Patent Publication Number: US-7591342-B2

Title: Apparatus and method for steering a vehicle

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This is a divisional application of U.S. application Ser. No. 11/016,039, filed Dec. 17, 2004, which is a continuation-in-part of U.S. patent application Ser. No. 10/765,731, filed Jan. 26, 2004, which is a continuation application of U.S. patent application Ser. No. 10/262,751, filed Oct. 1, 2002, (now U.S. Pat. No. 6,705,423), which is a divisional of U.S. patent application Ser. No. 09/920,181, filed Aug. 1, 2001 (now U.S. Pat. No. 6,488,115), which is related to U.S. patent application Ser. No. 09/664,850, filed Sep. 19, 2000, wherein the contents of all of the above listed applications and patents are incorporated in their entirety herein by reference. 
     This application also claims priority to U.S. Provisional Patent Application 60/540,643 filed on Jan. 30, 2004, wherein the contents are incorporated in its entirety herein by reference. 
     This application is also related to U.S. patent application Ser. No. 09/650,869, filed Aug. 30, 2000, the contents of which are incorporated herein by reference thereto. 
     This application is also related to U.S. patent application Ser. No. 09/663,549, filed Sep. 18, 2000, the contents of which are incorporated herein by reference thereto. 
    
    
     FIELD OF THE INVENTION 
     This invention is related generally to steering systems, and, more particularly, this invention is related to an interface between a rotary to linear actuator and a linear section of the steering system 
     BACKGROUND OF THE INVENTION 
     Some current steering system designs have replaced the hydraulic power steering pump with electrically assisted systems based on fuel economy, modularity, engine independence, and environmental issues. 
     With electrically actuated or electrically assisted steering systems there is a significant servo mechanism design challenge associated with the need to maintain proper kinematical constraint, while at the same time, providing reasonable insulation from the drawbacks of tolerance stack up which may produce system lock up. 
     Although a successful servo mechanism design may appear to be a combination of basic “catalogue” mechanisms (e.g. ball-screw, gears, belts, various joints, etc.), the way these are used in combination represents an unmistakably cardinal feature of this art. 
     The current state of engineering meets these concerns by anticipating the stresses likely to be encountered by designing heavy-duty components. Needless to say, these designs are expensive to manufacture, have excessive performance challenges because of the increased inertia and friction, and add to the overall weight of the vehicle. 
     In most steering applications development of the actuator for power assist follows the synthesis and design of the suspension and steering linkages. Steering linkages could be steering the front wheels or rear wheels or both. Thus power assist steering may take the form of assisting front steering mechanism, rear steering mechanism or both. The steering linkage could also be connected to the steering wheel mechanically or via electronics that follow certain logic such as in “steer-by-wire” applications. 
     BRIEF SUMMARY OF THE INVENTION 
     In one exemplary embodiment, a steering system for a vehicle may include a steering wheel being positioned for manipulation by a vehicle operator, a steering mechanism for transmitting a steering operation of the steering wheel to vary the angular configuration of at least one wheel of the vehicle, a power assist mechanism for providing an assisting force to the steering mechanism, the power assist mechanism being activated in response to the steering operation of the steering wheel and a load displacement system being operatively coupled to the power assist mechanism, the load displacement system allowing transient loads of the steering mechanism to be displaced. 
     In another exemplary embodiment, a steering system for a vehicle includes a rack being movably mounted within a rack housing, the rack being coupled to a steerable road wheel, a ball-screw mechanism being coupled to the rack at one end and an electric motor at the other, the electric motor providing an actuating force to the ball-screw mechanism, the actuating force causing the rack to move linearly within the rack housing, a first coupling mechanism coupling the electric motor to the rack housing, and a second coupling mechanism coupling the ball nut to said rack. 
     In another exemplary embodiment, a method for providing an actuation force to a rack of a vehicle, includes isolating non-axial loads from an electric motor of a steering system, the motor providing a rotational force to a rotatable member of a rotary-to-linear conversion device, and isolating non-axial loads from a linearly actuatable member of said rotary-to-linear conversion device, the linearly actuatable member being coupled to a rack of said steering system. 
     In yet another exemplary embodiment, a steering system for a vehicle includes a rack being movably mounted within a rack housing, the rack being coupled to a steerable road wheel, a rotary-to-linear mechanism being coupled to the rack at one end and an electric motor at the other, the electric motor providing an actuating force to the rotary-to-linear mechanism, the actuating force causing the rack to move linearly within the rack housing, a first coupling mechanism coupling the electric motor to the rack housing, and a second coupling mechanism coupling the ball nut to the rack. 
     In another exemplary embodiment, an actuator for a steering system, may include a rotary to linear actuator, a movable linear section, and an interface between the rotary to linear actuator and the linear section, wherein the interface is limited to three degrees of freedom and the actuator is limited to one degree of freedom. 
     In another exemplary embodiment, an interface for an actuator may adjoin a movable linear section and a rotary to linear actuator, and the interface may comprise a block on a plane joint. 
     Other systems and methods according to embodiments will be or become apparent to one with skill in the art upon review of the following drawings and detailed description. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows an illustration of a steering system for a vehicle; 
         FIG. 2  is an illustration of a portion of the steering system in  FIG. 1 ; 
         FIG. 3  is a perspective view of exemplary embodiments of a rack-independent actuator; 
         FIG. 4  is a cross-sectional view of exemplary embodiments of a rack-independent actuator; 
         FIG. 5  is another perspective view of a rack-independent actuator; 
         FIG. 6  is an end view of exemplary embodiments of a rack-independent actuator; 
         FIG. 7  is a top plan view of exemplary embodiments of a rack-independent actuator; 
         FIGS. 8 and 9  are perspective views of a rack-independent actuator illustrating the universal joints in an exploded view; 
         FIG. 10  is an end perspective view of exemplary embodiments of the rack-independent actuator; 
         FIG. 11  is a partial cross sectional perspective view of exemplary embodiments of a rack-independent actuator; 
         FIG. 12  is a partial cross sectional perspective view of exemplary embodiments of a universal joint of a rack-independent actuator; 
         FIG. 13  is a partial cross sectional perspective view of exemplary embodiments of a rack-independent actuator; 
         FIG. 14  is a partial cross sectional perspective view of exemplary embodiments of a universal joint of a rack-independent actuator; 
         FIG. 15  is a block diagram of a rack-independent actuator system; 
         FIG. 16  a diagrammatic view of a steer by wire system; 
         FIG. 17  is a diagrammatic view of a steer by wire system with independent actuators for each steerable wheel of a vehicle; 
         FIG. 18  is a diagrammatic front view of an interface location between a rotary to linear actuator and a linear section of an actuator; 
         FIG. 19  is a diagrammatic front view of a collinear load acting on a ballscrew-screw; 
         FIGS. 20 and 21  are cross-sectional views of a system incorporating the concepts of  FIG. 19 ; 
         FIG. 22  is a perspective view of the special case actuator of  FIG. 19 ; 
         FIG. 23  is a perspective view of the interface of  FIG. 19  with respect to a ball screw nut and a rack; 
         FIG. 24  is a perspective view of an overall appearance of a special case actuator shown in  FIG. 22 ; 
         FIG. 25  is a diagrammatic front view of an alternate interface between a rotary to linear actuator and a linear section of an actuator; 
         FIG. 26  is a perspective view of an actuator incorporating the mechanism of  FIG. 25 ; 
         FIGS. 27-29  are cross-sectional views of the actuator of  FIG. 26 ; 
         FIG. 30  is an enlarged detail showing a ballscrew nut and a plane; 
         FIG. 31  is a cross-sectional view of an alternate embodiment of the actuator of  FIG. 26 ; 
         FIG. 32  is a cross-sectional view of the actuator of  FIG. 26 ; 
         FIG. 33  is a perspective view of an interface between a rotary to linear actuator and a linear section; 
         FIG. 34  is a perspective view of an alternate interface between a rotary to linear actuator and a linear section; and, 
         FIG. 35  is a perspective view of another alternate interface between a rotary to linear actuator and a linear section. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Aspects of these embodiments relate generally to an apparatus and method for steering a vehicle, and more specifically to a rack-independent actuator. A steering system for a vehicle may include a rack-independent actuator. The rack-independent actuator may include component parts that isolate from undesirable loads by two universal joints that may isolate mechanical components of the actuator from transient loads that may be encountered by the rack or rack housing. 
     The system may be powered by a rotary type electric motor. The motor has speed reducers and rotary-to-linear actuators to achieve feasible size and linear actuation. The actuation unit is decoupled from the directionally unwanted loads by providing universal joints (or an equivalent degree of freedoms) at either end. One universal joint is mounted to the housing that holds the motor rotary-to-rotary speed reducer and the movable shaft of the linear-to-rotary actuator, and the other is mounted to a member that is linearly moved by the linear-to-rotary actuator. 
     The use of universal joints (or gimbals), which provides kinematical degrees of freedom to prevent non-axial loads, also prevents bending moments on the rotary-to-linear actuator. In particular, such loads may result from the misalignment of the shafts and/or non-axial loading from other components. This situation may produce undesirable friction and high stresses resulting in loss of efficiency and/or undesirable steering feel. By avoiding the non-axial loads, the mechanization becomes feasible for all types of linear-to-rotary mechanizations, which today are limited to very special ball-screws. 
     Exemplary embodiments of the independent actuator system of employ the judicious use of universal joints, (gimbal) expansion joints, or other equivalents to achieve freedom from lock-up as well as compensation for reasonable tolerance stack-up errors, which must be designed around current steering system designs. 
     A benefit of the Electric Power Steering and Steer-by-Wire system is the enhanced comfort to the driver of a vehicle equipped with this system. The driver of such a vehicle would experience improved handling over less-than-smooth terrains e.g., potholes, graded surfaces, etc. 
     Less-than-smooth terrain increases the loads and deflections encountered by the steering system. Thus, any bumps experienced by the vehicle may increase the wear and tear to the steering system, thus shortening and reducing its effective life. 
     Referring now to  FIGS. 1 and 2 , a steering system  10  for use in a vehicle  12  (not shown) is illustrated. Steering system  10  allows the operator of vehicle  12  to control the direction of vehicle  12  through the manipulation of steering system  10 . 
     A steering column  14  provides mechanical manipulation of the vehicle&#39;s wheels in order to control the direction of the vehicle. Steering column  14  includes a hand wheel  16 . Hand wheel  16  is positioned so that a user can apply a rotational force to steering column  14 . An upper steering column shaft  18  is secured to hand wheel  16  at one end and column universal joint  20  at the other. Column universal joint  20  couples upper steering column shaft  18  to a lower steering column shaft  22 . Lower steering column shaft  22  is secured to column universal joint  20  at one end and a gear housing  24  at the other. Gear housing  24  includes a pinion gear  26  ( FIG. 2 ). Pinion gear  26  of gear housing  24  is positioned to make contact with a matching toothed portion  28  of a rack assembly  30 . Pinion gear  26  has helical teeth that are meshingly engaged with straight-cut teeth of matching toothed portion  28 . 
     The pinion gear, in combination with the straight-cut gear teeth of the rack, form a rack and pinion gear set. The rack  45  is coupled to the vehicle&#39;s steerable wheels with steering linkage in a known manner. 
     Tie rods (only one shown)  32  are secured to rack assembly  30  at one end and knuckles  34  (only one shown) at the other. 
     As a rotational force is applied to steering column  14 , through the manipulation of hand wheel  16  or other applied force, the pinion gear of gear housing  24  is accordingly rotated. The movement of the pinion gear causes the movement of rack assembly  30  in the direction of arrows  36 , which in turn manipulates tie rods  32  and knuckles  34  in order to reposition wheels  36  (only one shown) of the motor vehicle. Accordingly, when the steering wheel  16  is turned, rack  45  and pinion gear  26  convert the rotary motion of the steering wheel  16  into the linear motion of rack  45 . 
     In order to assist the user-applied force to the steering system, an electric motor  38  is energized to provide power assist to the movement of rack  45 , aiding in the steering of the vehicle by the vehicle operator. 
     Electric motor  38  provides a torque force to a motor pulley  40  via motor shaft  42 . The rotation force of motor pulley  40  is transferred to a belt  44 . There are retaining walls  41  on either one of the pulleys  40  and/or ball-screw pulley  62  to help prevent belt  44  from slipping completely off. Alternatively, motor pulley  40  can be configured to have no retaining walls. In yet another alternative, belt  44  is replaced by a chain or gear system or any rotary to rotary drives that provides a rotational force to the screw  64  of the ball-screw mechanism. 
     Accordingly, and as a torque force is applied to the belt  44 , the rotational force is converted into a linear force via the rotary-to-linear actuator (ball-screw assembly  66 ), and rack  45  is moved in one of the directions of arrows  36 . Of course, the direction of movement of rack assembly  30  corresponds to the rotational direction of motor pulley  40 . Belt  44  has an outer surface  46  and an inner engagement surface  48 . The configuration belt  44  and the position of electric motor  38  allows inner engagement surface  48  of belt  44  to wrap around and engage both the motor pulley  40  and ball-screw pulley  62 , that are fixed to the rotary portion of a ball-screw  66  (rotary to linear actuator) mechanism. 
     Electric motor  38  is actuated by a controller  52  that receives inputs from a torque sensor  54  and a rotational position sensor  56 . Sensor  56  provides a steer angle signal to controller  52 . 
     In addition, and as the motor shaft  42  of electric motor  38  turns, the motor shaft position signals of each phase are generated within electric motor  38  and are inputted into controller  52  through a bus  58 . 
     Controller  52  also receives an input in the form of a vehicle speed signal. Accordingly, and in response to the following inputs: vehicle velocity input; operator torque input (sensor  54 ); steering pinion gear angle (sensor  56 ); and motor shaft  42  position signals (bus  58 ), controller  52  determines the desired electric motor&#39;s current phases and provides such currents through a bus  60 . 
     Motor pulley  40  is rotated by motor shaft  42  of electric motor  38 . A second pulley  62  is fixedly secured to the ball-screw  64  screw (or the rotary part of a rotary to linear actuator) of a ball-screw assembly  66 . The ball-screw assembly  66  converts the rotary force of belt  44  into the linear movement of a ball nut  68 . 
     Motor pulley  40  and ball-screw pulley  62  may be constructed out of a lightweight material such as aluminum or composites. This allows the overall mass and inertia of steering system to be reduced in order to improve manufacturing costs and performance, as well as vehicle fuel efficiency. 
       FIGS. 1 and 2  illustrate a power assist steering system that includes a mechanical connection between (rack and pinion) hand wheel  16  and rack assembly  30 . 
     Alternatively, and in applications in which a “steer-by-wire system” is employed, there is no direct mechanical connection between hand wheel  16  and rack assembly  30 . In this application, the driver&#39;s rotational movement of the hand wheel  16  (and /or signal from an equivalent driver control device such as a joystick, pedal(s) and other mechanism for manipulation by the vehicle operator) is input into the controller  52  while electric motor  38  provides the necessary force to manipulate rack assembly  30 . 
     Referring now to  FIGS. 3-14 , a rack-independent actuator  70  is illustrated. In accordance with an exemplary embodiment, rack-independent actuator  70  provides the necessary force to effect the linear movement of a rack  45  coupled to the steerable wheels of a vehicle. Rack-independent actuator  70  performs the functions of rotating the steerable wheels of a vehicle in response to an input such as driver manipulation of a steering wheel. In addition, and while performing this function the rack independent actuator  70  isolates its reduction mechanisms and/or conversion mechanisms necessary to effect the rotation of the steerable wheels from transient and non-axial (to the rack) loads by a pair of universal joints  72  and  74 . 
     Rack-independent actuator  70  is also contemplated for use with a power assist steering system ( FIGS. 1 and 2 ) and/or a “steer-by-wire system” ( FIGS. 16 and 17 ) and/or rear wheel steering and/or four-wheel steering. 
       FIGS. 8 and 9  illustrate universal joints  72  and  74  in an exploded view in order to illustrate the component parts of the same. 
     Universal joint  72  secures a housing  75  to a mounting member  76  of rack assembly  30 . Universal joint  72  contains two sets of hinge pins, or pivots  78  and  80 , the axis of each set being perpendicular to the other. Each set of pins is connected to the other by a central gimbal ring  82 . 
     As an alternative, universal joints  72  and  74  may be replaced by a compliant member that allows similar degrees of freedom for the range of motion necessary to isolate the reduction mechanisms from transient and non-axial (to the rack) loads. For example, gimbal ring  82  is replaced by a rubber ring that is inserted into mounting member  76  while also covering a portion of housing  75 . The rubber ring is compressible and thus capable of providing kinematic freedom. Similarly, gimbal ring  92  may be replaced by a compliant rubber ring. 
     In yet another alternative, rack independent actuator may be constructed with a universal joint and a rubber compliant member. For example, universal joints  72  and a rubber compliant member replacing universal joint  74  or vice versa. 
     In an exemplary embodiment, pins  78  and  80  are pressed at their respective openings in gimbal ring  82 . This allows the rotational movement of gimbal ring  82  while also providing a means for securing the same. Alternatively, pins  78  and  80  slip in openings in housing  75  and mounting member  76 . 
     Alternatively, pins  78  and  80  and their respective openings in gimbal ring  82 , housing  75  and mounting member  76  are configured to provide a movable means of securing the same. 
     Pins  78  movably connect gimbal ring  82  to housing  75 . In an exemplary embodiment, housing  75  is configured to have an elongated cylindrical shape allowing a portion of housing  75  to be inserted within an inner opening of gimbal ring  82 . Thus, pins  78  allow gimbal ring to be movably secured to housing  75 . 
     In addition, pins  80  movably connect gimbal ring  82  to mounting member  76 . Mounting member  76  is fixedly secured to an outer housing  77  of rack assembly  30 . In an exemplary embodiment, mounting member  76  defines an inner opening  88  sufficiently large enough to pass over gimbal ring  82 . 
     Accordingly, gimbal ring  82  is movably secured to housing  75 , and housing  75  is sufficiently long enough to position gimbal ring  82  within opening  88  of securement member  76 , thus gimbal ring  82  connects housing  75  and securement member  76  by pins  78  and  80 . Pins  78  pass through openings  73  in securement member  76  and movably secured gimbal ring  82  to securement member  76 , while pins  80  movably secure gimbal ring  82  to housing  75  by engaging openings  81  in housing  75 . In an exemplary embodiment, pins  78  and  80  are positioned at right angles with respect to each other. Of course, the angular positioning of pins  78  and  80  may vary as long as the intended effect of isolating potions of the rack independent actuator from unwanted loads is achieved. 
     For example, pins  80  prevent a load from being transferred in-between mounting member  76  and gimbal ring  82  in a first direction while pins  78  prevent a load from being transferred in-between housing  75  and gimbal ring  82  in a second direction. The first and second directions being different from each other. 
     As an alternative, and in order to prevent a load from being transferred to gimbal ring  82  and/or gimbal ring  92 , the pins that secure the gimbal rings are covered with plastic and/or rubber to further enhance the isolation of the mechanism from unwanted loads. 
     Rack-independent actuator  70  has an electric motor assembly  90 . Electric motor assembly  90  includes electric motor  38 , rotatable shaft  42 , and motor pulley  40  that is fixedly secured to motor shaft  42 . As pulley  40  is rotated by motor shaft  42 , belt  44  engages with pulley  40  as well as pulley  62 . Since pulley  62  is fixedly secured to screw  64  of the ball-screw mechanism, the rotational movement of pulley  62  causes screw  64  of the ball-screw mechanism to rotate. Accordingly, motor  38 , belt  44 , pulleys  40  and  62  provide a rotary to rotary conversion, which is determined by the dimensions of pulley  40  and  62  with respect to each other (e.g. gear ratio). 
     As an alternative and in accordance with the exemplary embodiments, it is contemplated that other mechanisms and means for rotary to rotary conversion may be employed with the exemplary embodiments. For example, pulleys  40  and  62  and belt  44  can be replaced by a direct mechanical linkage such as a gear train rotary to rotary drive or equivalent thereof. 
     One end of screw  64  of the ball-screw mechanism is mounted for rotation within a plurality of bearings  65  located within housing  75  proximate to pulley  62 . A pre-load nut adjuster or locking nut  67  screws onto the screw  64  of the ball-screw mechanism adjacent to bearings  65 , once in position locking nut is secured to screw  64  of the ball-screw mechanism through the use of a plurality of locking screws  63  which when rotated lock locking nut  67  onto screw  64  of the ball-screw mechanism. Thus, bearings  65  are positioned between locking nut  67  and pulley  62  allowing for the rotational movement of screw  64  of the ball-screw mechanism. The other end of screw  64  of the ball-screw mechanism is rotatably supported by ball-screw nut  68  of ball-screw mechanism  66 . Accordingly, the rotational movement of screw  64  of the ball-screw mechanism by motor  38  is isolated at one end by universal joint  72 . 
     A portion of screw  64  of the ball-screw mechanism passes through ball-screw nut  68 , and the respective surfaces of screw  64  of the ball-screw mechanism and ball-screw nut  68  are configured to effect the linear movement of ball-screw nut  68  as screw  64  of the ball-screw mechanism is rotated. In an exemplary embodiment, a plurality of balls  69  are received within a pair of threaded or grooved surfaces  71  positioned on the inner surface of ball-screw nut  68  and the outer surface of screw  64  of the ball-screw mechanism. The interface of screw  64  of the ball-screw mechanism and ball-screw nut  68  of ball-screw mechanism  66  are constructed in a known manner. 
     Accordingly, and as screw  64  of the ball-screw mechanism is rotated by the rotational movement of pulley  62  by motor  38 , the rotational movement of screw  64  of the ball-screw mechanism is converted into linear movement of ball-screw nut  68 . It is here that rotary to linear conversion occurs. As an alternative, other means for rotary to linear conversion are contemplated for use with the exemplary embodiments. 
     The interface between ball-screw nut  68  and rack  45  is isolated by universal joint  74 . Ball-screw nut  68  is secured to a gimbal ring  92  of universal joint  74 . Similarly to universal joint  72 , universal joint  74  contains two sets of hinge pins or pivots  94  and  96 , the axis of each set being perpendicular to the other. Each set of pins is connected to the other by central gimbal ring  92 . 
     In an exemplary embodiment, pins  94  and  96  are pressed in their respective openings in gimbal ring  92 . This allows the rotational movement of gimbal ring  92  while also providing a means for securing the same. 
     Alternatively, pins  94  and  96  and their respective openings in gimbal ring  92 , ball-screw nut  68  and housing member  100  are configured to provide a movable means of securing the same. 
     Pins  94  movably connect gimbal ring  92  to ball-screw nut  68  allowing for movement in a first direction. In an exemplary embodiment, gimbal ring  92  is configured to have a cylindrical shape slightly larger than ball-screw nut  68 , allowing a portion of ball-screw nut  68  to be inserted within gimbal ring  92 . Pins  94  are received within a pair of pin openings  98  in the ball-screw nut  68 . It is noted that universal joint  74  and ball-screw nut  68  are shown in  FIGS. 8 and 9  in an exploded manner so as to illustrate the attachment of universal joints  72  and  74 . 
     Pins  96  movably connect gimbal ring  92  to a housing member  100  allowing for movement in second direction, the second directional plane being orthogonal to the first directional plane. Pins  96  pass through a pair of apertures  102  in housing  100 , thus movably connecting gimbal ring  92  to housing  100 . 
     The gimbal mechanisms or in particular universal joints  72  and  74  provide the necessary kinematic degrees of freedom to prevent non-axial loads and for turning or bending moments on the ball-screw nut or screw, such as those that would result from misalignment of the shafts, from producing undesirable friction and the resultant loss of efficiency on the rotary to linear motion conversion mechanism. 
     In so doing, the torque output and power consumption requirements of the mechanism used to turn the ball-screw such as the electric motor is reduced. This allows the electric motor to be reduced in size as well as the components of the rotary to linear actuator. This is particularly useful for applications such as vehicular electric steering actuators, where the dynamic loads experienced by the vehicle and the requirements placed on the mechanism can significantly impact the motor and actuator mechanism requirements. The reduction in power consumption of the motor and the weight reductions associated with a smaller electric motor and mechanism represent desirable to design parameters. 
     Referring now in particular to  FIG. 4 , housing  100  is fixedly secured to rack  45  through a plurality of bolts  104  which pass through complementary bolt openings  106  in rack  45  and housing  100 . Accordingly, and as a rotational force is applied to screw  64  of the ball-screw mechanism, ball-screw assembly  66  converts the rotary movement of screw  64  of the ball-screw mechanism into the linear movement of ball-screw nut  68 . Ball-screw nut  68  is connected to rack  45  through a universal joint  74 , which is connected to ball-screw nut  68  at one end and housing  100  at the other. Housing  100  is fixedly secured to rack  45  and accordingly, as ball-screw nut  68  moves in the direction indicated by arrows  36 , a similar movement of rack  45  is produced. 
     Housing member  100  is configured to have a mounting portion  101  that is configured to be received within opening  108 . Mounting portion  101  is configured to be slidably received within opening  108  and contains the apertures into which bolts  104  are received. 
     Universal joints  72  and  74  isolate electric motor assembly  90  and ball-screw pulley  62  from transient non-axial loads, which may damage or misalign pulleys  40  and  62 . Moreover, universal joints  72  and  74  isolate the system from undesirable loads or stack buildup that may be the result of misalignment of a component part such as rack  45 , ball-screw  64  and/or any other component part that may produce an undesirable load or stack buildup. 
     The rack-independent actuator also allows the two pulleys on the belt and pulley mechanism to be mounted to the same housing and to eliminate all force components that could alter their parallelism. 
     Moreover, the rack-independent actuator of an exemplary embodiment no longer requires the motor shaft of motor  38  or the screw  64  of the ball-screw mechanism to be parallel to rack  45 , as motor assembly  90  and screw  64  of the ball-screw mechanism are isolated from rack  45  through the use of universal joints  72  and  74 . Thus, any misalignment of screw  64  of the ball-screw mechanism with regard to rack  45  is accommodated for by universal joints  72  and  74 . Accordingly, motor shaft  42  need only be parallel to screw  64  of the ball-screw mechanism, or alternatively, pulleys  40  and  62  need only be parallel to each other. Accordingly, and since they are mounted to the same housing, this is easily achieved and maintained. Moreover, any loads that may cause misalignment are isolated from the motor assembly through the use of universal joints  72  and  74 . 
     Also, pulleys  40  and  62  may be configured with or without retaining walls because, as stated above, belt  44  is isolated from transient forces, thus reducing belt/pulley production costs, since the belt and pulley system does not have to be designed to withstand large forces. 
     Referring back now to  FIGS. 4 ,  8 ,  9  and  11 - 14 , outer housing  77  of rack assembly  30  is configured to have an elongated opening  108 . In order to prevent the rotational motion of the rack  45 , an anti-rotation device  110  is secured to rack  45  ( FIG. 4 ) that moves within the confinement of the elongated opening  108 . 
     In an exemplary embodiment, anti-rotation device  110  is a plug  112  fixedly secured within an opening  114  of rack  45 . Plug  112  has an upper member depending outwardly from rack  45 , and is sized and configured to pass along in elongated opening  108 . In addition, and in order to reduce any frictional buildup between plug  112  and the elongated opening  108 , a plurality of bearings  116  are positioned around the periphery of anti-rotation device  110 . Accordingly, anti-rotation device  110  prevents rotational movement of rack  45  while allowing linear movement of the same. 
     Rack assembly  30  is also configured to have a pair of mounting members  118 . Mounting members  118  are configured to secure rack-independent actuator  70  to a vehicle frame (not shown). 
     In addition, and referring now to  FIG. 4 , housing  77  of rack assembly  30  has a pair of apertures  120 . Apertures  120  are positioned to allow a tool such as a screwdriver or other type of tool to be inserted into openings  120  in order to facilitate the securement of bolts  104  to housing  100  and rack  45 . 
     The steering system is equipped with several sensors that relay information to the electric motor  38  by way of a controller  52  ( FIG. 1 ). Controller  52  will track the position and force upon rack  45  at all times by means of a pair of force sensors  122 . Force sensors  122  provide input into controller  52  corresponding to the amount of force included at the ends of rack  45 . 
     A pair of absolute position sensors  124  and a high-resolution sensor  126  also provide input into controller  52  in the form of a rack position location. For example, an on-center position sensor may comprise Hall-Effect devices, which are mounted within rack-independent actuator  70 . It may be understood that the sensors and controller  52  comprise a calibration means for maintaining the values of the steering position signals that correspond with the actual steering positions. 
     Rack  45  has a center position in which the steerable wheels of a vehicle are directed straight ahead relative to the vehicle. In an exemplary embodiment, rack-independent actuator  70  will provide a return torque that assists in returning the steering system to a center position. 
     In this system, the return torque is generated by electric motor  38 , and a return torque component of the total desired torque signal is generated in controller  52  based upon the input received from sensors  122 ,  124 , and  126 . Thus, an accurate signal of the steering position is derived from absolute position sensor  124 . 
     In order to express the full range of steering angles as the output of absolute position sensor changes, the apparatus utilizes an algorithm in controller  52 . The algorithm may be embodied in a programmed digital computer or a custom digital processor (not shown). 
     Referring now to  FIG. 15 , a block diagram illustrates the use of the universal joints and the unit interaction between various components of the rack-independent actuator system. 
     Block  130  represents the electric motor. Block  130  interfaces with block  132  that represents the rotary-to-rotary assembly of the rack-independent actuator system. Block  130  also interfaces with the housing of the ball-screw indicated at block  134 . Block  132  interfaces with a block  136  that represents a rotary-to-linear assembly. Block  136  interfaces with a block  138  that represents the bearings of the ball-screw, and block  138  interfaces with the ball-screw housing. Block  140  represents a high-resolution sensor that interfaces with the housing (block  134 ) and the rotary to linear assembly (block  136 ). 
     Block  142  represents an interface between the rotary-to-linear assembly and the housing of the rack assembly. 
     Block  144  represents the housing of the rack assembly. Block  146  represents an absolute position sensor that interfaces with box  136  and box  144 . Block  148  represents a tie rod and force sensor that interfaces with the housing of the rack assembly (block  144 ). 
     Block  150  represents the interface between housing  134  and the rack housing  144 . It is here at block  150  in which universal joint  72  or stationary universal joint  72  is inserted to isolate the motor and belt and pulley assembly from the housing of the rack assembly. 
     Block  142  represents the interface between the rotary-to-linear assembly housing and the rack assembly. It is here at block  142  in which universal joint  74  or mobile universal joint  74  is inserted to isolate the movement of the rack assembly from the ball-screw nut of the ball-screw assembly. 
     This system accomplishes compensation through a series of sensors that provide feedback to several components. For instance, the rotary-to-linear assembly at block  136  receives inputs from the absolute position sensors at block  146 . In this embodiment, the absolute position sensors are mounted to the ball-screw assembly. The absolute position sensor at block  146  provides steer angle signals that are sent to the controller. 
     While exemplary embodiments have been described with reference to a steering system for a vehicle, the rotary-to-linear mechanism is not intended to be limited to such applications. It is contemplated that in accordance with the exemplary embodiments, a rotary-to-linear conversion mechanism utilizing a pair of universal joints for isolating the mechanism from misalignment and/or uneven loading can be applied to any application. 
     In related embodiments, this system is related to the power assist section, with the output being a linear motion, of any kind of steering application. The power assist mechanism may be powered via a rotary type electric motor with potentially additional speed reducers, such as belt and pulley, gearbox, harmonic drive, etc., for torque multiplication, and the linear output is achieved by moving a shaft or linear section, such as a rack, along its axis. Between the power section and the linear output there may be a rotary-to-linear actuator (such as ballscrew, screw, ACME screw, rolling ring, etc.). It should be understood that other types of appropriate speed reducers, shafts, and rotary-to-linear actuators not specifically described herein are also within the scope of this system. 
     As shown in  FIG. 18 , a mechanism  210  may include an interface B  212  that may connect the power section plus rotary-to-linear actuator  214  to the linear section (e.g., rack)  216  such that the individual subcomponents constraints are all met. Thus, in a design phase of the mechanism  210 , optimization of the mechanism  210  (in efficiency, size and durability) may be possible in the subcomponent level using the technology. This may save time and have cost reductions in a manufacturing process, as the technology risk is minimized. For simplicity, the interface  212  may be provided between the rotary-to-linear actuator  214  and the linear section (e.g. rack)  216 , as shown in  FIG. 18 . 
     It should be noted that while a rack is specifically described with respect to this system, the mechanisms and systems described herein may be incorporated into any rack based or drag link based system wherein the ground may be the chassis, components that do not move, a suspension system, or any other suitable components. 
     A characteristic of the interface B  212  described above may be to eliminate side loads (perpendicular to the axial direction of the linear movement) and moments, which may be produced by geometric or dynamic means through external forces  218 . Such conditions, if not avoided, may lead to undesirable friction increase. 
     In one embodiment of the mechanism  210 , a ballscrew  220  may be used as the rotary-to-linear actuator  214  and the linear section  216  may be a rack. In this example, the ballscrew-screw  222  may rotate about the axis  226  and the ballscrew-nut  224  may translate along the axis  226 , as shown in  FIG. 18 . The nominal angle  228  between the two axes  226  and  230  is selected to be zero degrees, which would lead to the ball screw  222  and the rack  216  being parallel. In actual applications, however, perfectly parallel axes may be difficult to maintain, and therefore the axes  226 ,  230  become skewed, as shown in an exaggerated skew, in  FIG. 18 . In actuality, the skew is preferably not more than one or so degrees. Furthermore, in other embodiments, deviation from perfect conditions are still within the scope of the embodiments. Special cases of the general form of the actuator shown in  FIG. 18  may be created such as if the two mentioned axes  226 ,  230  are parallel, the two mentioned axes  226 ,  230  are collinear, or if side load effects (such as deflection of rack etc.) are negligible, or if the load could be acting in only one side of the rack  216 , or in various combinations of the above situations. It should also be noted that the load may also act on the ballscrew-nut  224  or the ball screw-screw  222 . 
     In determining a properly constrained system (mechanism), the boundary conditions may be set as follows: the ballscrew-screw  222  may turn about the axis  226  (the A interface  232 ) but may not displace (thus, a revolute joint); the rack  216  may travel along the axis  230  and may rotate about the axis  230  (thus, a cylindrical joint, even though there are two cylindrical joints between the rack  216  and ground, it may be counted as one); and, the ballscrew-nut  224  may travel a lead length along the axis  226  as long as when the ballscrew-screw  222  makes one revolution the nut  224  does not rotate (with respect to axis  226 ). It should be understood that the basic kinematics of constrained rigid bodies includes many different types of pairs in spatial mechanisms, including spherical pairs, plane pairs, cylindrical airs, revolute pairs, prismatic pairs, and screw pairs, where each pair may define a joint within a mechanical system. A cylindrical pair, or joint, keeps two axes of two rigid bodies aligned, where the bodies will have an independent translational motion along the axis and a relative rotary motion around the axis. Therefore, a cylindrical pair removes four degrees of freedom from spatial mechanism, and the DOF=2. A revolute pair, or joint, keeps the axes of two rigid bodies together, where the bodies have an independent rotary motion around their common axis. Therefore, a revolute pair removes five degrees of freedom in spatial mechanism, and the DOF=1. 
     Interface B  212 , shown in  FIG. 18  between the ballscrew-nut  224  and the rack  216 , may be used to constrain the ballscrew-nut  224  properly (as described in the third boundary condition described above). There are issues that need to be considered before an appropriate linkage is designed. It should be understood that an ideal joint has nothing but the number of degrees of freedom that it should have, however, unless the joint is preloaded, a joint is always non-ideal since lash will add more degrees of freedom. First, the tolerance of parts may force for non-ideal joints and linkages, and, second, the loads may result in component deformation. As a result of these conditions, it may be assumed that the components are imperfect and that there will be positional errors at any given instant but the imperfections are expected to be small relative to the displacements and size of the components. Thus, for all practical purposes the two axes  226 ,  230  may be assumed to be slightly skew from this point on and that the side loads on the rack  216  exist. Then, there may be a series of mechanisms that may be correct based on kinematics (degree of freedom allows for one input) as well as dynamics. For a properly constrained system, the interface B  212  may have three rotational degrees of freedom, while the system as a whole has one degree of freedom. In prior art systems, to compensate for the irregularities between the axes  226 ,  230 , the quick fix has usually been to provide rubber within a connection that under-constrains the system by providing too many degrees of freedom. Thus, the prior art mechanisms and systems are usually under-constrained, that is, are provided with too many degrees of freedom and therefore not consistent in dynamic performance. 
     Turning now to  FIG. 19 , the ballscrew nut  224  is shown being loaded, through load  302 , collinear to the ballscrew axis  226  at one side  304 , which is a special case mechanism  300 . However, even if load  302  is not perfectly collinear, the mechanism may still be within the scope of these embodiments. Thus, it may be possible to deviate the load  302  from the axis  226  a couple or so degrees. Combination joint  306  represents a revolute joint  272  at the rack cylindrical joint  244 , which is possible via deflecting the joint. A calculation of the degrees of freedom “d.o.f.” is shown to equal one for the whole system, and therefore mechanism  300  is properly constrained. The d.o.f. may be calculated using the following equation: 
     d.o.f.=λ(L−J−1)+Σf i , wherein λ is the degree of the space, wherein 6 degrees in the space means the system is operating in 3-dimensional space, L is the number of links in the system, J is number of joints in the system, and f i  is the degree of freedom for each individual joint (for example, f i =1 for revolute and slider joints, f i =2 for cylindrical joints, f i =3 for balljoints, etc. 
     For the  FIG. 19  embodiment, the d.o.f. calculation is as follows:
 
 d.o.f .=λ( L−J− 1)+Σ f   i =1
         λ=6   L=5   J=5   Σf i =2 revolute+2 cylindrical+1 ball screw=2(1)+2(2)+(1)=7       

     For a d.o.f. calculation for the mechanism  300  of  FIG. 19 , it is noted that the 5 th  link is the 5 th  joint. That is, the fifth link in the actuator is the bushing that forms the cylindrical joint  244 . Thus,  FIG. 19  shows the collinear representation of the ballscrew  222  and nut  224  and the force. The load previously acting at the end of the rack  216  (as in  FIG. 18 ) is now a load  302  acting on the ballscrew nut  224 . The cylindrical joint  245  at the end of the ballscrew nut  224  is for dynamic loading concerns and kinematically not required, therefore that particular cylindrical joint  245  need not be included in the d.o.f. calculations. The cylindrical joint  245  at the end of the ballscrew nut  224  is a redundant cylindrical joint  245  which should be collinear to the ballscrew axis  226 . 
       FIG. 20  shows a cross-sectional view of an implementation of the mechanism  300  in an actuator  310 . The “ground” or housing  312  is shown about the mechanism  300 .  FIG. 21  shows an additional cross-sectional view similar to  FIG. 20 , and revealing the ballscrew screw  222  within the revolute joint  272 .  FIGS. 22-24  show additional interior and exterior views of the mechanism  300  as housed within the special case actuator. 
       FIG. 25  shows another embodiment of an interface between a movable linear section (e.g. rack  216 ) and a rotary to linear actuator (e.g., ballscrew screw  222  and ballscrew nut  424 ). This embodiment employs a mechanism  420  that includes a “block on a plane” joint. A block on a plane joint has three degrees of freedom. A block may not separate from the plane to be considered a true block on a plane joint, and therefore it may not “rock” relative to the plane. It may, however, slide relative to the plane and spin. The block on a plane joint is used in this mechanism  420  by employing a ball nut  424  that has an angled face  440  for sliding relative to a plane  436  that is connected to the rack  216  such as through connector  442 . Plane  436  thus moves with the rack  216 . Side loads  426  and  428  are shown acting on rack  216 , which come from external forces such as from a wheel, suspension system, etc. The angle φ is similar to the angle  228  in  FIG. 18 , and represents an angle between the ballscrew screw axis  226  and the rack axis  230 . 
     The angle between the ballscrew screw axis  226  and the plane  436 , angle β  430 , will determine side load to the ballscrew screw  222 . The block on a plane joint as used in this embodiment can center forces between the ballscrew screw  222  and the ballscrew nut  424  about a center of the ballscrew nut  424 , without the need for fine adjustments. That is, as will be further explained below, the rack  216  and the ballscrew nut  424  are constrained from rotation about their axes, however, due to inevitable imperfections there may be slight rotation of these elements. The slight rotation actually serves to self-correct the interface by centering the forces between the ballscrew screw  222  and the ballscrew nut  424  about a center of the ballscrew nut  424 . This self-correcting action eliminates the need for tedious, time-consuming fine adjustments between the elements during assembly. 
     If the angle β  430  between the ballscrew screw axis  226  and the plane  436  is 90 degrees, then a separate anti-rotation for the ballscrew nut  424 , to prevent the ballscrew nut  424  from rotating, would be needed. Although the side load to the ballscrew screw  222  would be removed, the ballscrew nut  424  would require an anti-rotation device. As can well be imagined, it β  430  was 90 degrees, then the ballscrew nut  424  would rotate relative to the plane  436 , and therefore the rack  216  would not move with the ballscrew nut  424 . Thus, such an angle for β  430  is not desirable. If the angle β  430  is 0 degrees, then the plane  436  would be parallel to the ballscrew screw axis  226 , and the rack  216  will again not move when the ballscrew nut  424  moves. The larger the deviation of the angle β  430  from 90 degrees, the larger the side load will be on the ballscrew mechanism. It has been found that arranging the ballscrew screw  222  to have an angle β  430  less than 90 degrees, but greater than 81 degrees, works well with the mechanism  420 . Manufacturers often specify that the sideloads to the ballscrew mechanism be less than 10% of the axial load it carries. Thus, since 10% of 90 degrees is 9 degrees, an appropriate angle for β  430  would be 81&lt;β90. The closer to 90 degrees β  430  is, the closer the ballscrew nut  424  is to rotating, and the further from 90 degrees β  430  is, the greater the side load is on the ballscrew mechanism. Thus, a compromise between possible rotation of the ballscrew nut  424  and side loads to the ballscrew mechanism may be reached by selecting an angle of β  430  between 81 and 90 degrees. It should be understood that although 81 degrees is specified, in some instances, if greater side loads than 10% of an axial load that a ballscrew mechanism carries are acceptable, then β  430  may be less than 81 degrees. 
     For the  FIG. 25  embodiment, the actuator or mechanism  420  as a whole has only one degree of freedom, where the d.o.f. calculation is as follows:
 
 d.o.f .=λ( L−J− 1)+ρ f   i =1
         λ=6   L=4   J=4   Σ f l =1 revolute joint+1 cylindrical joint+1 ballscrew screw+1 block on plane=1(1)+1(2)+1(1)+1(3)=7       

       FIG. 26  shows an exterior view of the actuator housing for the mechanism  420  described herein for providing a properly constrained interface. The tie rods  422 , motor  332 , and the housing (ground)  312  are shown. 
       FIG. 27  shows a partial cross-sectional view of the mechanism  420 , revealing the rack  216 , the ballscrew screw  222 , an the ballscrew nut  424  and bolts  438  which may be employed to hold the plane  436  relative to the ballscrew nut  424 .  FIG. 28  is another partial cross-sectional view of the mechanism  420 , similar to  FIG. 27 , but additionally exposing a cross-section of the revolute joint  272 , and displaying the rack  216  and ballscrew screw  222  within the ballscrew nut  424 .  FIG. 29  is another partial cross-sectional view of the mechanism  420 , similar to  FIGS. 27 and 28 , but additionally showing the plane  436  that the ballscrew nut  424  may abut against, and the angled face  440  of the ballscrew nut  424 .  FIG. 30  shows an enlarged view of the relevant area where the angled face  440  of the ballscrew nut  424  engages the plane  436 . 
     It should be understood that there are alternative constructions of a block on a plane, using a ballscrew nut  424  as the block, not disclosed herein that would also be within the scope of the mechanism  420 . For exemplary purposes only, the ballscrew nut  424  is shown as abutting spacer element  434  which may include bearings (balls)  444  and the plane  436  may include bearing surfaces  446  for engaging with the bearings  444 . The bearing surfaces  446  may comprise a washer that is placed against the plane  436  for providing a hardened surface upon which the bearings  444  can ride. It should be understood that the face  440  of the ballscrew nut  424  may additionally include a bearing surface such as a washer for providing a hardened surface upon which the bearings  444  can ride. The spacer element  434  may be a physical element that holds the bearings  444  such as for proper spacing during assembly, or may simply be a space between the face  440  (or bearing surface/washer on face  440 ) and the bearing surfaces  446 . Also by example only, the plane  436  may be embodied within an angled plate-like extension that extends from a connector  442  that connects the angled plate-like extension, plane  436 , to the rack  216 , as clearly shown in  FIG. 31 . The plane  436  may be rigidly connected to the rack  216  such that the longitudinal motion of the rack  216  along its longitudinal axis  230  is translated to motion of the plane  436 , in an equivalent direction. Except due to imperfections, the rack  216  and the ballscrew nut  424  do not rotate about their axes. The plane  436  may be held in place relative to the rack  216  using bolts  438 , which are further employed to maintain the ball nut  424  in place relative to the plane  436 . It should be understood that, in a block on a plane joint, the block may not depart from the plane, and thus is may not rock relative to the plane. Thus, in the mechanism  420 , the ballscrew nut  424  is clamped to the plane  436  using bolts  438 , and held thereto with nuts  450 , where the nuts  450  are threaded onto the shafts of the bolts  438 . The bolt heads  452  connect with the shafts of the bolts  438  and provide a means for tightening the bolts  438  and nuts  450 . The shafts of the bolts  438  may travel through a flange  454  of the ballscrew nut  424  so as not to interfere with the ballscrew nut  424 /ballscrew screw  222  operation. One side of the flange  454  has been described as angled face  440 . The other side of flange  454  is face  456  which may be provided with a bearing surface, such as a washer,  458 , for engaging with bearings  444  that abut a second plane  460 . The second plane  460  may have an angled face that is parallel with the angled faces of the first plane  436  and angled face  440 . The planes  436  and  460  may be apertured, that is, have an opening, to allow passage of the ballscrew screw  222  therethrough. The opening of the plane  460  may be larger than the opening of the plane  436 , since the opening of the plane  460  may also be large enough to allow the passage of the ballscrew nut  424  therethrough. Thus, it should be understood that the ballscrew nut  424  is effectively “sandwiched” in between two plates (planes  436  and  460 ) via bearings  444  and bearing surfaces. This sandwiching ensures that movement of the ballscrew nut  424  will translate to movement of the rack  216 , and movement of the rack  216  will translate to movement of the ballscrew nut  424 . That is, there is a lash free motion between the ballscrew nut  424  and the rack  216 . When the motor  332  operates to rotate the ballscrew screw  222 , the rotation of the ballscrew screw  222  translates into longitudinal movement of the ballscrew nut  424 . Depending on the direction of rotation of the ballscrew screw  222 , the ballscrew nut  424  will either push against the plane  436  or the plane  460 . Because the ballscrew nut  424  and planes  436 ,  460  are all clamped together, movement against either plane will cause a corresponding movement to the rack  216  via the connector  442 . 
     As shown in  FIG. 31 , it should further be understood that a similar “reversed” angle may be accomplished by angling the plane  436  away from the ball nut as it extends away from the rack  216 , and having the face  440  angled to complement the plane  436 . The elements utilized in such an embodiment would otherwise be the same.  FIG. 32  shows another cross-sectional view of a potential configuration for the mechanism  420 . 
     The previously described mechanisms and configurations may be achieved through deflecting components or joints appropriately along the particular direction or twisting about an appropriate axis. The next generation mechanization may eliminate the joints at interface B  212  in  FIG. 18  and fill the interface B  212  with a flexible component that is attached in a fixed manner to both the rack  216  and to the ballscrew-nut  224 . Thus, for such a mechanism, gaps between components (or joints as there are none), thus noise and vibration, the nonlinearity (in controls) and number of components (reliability and assembly) may be reduced. 
     Turning to  FIGS. 33-35 , examples of mechanisms that use a flexible component may provide a compliant member adjacent the ballscrew nut as shown. That is, interface B  212  shown in  FIG. 18  is replaced by a flexible member, such as rubber or deflectable strips. To prevent under constrainment, a coupler as will be described may be used. 
     Enough degrees of freedom are achieved with the following mechanisms for approximately matching kinematics. Turning now to  FIG. 33 , one exemplary coupler  340  is shown which is suitable for use as the coupler  334  within an actuator as previously described. The coupler  340  houses the compliant member  324  at interface B  212  in  FIG. 18 . The coupler  340  may include a first longitudinal opening  342  corresponding to the rack axis  230  and a second longitudinal opening  344  corresponding to the ballscrew axis  226 . Although the coupler  340  may have one unitary body  346 , the body  346  may include a first body portion  348  for surrounding the rack  216  and a second body portion  350  for surrounding the ballscrew nut  224 . The unitary body  346  may be formed from a single, unjointed piece of material. A connecting portion  352  may be provided between the first body portion  348  and the second body portion  350  for appropriately spacing the coupler  340  about the rack  216  and the ballscrew nut  224 . The second body portion  350  may further include a compliant member  324  positioned within the second longitudinal opening  344 . 
     Turning now to  FIG. 34 , another exemplary coupler  360  is shown. The coupler  360  may include a first longitudinal opening  362  corresponding to the rack axis  230  and a second longitudinal opening (hidden from view) corresponding to the ballscrew axis  226 . Although the coupler  360  may have one unitary body  366 , the body  366  may include a first body portion  368  for surrounding the rack  216  and a second body portion  370  for surrounding the ballscrew nut  224 . The unitary body  366  may be formed from a single, unjointed piece of material. The second body portion  370  may include a first end  372  having a U-shaped member  374 , and a second end  376  having a ring shaped member  378 . The ring shaped member  378  and the U-shaped member  374  may be connected by strips  376  which extend parallel to the longitudinal axis  226 . The ballscrew nut  224  may include a cylindrical shaped portion  380  nestled between the strips  376  and a ring shaped portion  384  abutting the ring shaped member  378 . The strips  376  may pass through slots  382  in the ring shaped portion  384  of the ballscrew nut  224 . The first body portion  368  and the second body portion  370  may be connected by a connecting portion  386 . In the coupler  360 , compliance may be achieved through deflecting material of the strips  376 . The compliance is met in three (up-down, side to side, and twisting) directions while maintaining axial rigidity. Thus, this embodiment achieves compliance without using rubber and without using a jointed interface for the interface B  212 . 
     Turning now to  FIG. 35 , another exemplary coupler  390  is shown. The coupler  390  may include a first longitudinal opening  392  corresponding to the rack axis  230  and a second longitudinal opening  394  corresponding to the ballscrew axis  226 . Although the coupler  390  may have one unitary body  396 , the body  396  may include a first body portion  398  for surrounding the rack  216  and a second body portion  400  for surrounding the ballscrew nut  224 . The unitary body  396  may be formed from a single, unjointed piece of material. The second body portion  400  may include a first end  402  and a second end  404 . Each end may include a main circular portion  406  with four smaller circular portions  408  evenly spaced about the outer periphery of the main circular portion  406 . Also for each end, a first C shaped portion  410  may surround an upper pair of circular portions  408  and a second C shaped portion  412  may surround a lower pair of circular portions  408 . A first connecting strip  414  may connect the first C shaped portion  410  on the first end  402  to the first C shaped portion  410  on the second end  404 . A second connecting strip  416  may connect the second C shaped portion  412  on the first end  402  to the second C shaped portion  412  on the second end  404 . The ballscrew nut  224  may be positioned between the main circular portions  406  and within the first and second connecting strips  414 ,  416 . Compliance in the coupler  390  may be achieved through deflecting material, such as in C-shaped portions  410 , and first and second connecting strips  414 ,  416 . Thus, compliance is met in three directions while maintaining axial rigidity. 
     Thus, in the above described couplers shown in  FIGS. 33-35 , only three degrees of freedom are allowed for the interface (coupler) giving the mechanism utilizing such a coupler a total of one degree of freedom, as in the prior embodiments, and thus such mechanisms are correctly constrained. 
     It should be understood that the interfaces described with respect to the above embodiments, whether they be joints, joint combinations, linkages, and/or couplers, will most likely be non-ideal interfaces. Although ideal interfaces are preferred, such perfection is sometimes unrealistic. In any interface, the most degrees of freedom that it could have is six. In the embodiments described herein, the interfaces have been constrained to only have three degrees of freedom. The other degrees of freedom that have been eliminated may actually exist, even if only to a very small degree. Thus, it should be understood that if movement of a joint is enabled past a tolerance for that degree of freedom, then it may be counted as a degree of freedom. The tolerance may be different depending on the type of movement for the degree of freedom and depending on the particular mechanism. For example only, if a tolerance of movement in one direction is 0.75 mm, and if movement of a joint in one direction is limited to no more than 0.5 mm, then the joint may be seen as constrained in that direction, and therefore that movement would not qualify as a degree of freedom. If, however, that same joint is movable in that direction more than 0.75 mm, then it would be considered to have a degree of freedom in that direction. In another example, if the tolerance of twisting in one direction is one degree, then any joint that twists for less than one degree would be considered constrained in that direction. In most cases, movement of a joint in a constrained direction, such as movement due to lash, is so negligible that the joint is easily recognizable as constrained in that direction, and therefore not a degree of freedom, and a joint having a degree of freedom in a particular direction is so obviously movable in that direction that it is easily recognizable as having a degree of freedom in that direction. 
     While the embodiments have been described with reference to exemplary embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the embodiments. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the embodiments without departing from the essential scope thereof. Therefore, it is intended that the embodiments not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out these embodiments, but that the embodiments will include all embodiments falling within the scope of the appended claims. Moreover, the use of the terms first, second, etc. do not denote any order or importance, but rather the terms first, second, etc. are used to distinguish one element from another.