Abstract:
A golf training and simulation device measures a signal indicative of the displacement of a club and in an alternate embodiment, the detection of a golf ball after being struck. The measurement system can be used in conjunction with a golf simulator or as a golf training apparatus for diagnosing a golf swing. In one application, a putting stroke training device is described with the object to develop a smooth, consistent putting stroke by feedback to the golfer when the putter head has accelerated or decelerated too rapidly or when the golfer opens or closes the club face when striking a golf ball. Positive feedback can also be provided when the putting stroke is square at impact with the ball. The consistency in the repetition of a stroke may also be measured, statistically analyzed, recorded and displayed and thus used in advanced training.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application claims the benefit of the filing date of U.S. Provisional Patent Application Ser. No. 60/742,158, filed 2 Dec. 2005. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     Not applicable. 
     REFERENCE TO A MICROFICHE APPENDIX 
     Not applicable. 
     TECHNICAL FIELD 
     The present invention generally relates to an apparatus and means for processing a signal indicative of the moving state of a club head and golf ball and more particularly to an electronic golf trainer or golf simulation device. 
     BACKGROUND INFORMATION AND DISCUSSION OF RELATED ART 
     It is well known in prior art that the club orientation and acceleration up to golf ball impact, are critical parameters in determining an effective and repeatable stroke for any shot in golf. This is also known to be most problematic in putting, where the stroke pendulum is varied in response to the required putting distance, state of the greens, topography and the possible grain of the putting surface. A golfer assesses the conditions and required ball length to be traversed, and alters the length and perhaps speed of the putting stroke. 
     Deceleration during the downswing prior to contact with the ball is a particularly problematic condition known as the yips and is associated with an erratic stroke. More specifically, it is known that (1) Accelerating too quickly on the backstroke, during the transition stroke between the backstroke and the forward stroke, or during the forward stroke; and (2) Decelerating during the transition stroke or during the forward stroke are to be avoided. 
     At the time of ball contact, the club face should be perpendicular to the path of the putter head and the club face should strike the ball such that the club center of mass (or sweet spot) is aligned with the center of the ball. 
     In contrast to putting strokes, iron and wood shots are full shots, where a complete swing is used, and ball carry is primarily determined by the loft of the club and the momentum imparted to the ball from the club impact. In this case, the timing of the pendulum back-swing and downswing in relation to weight-shift are important in determining a repeatable stroke, but the length of the backswing and carry through should remain constant. In order to have a long carry with greater accuracy, the golf ball should be struck within a zone known as the sweet spot of the club and the swing should be such that the club face is aligned perpendicular to the golf ball at time of impact. Since both the arms and the wrists rotate during the downswing it takes precise timing of the swing to achieve club head alignment at impact. In such swings, the face of the club also can move at 30 m/s, making the observation and correction of the swing orbit and head position impossible to achieve by eye. 
     There are a number of golf swing practice devices which attempt to determine the face angle of a golf club head at the time of ball impact. For example, U.S. Pat. No. 4,615,526 uses a special club and magnetic sensors to measure club head velocity, and calculate face angle and ball carry using at least two or three discrete point sensors to sample the trajectory of the club. The relative timing between the sensor outputs are used together with dimensional knowledge of the distance between points to calculate swing parameters. U.S. Pat. No. 5,474,298 and U.S. Pat. No. 5,935,014 describe a golf swing apparatus that uses a number of coil loops in a planar detector mounted below the ball position and one or two magnets mounted in a spaced recess within the club. U.S. Pat. No. 5,435,561 describes a modified club that contains an inertial sensor device. These approaches have a severe shortcoming in that the sensors and technique requires the use of a special golf club or a golf club with special attachments, thus preventing the golfer from using his or her own clubs. 
     An alternate approach is to use optical sensors as described in U.S. Pat. No. 4,306,703, U.S. Pat. No. 5,614,823, U.S. Pat. No. 5,718,639, U.S. Pat. No. 5,976,022 and U.S. Pat. No. 6,375,579 B1. These and similar techniques are generally complex in construction and therefore expensive to manufacture or they utilize methods for detecting face angle which are not sufficiently accurate. 
     There are also a number of putting stroke training devices, for example U.S. Pat. Nos. 5,441,269 and 5,792,001 describe a putter club with orthogonal accelerometers that either contained within or mounted on the club and a system designed to train golfers. U.S. Pat. No. 5,435,561 describes the use of inertial sensors and an audio alarm to prevent rotation during a putt. A visual impact teaching system is described in U.S. Pat. No. 6,248,021 B1 uses an LED display matrix and pressure sensor on the face of the putter to display the ball impact point after a stroke. U.S. Pat. No. 4,180,270 describes a system for simulating a putting stroke using mechanically retractable pivot switch sensors, measuring the timing of these switches and relating them to swing training or the simulation of the path of an imaginary ball from a stroke. Some of the examples in the prior art describe methods determining where the ball strikes a putter, the alignment of the putter, aspects of the trajectory of the putter and feedback to the user. However, they are also either too complex in construction, or require the use of a special golf putter or putter with special attachments, thus preventing the golfer from readily using his or her own putter. 
     Golf simulators have become an important part of golf training and recreation. Various computer systems have been developed with advanced graphics to create a virtual golf environment. The most realistic systems make use of an actual golf ball, which is hit using conventional golf clubs in a netted booth. The trajectory of the ball is calculated using sensor technology which usually comprises complex optical, camera or radar systems. Radar systems have a particular shortcoming in that they are not able to accurately determine the ball trajectory. In addition, it is well known that putting makes up about 50% of the shots played in a typical round of golf. A method for accurately representing the trajectory of a putt and club head orientation is thus required for an enhanced golf simulator. 
     The principal object of the present invention and its embodiments is to provide a club head and/or ball displacement measurement apparatus that requires no attachments onto or modifications to the user golf club. The invention can be implemented as a golf training apparatus or as a sensor component for a golf simulator. A further object of the invention is to develop sensor technology that can be used with a users own set of clubs, that is suitable for measuring the state of the club head continuously over a zone just prior to and after ball impact, a means for transforming the path of the club head into a set of parameters to be used in training the user and a sensor technology that can utilized on both putting, iron and (driver) woods clubs. 
     The foregoing patents reflect the current state of the art of which the present inventor is aware. Reference to, and discussion of, these patents is intended to aid in discharging Applicant&#39;s acknowledged duty of candor in disclosing information that may be relevant to the examination of claims to the present invention. However, it is respectfully submitted that none of the above-indicated patents disclose, teach, suggest, show, or otherwise render obvious, either singly or when considered in combination, the invention described and claimed herein. 
     SUMMARY OF THE INVENTION 
     This invention relates generally to the field of golf training and simulation devices. More specifically, the invention is directed towards measuring a signal indicative of the displacement of a club head and in an alternate embodiment, the detection of a golf ball after being struck. The invention can generally be used on all clubs that are used in golf. In particular, the invention provides an improved putting stroke training means to develop a smooth, consistent putting stroke by alerting the golfer to imperfections—for example when the putter head has accelerated or decelerated too rapidly or when the golfer opens or closes the club face when striking a golf ball. 
     The golf practice apparatus of the present invention includes a structure which defines a normal path direction and a normal zone of impact of a golf club head during a practice swing, and further includes mechanisms for representing the face angle of the swinging club head up to and beyond the time of impact, utilizing at least two parallel planar displacement sensors aligned in the direction of the intended swing. A preferred displacement sensor for this application comprises planar point coupled inductive displacement sensors which are normally positioned such that the sensors linear range produces a signal proportional to the position of swinging club head with respect to time. 
     The inductive point coupled displacement sensor magnetically couples the field produced by a planar primary winding into two co-located differential, geometrically stepped secondary planar coils. The material within the golf club head (or target) is sufficiently permeable to magnetically couple between the coils at a point along the length of the windings. The width D of the point coupled sensors is much less than the length L. The output of the sensors is proportional to the position of the target, or golf club head position (displacement) along the length of the sensor. Since the length of the point coupled sensor is finite, the club may transverse beyond the complete length of the sensor during a stroke trajectory. In this case, the non-linearity associated with the coil ends will be encountered. This non-linearity is a relatively sharp transition in sensor output and can be utilized or corrected for in the signal processing. 
     Detection circuitry is used to signal process the displacement representative of the position of the swinging club head for each of the point coupled inductive displacement sensor outputs. Each sensor signal (over the linear range of the sensor) can be differentiated once to obtain velocity and differentiated twice to obtain acceleration waveforms that are representative of the kinematics of the club head. 
     Simultaneous information on the club head orientation during the swing prior and after impact with a target ball can be obtained from the comparison of the displacement waveforms from two or more adjacent sensors. If the club head target is not normal to the sensor, there will be a measurable difference in phase between the displacement waveforms between the sensors. A microprocessor or computer can be used to make this comparison and extract in real time, the change in acceleration, club face orientation and swing trajectory. 
     An output means or device is further provided for utilizing the signals from these sensors and signal processing electronics as a representation of the face angle of the club head. In a golf training application, optional means for visual, audio and vibrotactile feedback to the user are provided so that real-time corrections can be made. Vibrotactile and audio feedback are preferable to visual feedback as these methods of feedback are continuous, positive and if used appropriately, may not interfere or distract the user, keeping the head and eye position associated with a normal golf swing. For example, a good stroke may be acknowledged with an audio tone, while an inconsistent stroke may be alerted with a tactile vibration stimulus. 
     In an alternate embodiment, the output of the golf swing measurement apparatus may be input to a virtual reality golf simulator. The sensors and detection circuitry and processing measure a signal indicative of the displacement of a club head and can calculate the club head velocity thus providing a basis for the calculation of ball carry and the direction. This may be further enhanced by combining this invention with existing radar based detectors, for example the PureFlight system manufactured by Zelocity Corporation. 
     An improved golf simulator device is also provided using a two dimensional embodiment of the planar inductive coil sensors to detect the displacement of a special metal filled golf ball, for example the Titanium cored balls available from NanoDynamics, Inc. The two dimensional position with respect to time is output as two voltage signals. These signals can be used to compute the XY trajectory of the ball and thus feed information about its path back to the user or into a computerized golf simulator system. 
     Other novel features which are characteristic of the invention, as to organization and method of operation, together with further objects and advantages thereof will be better understood from the following description considered in connection with the accompanying drawings, in which preferred embodiments of the invention are illustrated by way of example. It is to be expressly understood, however, that the drawings are for illustration and description only and are not intended as a definition of the limits of the invention. The various features of novelty which characterize the invention are pointed out with particularity in the claims annexed to and forming part of this disclosure. The invention resides not in any one of these features taken alone, but rather in the particular combination of all of its structures for the functions specified. 
     There has thus been broadly outlined the more important features of the invention in order that the detailed description thereof that follows may be better understood, and in order that the present contribution to the art may be better appreciated. There are, of course, additional features of the invention that will be described hereinafter and which will form additional subject matter of the claims appended hereto. Those skilled in the art will appreciate that the conception upon which this disclosure is based readily may be utilized as a basis for the designing of other structures, methods and systems for carrying out the several purposes of the present invention. It is important, therefore, that the claims be regarded as including such equivalent constructions insofar as they do not depart from the spirit and scope of the present invention. 
     Further, the purpose of the Abstract is to enable the U.S. Patent and Trademark Office and the public generally, and especially the scientists, engineers and practitioners in the art who are not familiar with patent or legal terms or phraseology, to determine quickly from a cursory inspection the nature and essence of the technical disclosure of the application. The Abstract is neither intended to define the invention of this application, which is measured by the claims, nor is it intended to be limiting as to the scope of the invention in any way. 
     Certain terminology and derivations thereof may be used in the following description for convenience in reference only, and will not be limiting. For example, words such as “upward,” “downward,” “left,” and “right” would refer to directions in the drawings to which reference is made unless otherwise stated. Similarly, words such as “inward” and “outward” would refer to directions toward and away from, respectively, the geometric center of a device or area and designated parts thereof. References in the singular tense include the plural, and vice versa, unless otherwise noted. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will be better understood and objects other than those set forth above will become apparent when consideration is given to the following detailed description thereof. Such description makes reference to the annexed drawings wherein: 
         FIG. 1  shows a schematic of the golf swing measurement apparatus and putter; 
         FIG. 2  shows a schematic of the sequence representing the club face orientation while the club is moving in the down-swing, through the strike zone and the follow through; 
         FIG. 3  shows a schematic “exploded” view of the windings of a single point coupled inductive displacement sensor which senses position in one dimension; 
         FIG. 4  is a pictorial view of a conductive or magnetic target element in conjunction with two secondary windings which are shown spaced apart; 
         FIG. 5  is a pictorial view of the structure of a golf swing measurement apparatus consisting of dual planar displacement sensors for measuring the orientation of a common target; 
         FIG. 6  illustrates the sensor waveforms for calculating the orientation of a moving club head; 
         FIG. 7  illustrates a two dimensional planar point coupled inductive displacement sensor which senses the position of a target in two dimensions; 
         FIG. 8  illustrates the output signal of a point coupled position sensor which operates in two dimensions; 
         FIG. 9  illustrates using the two dimensional planar point coupled inductive sensor to detect the trajectory of club striking a non-magnetic ball within the sensor area; 
         FIG. 10  illustrates using the two dimensional planar point coupled inductive displacement sensor to detect the trajectory of a special golf ball after being struck; 
         FIG. 11  is a circuit diagram shown for the detection circuitry for a single planar point coupled inductive displacement sensor; 
         FIG. 12  illustrates the output display, audio and vibrotactile feedback to the golfer; and 
         FIG. 13  illustrates an example of a visual output display. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to  FIGS. 1 through 13 , wherein like reference numerals refer to like components in the various views, there is illustrated therein a new and improved apparatus for golf club swing training, generally denominated  10  herein. 
     Referring now to  FIG. 1 , the golf swing measurement apparatus  10  of the present invention includes structure  11 , the structure  11  defines a normal path direction  14 . 2  for club  13 , and golf ball  15 . Orthogonal to the normal path  14 . 2  is the axis  14 . 1  that defines a square impact of the golf club face with the ball  15 . The face  28  of club head  13  travels to impact with golf ball  15  between at least two planar point coupled inductive displacement sensors  24  aligned on parallel axes  14 . 3 ,  14 . 4 , that are also parallel to the normal path direction axis  14 . 2 . The ball  15  may be either struck to the left as shown, or to the right without any change to the apparatus. A thin carpet may be used to simulate turf and protect the sensors from abrasion. 
     An output means, and signal interface device  17  is provided which can display measured data on club head position, velocity and acceleration with respect to time and provide intelligent feedback to the user. The output means and signal interface device are drawn separate in  FIG. 1 , but may be integrated or partially integrated within the structure  11 , and the output device may be a screen, personal computer PC, PDA or the like. 
       FIG. 2  shows the trajectory of a club during a golf swing. The ball is initially addressed with a club face  28 , that is perpendicular to the desired normal path  14 . 2 . It is important that the initial address be accurate and in a golf training application, this invention allows the apparatus to measure the angle of address and potentially display this to the user.  FIG. 1  shows the club  13  and the club head  28  at initial address  16 . 
     The golf swing commences with a back-swing which for a putting stroke, may be of variable length, depending on the desired putting distance, conditions and topography. Two or more displacement sensors  24   i  and  24   ii , measure the displacement length from the end of each sensor to the portion of the club face target  28  that intersects with the each sensor. By way of example, sensors  24   i  and sensor  24   ii  will interact with club face  28  over cross sectional area d 1  and d 2  respectively. If only a single displacement sensor  24  is used, the position of the club can be measured (not its orientation). 
     Preferably two or more displacement sensors  24  of length L are used, located parallel and a distance D apart. In this case the club face  28 . 1 ,  28 . 2 ,  28 . 3  orientation will result in different measured displacements in sensors  24   i  and  24   ii . Thus information about the club face orientation can be extracted from a comparison between the displacement sensor signal outputs. The distance D in this embodiment, should be less than the width of the club. Preferably D should be less than 4.5 inches and greater than 1 inch. 
     Referring now to a more detailed explanation of the operation of a single point coupled planar inductive sensor that is depicted in  FIGS. 3 and 4 .  FIG. 3  shows a portion of the components of the point coupled planar displacement sensor. The sensor makes up a planar transformer with split primary winding A ( 26 ) and two secondary planar secondary windings B ( 24 . 1 ) and C ( 24 . 2 ). Each secondary winding is in the form of a stepped geometric pattern that is mirrored for the opposing secondary coil. The primary winding can be only one side or split into two series windings as shown in  FIG. 3 . For clarity, the coils have been drawn separate in  FIG. 3 , but in practise, these coils would be constructed using conventional multi-layer printed circuit board (PCB) fabrication techniques and thus have a very small vertical separation between the coils. 
     The number of turns of the first secondary winding  24 . 1  increases in the longitudinal direction, that is, from left to right and the number of turns of the winding  24 . 2  increases from right to left in the longitudinal direction. The windings thus taper in opposite directions to one another. The transverse lengths of the windings are shown as being skew to the longitudinal direction thereby to provide a smooth transition from section to section rather than a step-like transition. 
     A rectangular primary winding is shown at  26 . The winding  26  generates a magnetic flux to which the secondary windings  24 . 1  and  24 . 2  are subjected, and by the laws of magnetic induction, the current generated in each winding section is dependant on the number of turns.  FIG. 3  also shows a target object  28  which moves back and forth from left to right and the position of which is to be sensed. The element  28  can be electrically conductive or can have a different magnetic permeability to the medium, usually air, which surrounds it. The target core  28  element influences the coupling between the primary winding  26  and the secondary windings  24 . 1  and  24 . 2  according to the principle of a differential transformer as explained in more detail below. 
       FIG. 3  also shows how coupling from the primary winding to the secondary windings can be increased by laminating a layer of high permeability magnetic material  27  on one side of the sensor. A suitable material may be a single, or number of ferrite slabs such as 3F3 commercially available from Ferroxcube. Not shown on the figure are the insulating layers between each of the coil laminations  26 ,  24 . 1 ,  24 . 2  and the layer of high permeability material  27 . 
     In  FIG. 4  the secondary windings  24 . 1  and  24 . 2  are further illustrated as separate windings laid beside each other. The primary winding  26  is shown as a dashed line for clarity and target object  28  is also shown. The primary windings  26  and target object  28  are co-located with the secondary windings and therefore are coupled to both secondary windings  24 . 1  and  24 . 2 . 
     Dimensions X, X 1  and X 2  are designated in  FIG. 4  for the purposes of the following explanation. The length of the longest conductor is X, and all of the m conductors of the primary winding  26  are the full length X. The conductors of one secondary winding  24 . 1  run from x=0 to iX/n, where i is the endpoint of the ith of n conductors. The conductors of the other secondary winding  24 . 2  run from x=(n−i)X/n to X. 
     The difference between induced secondary currents I can be shown to be proportional to: 
     
       
         
           
             
               
                 
                   
                     
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     where A is some coupling factor representing the driving frequency and magnetic coupling (mutual inductance) between the primary  26  and the secondary coils  24 . 1  and  24 . 2 . The first bracketed component of this product represents the difference in coupling caused by the difference in permeability, the second bracketed component represents the size of the area of differing permeability, and the third bracketed component represents the location on the x axis of the area of differing permeability. The current difference is thus linear with respect to the position of the zone of differing permeability. Performance of the sensor thus depends on the sensor target object  28  providing efficient magnetic coupling between the primary and secondary coils and the output from each coil being proportional to the position of the target core. 
     The target object  28  is typically a metal, ferrite or paramagnetic material and this invention, is usually the material contained within the golf club head. In some cases, especially those club head designs that contain steel and composite resin materials, a small piece of high permeability material, for example a ferrite material such as 3F3 available commercially from Ferroxcube may be affixed to the back of the club face to enhance the permeability of the target  28  and thus augment the sensor sensitivity. In most applications, the material contained within the golf club head is sufficient to act as a target. 
     The outputs from the secondary windings are preferably connected to a circuit comprising a differential amplifier and a demodulator to provide a d.c. output (described later). The output from this demodulation is a signal—either a voltage or current proportional to displacement of the target object  28 . Differentiating the sensor output with respect to time, gives the velocity and a second derivative gives the target acceleration. 
       FIG. 5  shows a detail of the sensor configuration used to facilitate sensing of the orientation of a common target, such as a golf club head,  28 , as shown in  FIG. 2 . Two (or more) point coupled planar inductive displacement sensors  24   i  and  24   ii  are located, parallel to another on axes  14 . 4  and  14 . 3  respectively, with a common target  28 . Relative displacement between the two sensors can be continuously measured over the length of the two sensors. Any misalignment of the common target will be detected by a difference in displacement between the two sensor output signals. For the case of a moving common target  28 , any misalignment will be detected as a phase difference between the sensor output signals. This phase difference corresponds to a difference in displacement z and can be used together with the distance between the sensors y to calculate the club face angle θ. These parameters are related by a simple trigonometric identity θ=arctan (y/z). 
     For example,  FIG. 2  depicts a golf club orientation for a right handed stroke that may change from open  28 . 1 , square  28 . 2 , to closed  28 . 3  depending on the twist of the wrists during the swing. Most important is the orientation of the golf club head  28  in the immediate vicinity and up to striking the ball  15 . This invention provides a mechanism by which the club face orientation and kinematics (acceleration and velocity) can be measured continuously up to and beyond the point of impact with the ball  15 . 
     The initial address or aim in the set-up routine of the golfer is known to be important. The club head usually held just behind the ball  15  during the address  16 . In particular, the initial address should be accurate and consistent. In a golf training application, this invention measures the angle of address simply by measuring and recording the orientation of the club head target  28  prior to the initiation of the backswing and stroke. An inconsistent (variable) club head orientation and/or a misaligned club head can be displayed to the user at the end of the golf stroke or at the end of a session of strokes. Alternatively, the club orientation during address can be interactively displayed in real-time to the user, using visual, audio or vibrotactile means, preferably alerting the user as to when the golf club head is aligned or square  28 . 2 . 
     The point coupled planar inductive displacement sensors  24   i  and  24   ii  share a common target  28 , but must act as independent sensors. Therefore magnetic coupling between the sensors should be restricted for example, high permeability backing material  27  should be located only in the immediate vicinity of the sensor  24  windings. Further it is advantageous to operate each sensor  24   i  and  24   ii  at a different frequency. The detection circuitry (described below) has a bandwidth. The frequencies of each sensor primary coil  26  should be chosen to be separated in frequency by greater than the bandwidth of the detection circuitry. 
     Since the length of the point coupled sensor is finite, the club may transverse beyond the complete length of the sensor during a stroke trajectory. In this case, the non-linearity associated with the coil ends will be encountered. This non-linearity is a relatively sharp transition in sensor output. This is shown in  FIG. 6  which depicts a typical output from the detection circuitry (described later) and the golf swing analysis apparatus  10  for a swing that extends beyond the length of the sensors  24 . 
       FIG. 6  depicts the displacement time curves  80  and  81 , that result from the passage of a target  28  over sensors  24   i  and  24   ii  respectively. If the club swing extends beyond the range of the sensors during the forward swing will commence with a sensor output  86  and  84  that corresponds to the instant that the club target  28  begins to move over the two sensor ends. The sensor output is initially non-linear until points  87  and  85  where the sensor displacement is either maximum or minimum (depending on the configuration) this marks the start of the planar point coupled inductive displacement sensors linear range 93 and 94. The end of the linear range is reached when the club head target  28  reaches the end of the sensor length at instants  88  and  89 , decreasing non-linearly to a steady state value at instants  90  and  91 . Once the target exceeds the length of the sensor the output from the detector circuitry is its steady state value  92  and the output no longer tracks displacement of the target  28 . It should be noted that small swings will result in small excursions, thus the complete backswing and forward swing will be within the linear range of the sensor. 
     The instant that the ball is impacted will correspond to the club reaching the middle of the sensor  82  and  83 . For a square clubface at impact,  82  and  83  should be at the same instant. A measurement of  82  and  83  can therefore determine whether the club head is lead or lagging (as shown in  FIG. 5 ). Further, if the sensor outputs are either lagging or leading in time at any instant during the passage of the club target  28 , the club face is not square at that instant and the path of the club can therefore be calculated. 
     The linear portion of each of the sensor outputs  93  and  94  can also be differentiated to give the velocity and differentiated a second time to give the acceleration of the club head target  28 . This differentiation can be done electronically or preferably numerically as a numerical calculation allows the non-linear data at the start and end of a full swing to be parsed and omitted from the differentiation. 
       FIG. 7  shows the schematic construction of two dimension point coupled position sensor to be used to sense the location of a target  35  within a planar area. For clarity, the coils have been drawn separate in  FIG. 7 , but in practice, these coils would be constructed using conventional multi-layer printed circuit board (PCB) fabrication techniques and thus have a very small vertical separation between the coils. 
     The two dimensional sensor embodiment comprises of: a specially stepped spiral primary winding  34  for generating a magnetic flux, a first secondary winding  32 . 2  the number of turns of which increases in one direction, a second secondary winding  31 . 2  the number of turns of which increases in the opposite direction to that of the first secondary winding, both secondary windings being subjected to the magnetic flux generated by the primary winding whereby voltages are induced in said secondary windings, a third secondary winding  30 . 2  the number of turns of which increases in a direction transverse to said one direction, a fourth secondary winding  30 . 1  the number of turns of which increases in the opposite direction to that of the third secondary winding, the third and fourth secondary windings being subjected to the magnetic flux generated by the primary winding whereby voltages are induced in said secondary windings, and an element  35  movable with respect to the secondary windings, the element being of a magnetic or conductive material and distorting, in its vicinity, said magnetic flux generated by the primary winding. The outputs from the each pair of secondary windings, 32.2, 31.2 and 30.2, 30.1 are preferably connected to two circuits each comprising of a differential amplifier and a demodulator to provide a d.c. output proportional to X and Y displacement respectively. 
     Primary coil  34  ends and the spiral are shaped in a stepped spiral pattern that will reduce any non-uniformity or peaking in the magnetic field established by the primary coil  34  over the sensor area. It is known that a constant magnetic field across the measurement length of the sensor is desirable as it increases the available linear sensor measurement range. 
     An example of the output signal from each two dimensional point coupled sensor circuit is shown in  FIG. 8 . Each trace represents the sensor output for a common target that traverses the sensing area at 45 degrees through the XY axis. The output is substantially linear in the measuring range. The XY location of the target can be accurately measured within the linear range of the sensor. Areas of non-linearity exist at the portion of the sensor close to the winding edges. 
     Turning now to  FIG. 9 , this illustrates a further embodiment of the present invention.  FIG. 9  shows the top view of a two dimensional point coupled planar inductive sensor  30  for tracking the position of the golf club head  28 . The output of the two sensor coils is signal processed and adapted into a suitable display  17 . The golf ball  15  can be located within the linear sensing area and if a conventional golf ball is used, the ball will not affect the measurement. In a standard swing, the golfer will typically align both feet parallel to the dashed axis  31  line depicting the direction in which the ball  15  is to be struck. The trajectory of the club  13  and head  28  should be substantially parallel to the preferred direction. However, swing faults can result in variations on this path including arcs, out-to-in or in-to-out movement. These displacement paths are recoded as XY displacements and can be processed and displayed  17  to the user in real-time or just after the completion of the swing. 
       FIG. 10  illustrates an alternative embodiment of the present invention  30  using the two dimensional point coupled sensor to detect the trajectory of a special golf ball after being struck. The golf ball  15  in this case is a special ball containing some materials that have a permeability substantially different from air, for example the Titanium cored balls available from NanoDynamics, Inc. 
     Golf simulators have become an important part of golf training and recreation. Various computer systems have been developed with advanced graphics to create a virtual golf environment. An important application of the golf swing measurement apparatus  10 , is as the sensor component of a golf simulator. Prior-art golf simulator sensors do not adequately address putting and the measurement of putting stroke. Further, the golf simulator sensor components are usually optical, complex and add to the cost of the system. It is an object of this invention to apply the golf swing apparatus shown in  FIGS. 1 to 9  in a golf simulator, either replacing the conventional club head measurement sensor technologies or adding enhanced functionality such as the detection of the path of a putter, and/or the detection of club face angle to existing golf simulator sensor components (for example radar). 
       FIG. 10  thus reveals another embodiment of this invention including a method for accurately representing the trajectory of a putt is thus required for an enhanced golf simulator. In this case, the sensor signals from a two dimensional point coupled sensor are processed and converted into a form suitable for interface with a computer based golf simulator using processing system  27 . As further objects to the invention, the two dimensional planar point coupled sensor can be mounted onto a system of actuators to present a slope over which the putt must roll. This system could be driven in part by the golf simulator and thus accurately present conditions that are most similar to a virtual golf putting green. 
     Turning to  FIG. 11 , this illustrates a detection circuit for a single planar point coupled inductive displacements sensor  24 . The object of the detection circuit is to rectify the output signals of the secondary windings  24 . 1  and  24 . 2  and providing a demodulated d.c. output signal that is representative of the displacement of a target object  28 . The primary winding  26  is driven by an oscillator  36  which is also connected to a demodulator  38 . The sinusoidal oscillation frequency is usually chosen to be in the range 20 to 500 kHz. The secondary windings  40 . 1 ,  40 . 2  are connected to a differential amplifier  42  and the output of the amplifier  42  constitutes the input to the demodulator  38 . The output of the demodulator  38  is fed to a low pass filter  44 , the output of the filter  44  being the a d.c. signal representing the displacement of the target object  28 . 
     The displacement signal is input to processing electronics  45 , and may be further modified using a series of electronic differentiators  46 , to obtain signals representative of the target object  28  velocity and acceleration. These signals are also input to processing electronics  45  where they are conditioned and appropriately level shifted for analog to digital circuits  49 , in which multiple analog signal channels are converted into digital format for processing using a computer  47  or microcontroller. An alternative embodiment may be to perform differentiation digitally using a computer  47  or microcontroller. 
     The microcontroller and/or computer  47  may contain software for processing the signals and depending on the embodiment of this invention, extracting information about the start of the swing, the orientation of the club face head, club head velocity, club head acceleration, club head trajectory and ball trajectory. 
     A feature that can be extracted from signal processing is an indication of the club head height above the sensor. The sensitivity (sensor output voltage per inch) increases as the target  28  approaches the sensor surface. If the club head target  28  is located too far above the sensor, the calculated sensitivity will be below a threshold and the user will be warned that the stroke is not optimum. 
       FIG. 12  shows feedback to the user  60  that can be in the form of tactile  50 , audio or a visual display on a computer screen  58 . The connection  55  from the processing electronics (which also contains appropriate drive circuitry for the vibrotactile transducers) may be a wireless connection such as Bluetooth. 
     Intuitive body referenced vibrotactile stimulus, in addition, or to replace a visual or audio cue, is preferred. The vibrotactile input may convey information on the swing position, swing dynamics, club face orientation, timing or combination thereof. Feedback may be positive (indicating a correct position) or negative (indicating a fault). For example audio or tactile feedback to the user may be in the form of a frequency that is modulated with change in club head velocity during the portion of the down swing. The modulation may be frequency modulation for audio, changing the pitch of a tone proportional to acceleration. In a vibrotactile system, the body is less able to discriminate changes in frequency. Thus modulation would best be amplitude modulation or dual tone modulation. For example standard modulation might be 250 into an Engineering Acoustics C-2 tactor transducer and acceleration may be pulse modulated 250 Hz or combination of 250 and a lower frequency signal modulated between 230 and 249 Hz the output of which is known to simulate low frequency vibrotactile sensation. 
       FIG. 13  shows a typical visual display on a screen  58  for intuitive feedback to the user. Real-time positive feedback to the user is provided for the four cases shown depicted by A,B,C and D. A good stroke is shown as a square stroke  70 . This may be depicted by a representation of the club sweet spot illuminating after the stroke has completed. Typically zone  70  may be colored distinctively such as a green area. Any faults with a putting stroke are shown as off-zone conditions  71 ,  72 , and  73 . These conditions may be distinguished by a combination of shapes and colors or by the specific orientation of the club head at impact. Specifically, the club face orientation at impact may be off center (club heel) as depicted in  FIG. 13B , open or as depicted in  FIG. 13C , closed  72 , all are representative of a poor stroke. The height of the club face above the surface may also be displayed. Typical faults such as the club face being too high can be displayed as depicted in  FIG. 13D . 
     This display may be simultaneous with other feedback mechanisms to the user. Feedback may be negative feedback such as tones, and vibrotactile display, for ff zone conditions. Feedback may also be positive feedback with a different set of tones and/or vibrotactile display stimulus for strokes that achieve a correct stroke (square-zone). 
     It may also be desirable to display summary statistics for the swing parameters from a number of golf strokes to determine consistency and repeatability in stroke. The parameters outlined hereinbefore may be use and standard statistical techniques such as mean and standard deviation used to determine areas where the stroke is consistent and where there is variability. 
     Accordingly, the inventive apparatus may be characterized as a golf club swing measurement apparatus comprising at least two parallel planar displacement sensors aligned in the direction of the intended golf club swing; a detector connected to the at least two parallel planar displacement sensors; and means for processing signals from the detector to calculate the swing parameters of a golf club head moved over the at least two parallel planar displacement sensors. 
     Alternatively, the inventive apparatus may be characterized as a golf club swing measurement apparatus comprising a two dimensional planar inductive sensor including a stepped primary coil; a detector connected to the two dimensional planar inductive sensor; and means for processing signals from the detector to calculate the swing parameters of a golf club head moved over the two dimensional planar inductive sensor. 
     The invention may also be characterized as a method for detecting the displacement of a golf club during a swing, the method comprising the steps of: providing at least two parallel planar displacement sensors aligned in the direction of intended swing; connecting a detector to the at least two parallel planar displacement sensors; moving a golf club head over the at least two parallel planar displacement sensors; and processing the signals from the detector to calculate golf swing parameters. 
     Alternatively, the invention may also be characterized as a method for detecting the displacement of a golf club during a swing, the method comprising the steps of: providing a two dimensional planar inductive sensor including a stepped primary coil; connecting a detector to the two dimensional planar inductive sensor; moving a golf club head over the two dimensional planar inductive sensor; and processing the signals from the detector to calculate golf swing parameters. 
     The above disclosure is sufficient to enable one of ordinary skill in the art to practice the invention, and provides the best mode of practicing the invention presently contemplated by the inventor. While there is provided herein a full and complete disclosure of the preferred embodiments of this invention, it is not desired to limit the invention to the exact construction, dimensional relationships, and operation shown and described. Various modifications, alternative constructions, changes and equivalents will readily occur to those skilled in the art and may be employed, as suitable, without departing from the true spirit and scope of the invention. Such changes might involve alternative materials, components, structural arrangements, sizes, shapes, forms, functions, operational features or the like. 
     Therefore, the above description and illustrations should not be construed as limiting the scope of the invention, which is defined by the appended claims.