 
     In addition, the pivoting arm  176  serves as a fulcrum for the side-to-side tilting of the fork  52 . Specifically, as the steering shaft  104  rotates about steering axis  52 , the outward extending portion  170  of the steering shaft  104  urges the upper end  172  of the fork  52  in a first direction. This causes the fork  52  to tilt about the pivoting arm  176 , and urges the lower end  184  of the fork  52 , which supports the steering wheel  34   a , in an opposite second direction out-of-plane to the steering wheel&#39;s plane  88   a.    
     The steering shaft  104 , outward extending portion  170 , fork  52 , pivoting arm  176  and related components are all sized and shaped such that the point of contact  36  of the steering Wheel  34   a  is maintained within the controllability area  37  of the vehicle  30  throughout the entire range of motion of the steering shaft  104 . 
     An alternative angular fork movement linkage  32   d ′ is disclosed in FIGS. 16 and 17. This embodiment has substantially the same basic elements and construction of the first described embodiment. Accordingly, in order to avoid undue repetition, unless specifically identified otherwise below, reference numerals refer to like numbered elements having a like orientation and configuration as those elements identified in the discussion of the first preferred embodiment. 
     In particular, this out-of-plane, angular fork movement linkage  32   d ′ includes a fork mounting portion  100  extending from the base  48  and defining an elongate channel  102  for pivotally receiving a steering shaft  104  therein. A steering head  106  is rigidigly secured to the fork mounting portion  100  and preferably extends to one side of the fork mounting portion  100 , is substantially planar, is aligned substantially parallel with the planar surface  49  (FIG.  8 ), and includes a guide cam engaging portion  108  as shown in FIG.  17 . 
     The steering shaft  104  is operably secured within the channel  102  such that it pivots freely about the steering axis  54 . The steering shaft  104  includes a fork engaging portion  110  for pivotally securing the fork  52 . Preferably, this fork engaging portion  110  includes at least one shaft  112  extending from the fork engaging portion  110  and aligned generally longitudinally with the longitudinal length of the base  48 . 
     The fork  52  is operably secured to the fork engaging portion  110  of the sheering shaft  104 , preferably through openings  114  for receiving the shaft as shown, such that the point of contact  36  of the steering wheel  34   a  moves angularly about the shaft  112 , side-to-side with respect to the base  48  in the direction of arrow  186 , and generally perpendicular to the steering wheel&#39;s plane  88   a.    
     The fork  52  includes a guide cam portion  116  extending therefrom for operably.engaging the guide cam engaging portion  108  of the steering head  106 . Preferably, the guide cam engaging portion  108  is an elongate curved opening  109  in the steering head  106 , and the guide cam portion  116  is an elongate portion slidably received within the curved opening  109 . 
     The guide cam engaging portion  108 , the guide cam portion  116 , the fork  52 , and other components are all sized and shaped such that the point of contact  36  of the steering wheel  34   a  is maintained within the controllability area  37  of the vehicle  30  through the entire range of motion of the steering shaft  104 . More preferably, the cam engaging portion  108  is arcuate with its closest point to the fork mounting portion  100  being at one end of the cam engaging portion  108  as best shown in FIG.  17 . 
     b. Out-Of-Plane Axial Fork Movement 
     Referring specifically to FIGS. 18 and 19, a front steering wheel  34   a  that is operably secured to the vehicle base  48  with an out-of-plane axial fork movement linkage  32   e  is disclosed. This embodiment has substantially the same basic elements and construction of the first described embodiment. Accordingly, in order to avoid undue repetition, unless specifically identified otherwise below, reference numerals refer to like numbered elements having a like orientation and configuration as those elements identified in the discussion of the first preferred embodiment. 
     In this embodiment, the steering shaft  104  and fork  52  are a single, monolithic structure  190  operably secured to the fork mounting portion  100  of the base  48 . This structure  190  includes the wheel fork  192  extending below the fork mounting portion  100  and an outwardly extending portion  194  that preferably extends above and forward from the fork mounting portion  100 . 
     A wheel mounting portion  132  supporting the front wheel&#39;s axle  50   a  is slidably secured to the end of the wheel fork  192  as shown to permit the point-of-contact  36  of the steering wheel  34   a  to move side-to-side relative to the steering wheel&#39;s  34   a  plane  88   a . This movement is preferably regulated by mating sprockets  196   a ,  196   b . More preferably, at least one elongated substantially linear, or “rack,” sprocket  196   a  is secured to the wheel mounting portion  132 , and an axial, or “pinion,” sprocket  196   b  is secured to the wheel fork  192  for operably engaging the linear sprocket  196   a  as shown. More preferably, a pair of mating rack and pinion gears  196   a ,  196   b , one on each side of the steering wheel  34   a , are used. 
     A substantially straight, elongate, pivot arm  198  is pivotally secured to the fork mounting portion  100  at pivot point  200 . An upper end  202  of the pivot arm  198  is operably secured to the outwardly extending portion  194  of the monolithic structure  190  as shown. The opposite lower end  204  of the pivot arm  198  is operably secured to control cables  206   a ,  206   b.    
     The control cables  206   a ,  206   b  are secured to the pivot arm  198  as shown such that movement of the pivot arm  198  about its pivot point  200  pulls one end of the cables  206   a ,  206   b , and loosens the other ends of those cables  206   a ,  206   b . The cables  206   a ,  206   b  are operably secured to the axial sprockets  196   b  such that this movement causes the sprockets  296   b  to rotate about their pivot axes  208   a ,  208   b  in one direction or the other, thereby urging the linear sprockets  196   a  sideways, and moving the point of contact  36  of the steering wheel  34   a  side-to-side as described. 
     Preferably, the lower end  204  of the pivot arm  198  is operably secured to a slider assembly  210  as shown to maintain alignment of the pivot arm  198  with respect to the fork mounting portion  100  throughout the entire range of motion of the pivot arm  198 . 
     The steering shaft  104 , outward extending portion  194 , wheel fork  192 , pivot arm  198  and related components are all sized and shaped to such that the point of contact  36  of the steering wheel  34   a  is maintained within the controllability area  37  of the vehicle  30  throughout the entire range of motion of the steering shaft  104 . 
     c. Out-Of-Plane Linear Fork Movement 
     Referring specifically to FIGS. 20 and 21, a front steering wheel that is operably secured to the vehicle base with an out-of-plane linear fork movement linkage  32   f  is disclosed. In order to avoid undue repetition, unless specifically identified otherwise below, reference numerals refer to like numbered elements having a like orientation and configuration as those elements identified in the discussion of the first preferred embodiment. 
     In this embodiment, the steering shaft  104  and fork  52  are separate structures, with the steering wheel  34   a  mounted to the fork  52 . As best shown in FIG. 21, the fork  52  is slidably secured to the steering shaft  104  such that the fork  52  and attached wheel  34   a  move out of plane with respect to the steering wheel&#39;s plane  88   a  in the direction if arrows  220 . 
     This movement is preferably regulated by guide cam  136 . More preferably, the guide cam  136  is pivotally secured to the steering shaft  104  at pivot point  222  such that the guide cam  136  pivots about pivot point  222  as one end  224  of the guide cam  136  moves along the cam-engaging portion  108  of the steering head  106 . The opposite end  226  of the guide cam  136  is operably secured to the fork  52  such that rotation of the steering shaft  104  about the steering axis  54  causes the guide cam  136  to move along the cam-engaging portion  108  of the steering head  106 , thereby urging the fork  52  to move sideways as described. 
     Preferably, the steering head  106  is rigidigly secured to the fork mounting portion  100  and extends to one side of the fork mounting portion  100 , is substantially planar, and is aligned substantially parallel with the planar surface  49  (FIG.  8 ). More preferably, the cam engaging portion  108  is arcuate with its closest point to the fork mounting portion  100  being at one end of the cam engaging portion  108  as best shown in FIG.  21 . 
     As best shown in FIG. 20, the guide cam  136 , the cam engaging portion  108 , fork  52  and related components are all sized and shaped such that the point of contact  36  of the steering wheel  34   a  is maintained within the controllability area  37  of the vehicle  30  throughout the entire range of motion of the steering shaft  104 . 
     All of these exemplar linkages  32   a-f  operate in essentially the same way. A rider stands on the board of the base while the vehicle is moving forward. Using his sense of balance, the rider can tilt the board  49  sideways to command a turn. The previously described forces urge the steering wheel  34   a  to turn in the direction of the commanded turn. However, these linkages maintain the point-of-contact  36  in the controllability area  37  of the vehicle  30 , thereby allowing the rider to maintain control of the vehicle throughout a wide operating range of the vehicle  30  simply by tilting the board  49 . 
     D. Additional Features 
     In view of the wide variety of embodiments to which the principles of the invention can be applied, it should be apparent that the detailed description of a preferred embodiment is illustrative only and should not be taken as limiting the scope of the invention. For example, as shown in FIG. 22, both wheels  34   a ,  34   b  can be connected to the vehicle  30 ′ with a dynamically-variable linkage. In FIG. 22, a pair of in-plane, angular fork movement linkages  32   a  are shown. However, any dynamically-variable linkage could be used. 
     Moreover, to facilitate understanding, the presently described linkages have been described as providing either “in-plane” or “out-of-plane” movement. Obviously, any type of linkage movement, design, or structure, that maintains the point-of-contact  36  of at least one steering wheel  34   a  within the controllability area  37  of the vehicle can be used. 
     Also, the principles of the present invention work equally well whether the vehicle is self-propelled, rider-propelled, gravity propelled, or propelled by other sources, such as the wind. Accordingly, the vehicle of the present invention could readily include forms of propulsion, such as a motor, bicycle chain and peddle system, sail, or other forms of propulsion without compromising the principles of the present invention. 
     In addition, depending on the terrain in which the operator plans to ride the vehicle, traditional suspension linkages can also be included to offer a smoother ride to the rider without compromising the benefits of the present invention. Also, although not required to control or stabilize the vehicle, traditional handlebars, or a support bar can extend along the steering axis or from the base, to facilitate rider balance on the vehicle. 
     Accordingly, the claimed invention includes all such modifications as may come within the scope of the following claims and equivalents thereto.