Golf Free Swing Measurement and Analysis System

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First Claim
1. ) A golf swing measurement first module comprising;
 a) a housing that is adapted for attaching to and detaching from a golf club head and that contains electronics that further provide electronic functions comprising;
i) a means of measuring acceleration in three separate orthogonal directions exclusively, defining a measurement axes coordinate system, andii) a wireless radio frequency transceiver for transmitting signals and receiving signals andiii) a means of measuring receiver signal strength
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Abstract
The presented invention relates to a method for determining the effectiveness of a golfer'"'"'s swing without the requirement of the club head making contact with a golf ball. More specifically, the present invention relates to a measurement and analysis system comprising a first module that attaches to the club head and captures measurement data and relative position data during the entire swing, further first module wirelessly communicates bidirectionally with a second module that is further connected to a user interface device and computational engine where feedback results are calculated and conveyed to the golfer. The system provides comprehensive feedback for swing characterization including detailed swing timing metrics, dynamic club head orientation and motion metrics and dynamics shaft action metrics all referenced to the spatial domain.
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12 Claims
 1. ) A golf swing measurement first module comprising;
a) a housing that is adapted for attaching to and detaching from a golf club head and that contains electronics that further provide electronic functions comprising; i) a means of measuring acceleration in three separate orthogonal directions exclusively, defining a measurement axes coordinate system, and ii) a wireless radio frequency transceiver for transmitting signals and receiving signals and iii) a means of measuring receiver signal strength
 2. ) A golf swing measurement and analysis system comprising:
a) a golf club comprising a shaft, a club head, and the club head further comprising a club head top surface and a club head face; b) a first module that is i) attachable to and detachable from said club head top surface, and contains electronics to provide electronic functions comprises; (1) a means for measuring acceleration in three separate orthogonal directions exclusively, defining a measurement axes coordinate system (2) a wireless transceiver with means for measuring received signal strength from a second module wireless transmission signal transmitted from a predetermined location and transmitting synchronized acceleration and received signal strength measurements out of the first module wirelessly as first module transmitted measurements; c) a means for aligning said first module on said club head top surface defining an alignment of said first module, and a means for attaching said first module to a top surface of said club head top surface; d) said second module that is located at said predetermined location and module comprises a housing that contains electronics to provide electronic functions comprising; i) an antenna ii) a wireless radio frequency transceiver electrically connected to said antenna that receives signal carrying said first module transmitted measurements and transmits said second module wireless transmission signal to said first module iii) and a means of further transport of said first module transmitted measurements as second module second transmitted measurements to a computational engine having typical input/output port formats and a display; e) a golf swing model stored on the computational engine comprising i) multiple levers including at least one rigid lever and at least one nonrigid lever, and ii) a means for inputting constants based on a golfer and the golf club; f) a first computational algorithm that operates on said computational engine that interprets second module second transmitted measurements further specific to said first module transmitted measurements further specific to acceleration measurements within boundary conditions of said golf swing model and detects if said first module alignment is misaligned and calibrates said first module transmitted measurements further specific to acceleration measurements, and g) a second computational algorithm that operates on said computational engine that interprets said first module transmitted measurements further specific to acceleration measurements or said first module transmitted measurements further specific to acceleration measurements calibrated by the first computational algorithm within boundary conditions of said golf swing model to define dynamically changing relationships time line between an inertial axes coordinate system defined by said golf swing model and said measurement axes coordinate system during a golf swing. h) a third computational algorithm that operates on said computational engine that interprets said first module transmitted measurements further specific to said signal strength measurements made at said first module and defines the dynamic spatial relationship time line of said club head travelling on nonlinear travel path to predefined location and correlates to said dynamically changing relationship time line between an inertial axes coordinate system and measurement axes coordinate system during a golf swing.  View Dependent Claims (3, 4, 5, 6, 7, 8, 9, 10, 11)
 12. ) A golf swing measurement and analysis system comprising:
a) a golf club comprising a shaft, a club head, and the club head further comprising a club head top surface and a club head face; b) a first module that is i) attachable to and detachable from said club head top surface, and contains electronics to provide electronic functions comprises; (1) a means for measuring acceleration in three separate orthogonal directions exclusively, defining a measurement axes coordinate system and (2) a wireless transmitter for transmitting acceleration measurements out of the first module wirelessly as first module transmitted measurements; c) a means for aligning said first module on said club head top surface defining an alignment of said first module and a means for attaching said first module to a top surface of said club head top surface; d) a second module that is placed at a predetermined location and contains electronics to provide electronic functions comprising; i) a wireless transceiver that receivers said first module transmitted measurements at a single antenna and provides ii) a means for measuring signal strength of wireless signal carrying said first module transmitted measurements iii) a controller for synchronizing said first module transmitted measurements and, said signal strength measurements of said wireless signal carrying said first module transmitted measurements, and further transmitting synchronized measurements as second module second transmitted measurements e) a means for receiving said second module second transmitted measurements at a computational engine external to said second module, the computational engine having typical input/output port formats and a display; f) a golf swing model stored on the computational engine comprising i) multiple levers including at least one rigid lever and at least one nonrigid lever, and ii) a means for inputting constants based on a golfer and the golf club; g) a first computational algorithm that operates on said computational engine that interprets said second module second transmitted measurements further specific to said first module transmitted measurements within boundary conditions of said golf swing model and detects if said first module alignment is misaligned and calibrates said first module transmitted measurements; and h) a second computational algorithm that operates on said computational engine that interprets said second module second transmitted measurements further specific to said first module transmitted measurements or said first module transmitted measurements calibrated by the first computational algorithm within boundary conditions of said golf swing model to define dynamically changing relationships time line between an inertial axes coordinate system defined by said golf swing model and said measurement axes coordinate system during a golf swing. i) a third computational algorithm that operates on said computational engine that interprets said second module second transmitted measurements and defines time delay between first module transmitted measurements further specific to acquisition time of acceleration measurements and second module second transmitted measurements further specific to acquisition time of receiver signal strength measurements. Further third algorithm defines the dynamic spatial relationship time line of said club head to predefined location and correlates with said time delay removed to said dynamically changing relationship time line between an inertial axes coordinate system and measurement axes coordinate system during a golf swing.
1 Specification
This patent application is a continuationinpart application of patent application U.S. Ser. No. 12/777,334, filed May 11, 2010, entitled “Golf Free Swing Apparatus and Method” that is now U.S. Pat. No. 7,871,333 entitled “Golf Swing Measurement and Analysis System”
The presented invention relates to a method for determining the effectiveness of a golfers swing without the requirement of the club head making contact with a golf ball. More specifically, the present invention relates to a system comprising a first module that attaches to the club head and captures measurement data and relative position data during the entire swing, further first module wirelessly communicates bidirectionally with a second module that is further connected to a user interface device and computational engine where feedback results are calculated and conveyed to the golfer. The system provides comprehensive feedback for swing characterization for detailed swing timing results, dynamic club head orientation and motion metrics and dynamics shaft actions all referenced to the spatial domain.
There are numerous prior art external systems disclosures using video and or laser systems to analyze the golf swing. There are also numerous golf club attached systems using shaft mounted strain gauges and or single to multiple accelerometers and gyros to calculate golf swing metrics. However, none of these prior art approaches contemplate a mobile system with only accelerometers attached to the club head orthogonally configured on a threedimensional axes and use receiver signal strength measurements to correlate time line measurements with the spatial domain.
U.S. Pat. No. 3,945,646 to Hammond integrates threedimensional orthogonal axes accelerometers in the club head, and describes a means for wirelessly transmitting and receiving the resulting sensor signals. However, he does not contemplate the computational algorithms involving the multilever mechanics of a golf club swing required to solve for all the angles of motion of the club head during the swing with a varying swing radius. His premise of being able to obtain face angle only with data from his sensors 13, and 12 (x and y directions respectively described below) is erroneous, as for one example, the toe down angle feeds a large component of the radial centrifugal acceleration onto sensor 12 which he does not account for. He simply does not contemplate the effects of the dynamically changing orientation relationship between the inertial acceleration forces and the associated coordinate system acting on the club head constrained by the multilever golf swing mechanics and the fixed measurement coordinate system of the three orthogonal club head sensors.
U.S. Pat. No. 7,672,781 to Churchill uses receiver signal strength measurements with multiple directional antennas in combination with linear calculation methods based on acceleration measurements to determine the location of a movable bodies that could be a golf club. Churchill fails to contemplate using RSSI measurements without the use of directional sectorized antennas in combination with acceleration measurements analysis applied to a movable object with nonlinear travel.
The prior art disclosures all fail to offer a golf free swing analysis system that measures only acceleration forces on three orthogonal axes at the club head and interprets that limited data within the constraints of a multilever golf swing model using rigid and non rigid levers describing the mechanics of a swing, to determine the dynamically changing orientation relationship of inertial forces experienced at the club head and the orthogonal measurement axes fixed to the club head, resulting in the ability to accurately calculate numerous golf swing metrics over a time line and in addition correlate that time line with the spatial domain
The present invention is a golf swing measurement and analysis system that measures directly and stores time varying acceleration forces during the entire golf club swing. The measurement and analysis system comprises four major components; a golf club, a club head module (first module) that is attachable to and removable from the club head, a second module that is located and a predetermined location and a computer program. The golf club comprises a shaft and a club head with the club head comprising a face and a top surface where the module is attached. The first module comprise a means to measure acceleration separately on three orthogonal axes, and first module or second module or both modules have a means of measuring receiver signal strength. First module and second module have means to communicate wirelessly and second module has a means to transport the measured data to a computer or other smart device where the computer program resides. The computer program comprises computational algorithms for calibration of data and calculation of golf metrics described on a time line and further correlation of that time line to the spatial domain, and support code for user interface commands and inputs and visual display of the metrics.
During operation the module is attached on the head of the golf club, and during the entire golf swing it captures data from the three acceleration sensors axes. The acquired swing measurement data is either stored in the module for later analysis or transmitted immediately from the module to a receiver with connectivity to a computation engine. A computational algorithm that utilizes the computational engine is based on a custom multilever golf swing model utilizing both rigid and nonrigid levers. This algorithm interprets the measured sensor data to determine the dynamically changing relationship between an inertial coordinates system defined by the multilever model for calculation of inertial acceleration forces and the module measurement axes coordinate system attached to the club head. Defining the dynamically changing orientation relationship between the two coordinate systems allows the interpretation of the measured sensor data with respect to a nonlinear travel path allowing the centrifugal and linear acceleration components to be separated for each of the module'"'"'s three measured axes. Now with each of the module axes measurements defined with a centrifugal component (also called the radial component), and a linear spatial transition component the swing analysis system accurately calculates a variety of golf swing metrics which can be used by the golfer to improve their swing. These swing quality metrics include:
 1. Golf club head time varying velocity for a significant time span before and after maximum velocity of the swing.
 2. Time varying swing radius for a significant time span before and after maximum velocity of the swing.
 3. Golf club head face approach angle of the golf club head, whether the club face is “open”, “square”, or “closed”, and by how much measured in degrees, for a significant time span before and after maximum velocity of the swing.
 4. Wrist cock angle during the swing, for a significant time span before and after maximum velocity of the swing.
 5. Club shaft lag/lead flexing during the swing, for a significant time span before and after maximum velocity of the swing.
 6. Club head toe down angle during the swing, for a significant time span before and after maximum velocity of the swing.
 7. Club head acceleration force profile for the backswing that include time varying vector components and total time duration.
 8. Club head acceleration force profile for the pause and reversal segment of the swing after backswing that includes time varying vector components and total time duration.
 9. Club head acceleration force profile for the powerstroke after pause and reversal that includes time varying vector components and total time duration.
 10. Club head acceleration force profile for the follow through after powerstroke that includes time varying vector components and total time duration.
 11. Club head swing tempo profile which includes total time duration of tempo for the backswing, pause and reversal, and powerstroke and provides a percentage break down of each segment duration compared to total tempo segment duration.
 12. All analysis metrics listed above correlated to the spatial domain.
The module acceleration measurement process comprises sensors that are connected to electrical analog and digital circuitry and an energy storage unit such as a battery to supply power to the circuits. The circuitry conditions the signals from the sensors, samples the signals from all sensors simultaneously, converts them to a digital format, attaches a time stamp to each group of simultaneous sensor measurements, and then stores the data in memory. The process of sampling sensors simultaneously is sequentially repeated at a fast rate so that all acceleration forces profile points from each sensor are relatively smooth with respect to time. The minimum sampling rate is the “Nyquist rate” of the highest significant and pertinent frequency domain component of any of the sensors'"'"' time domain signal.
The sensor module also contains circuitry for storing measured digital data and a method for communicating the measured data out of the module to a computational engine integrated with interface peripherals that include a visual display and or audio capabilities. In the preferred embodiment the club head module also contains RF circuitry for instant wireless transmission of sensor data immediately after sampling to a RF receiver plugged into a USB or any other communications port of a laptop computer. The receiver comprises analog and digital circuitry for receiving RF signals carrying sensor data, demodulating those signals, storing the sensor data in a queue, formatting data into standard USB or other communication formats for transfer of the data to the computation algorithm operating on the computation engine.
An alternate embedment of this invention contemplates a similar module without the RF communication circuitry and the addition of significantly more memory and USB connectivity. This alternate embodiment can store many swings of data and then at a later time, the module can be plugged directly into to a USB laptop port for analysis of each swing.
Another alternate embodiment of this invention contemplates a similar club head module without the RF circuitry and with a wired connection to a second module mounted on the shaft of the club near the grip comprising a computational engine to run computational algorithm and a display for conveying golf metrics.
The above and other features of the present invention will become more apparent upon reading the following detailed description in conjunction with the accompanying drawings, in which:
The present invention comprises accelerometers attached to the club head that allow the motion of the club head during the swing to be determined. In the preferred embodiment as shown in
For the club head module 101 mounted perfectly on the club head 201 top surface 204 the following relations are achieved: The z_{f}axis 105 is aligned so that it is parallel to the club shaft 202. The x_{f}axis 104 is aligned so that is orthogonal to the z_{f}axis 105 and perpendicular to the plane 203 that would exist if the club face has a zero loft angle. The y_{f}axis 106 is aligned orthogonally to both the x_{f}axis 104 and z_{f}axis 105.
With these criteria met, the plane created by the x_{f}axis 104 and the y_{f}axis 106 is perpendicular to the nonflexed shaft 202. In addition the plane created by the y_{f}axis 106 and the z_{f}axis 105 is parallel to the plane 203 that would exist if the club face has a zero loft angle.
The mathematical label a_{sx }represents the acceleration force measured by a sensor along the club head module 101 x_{f}axis 104. The mathematical label a_{sy }represents the acceleration force measured by a sensor along the club head module 101 y_{f}axis 106. The mathematical label a_{sz }represents the acceleration force measured by a sensor along the club head module 101 z_{f}axis 105.
If the club head module of the preferred embodiment is not aligned exactly with the references of the golf club there is an algorithm that is used to detect and calculated the angle offset from the intended references of the club system and a method to calibrate and correct the measured data. This algorithm is covered in detail after the analysis is shown for proper club head module attachment with no mounting angle variations.
Club head motion is much more complicated than just pure linear accelerations during the swing. It experiences angular rotations of the fixed sensor orthogonal measurement axes, x_{f}axis 104, y_{f}axis 106 and z_{f}axis 105 of module 101 around all the center of mass inertial acceleration force axes during the swing, as shown in
The three orthogonal measurement axes x_{f}axis 104, y_{f}axis 106 and z_{f}axis 105 of module 101, along with a physicsbased model of the multilever action of the swing of the golfer 301, are sufficient to determine the motion relative to the club head threedimensional center of mass axes with the x_{cm}axis 303, y_{cm}axis 305 and z_{cm}axis 304.
The mathematical label a_{z }is defined as the acceleration along the z_{cm}axis 304, the radial direction of the swing, and is the axis of the centrifugal force acting on the club head 201 during the swing from the shoulder 306 of the golfer 301. It is defined as positive in the direction away from the golfer 301. The mathematical label a_{x }is the defined club head acceleration along the x_{cm}axis 303 that is perpendicular to the a_{z}axis and points in the direction of instantaneous club head inertia on the swing arc travel path 307. The club head acceleration is defined as positive when the club head is accelerating in the direction of club head motion and negative when the club head is decelerating in the direction of club head motion. The mathematical label a_{y }is defined as the club head acceleration along the y_{cm}axis 305 and is perpendicular to the swing plane 308.
During the golfer'"'"'s 301 entire swing path 308, the dynamically changing relationship between the two coordinate systems, defined by the module 101 measurements coordinate system axes x_{f}axis 104, y_{f}axis 106 and z_{f}axis 105 and the inertial motion acceleration force coordinate system axes x_{cm}axis 303, y_{cm}axis 305 and z_{cm}axis 304, must be defined. This is done through the constraints of the multilever model partially consisting of the arm lever 309 and the club shaft lever 310.
The multi lever system as shown in
There are several ways to treat the rotation of one axes frame relative to another, such as the use of rotation matrices. The approach described below is chosen because it is intuitive and easily understandable, but other approaches with those familiar with the art would fall under the scope of this invention.
Using the multilever model using levers, rigid and nonrigid, the rotation angles describing the orientation relationship between the module measured axis coordinate system and the inertial acceleration force axes coordinate system can be determined from the sensors in the club head module 101 through the following relationships:
a_{sx}=a_{x }cos (Φ) cos (η)−a_{y }sin (Φ)−a_{z }cos (Φ) sin (η) 1.
a_{sy}=a_{x }sin (Φ) cos (η)+a_{y }cos (Φ)+a_{z}(sin (Ω)−sin (Φ) sin (η)), 2.
a_{sz}=a_{x }sin (η)−a_{y }sin (Ω) cos (Φ)+a_{z }cos (η) 3.
The following is a reiteration of the mathematical labels for the above equations.
 a_{x }is the club head acceleration in the x_{cm}axis 303 direction.
 a_{y }is the club head acceleration in the y_{cm}axis 305 direction.
 a_{z }is the club head acceleration in the z_{cm}axis 304 direction.
 a_{sx }is the acceleration value returned by the club head module 101 sensor along the x_{f}axis 104.
 a_{sy }is the acceleration value returned by the club head module 101 sensor along the y_{f}axis 106.
 a_{sz }is the acceleration value returned by the club head module 101 sensor along the z_{f}axis 105.
During a normal golf swing with a flat swing plane 308, a_{y }will be zero, allowing the equations to be simplified:
a_{sx}=a_{x }cos (Φ) cos (η)−a_{z }cos (Φ) sin (η) 4.
a_{sy}=a_{x }sin (Φ) cos (η)+a_{z }(sin (Ω)−sin (Φ) sin (η)) 5.
a_{sz}=a_{x }sin (η)+a_{z }cos (η) 6.
These equations are valid for a “free swing” where there is no contact with the golf ball.
The only known values in the above are a_{sx}, a_{sy}, and a_{sz }from the three sensors. The three angles are all unknown. It will be shown below that a_{x }and a_{z }are related, leaving only one unknown acceleration. However, that still leaves four unknowns to solve for with only three equations. The only way to achieve a solution is through an understanding the physics of the multilever variable radius swing system dynamics and choosing precise points in the swing where physics governed relationships between specific variables can be used.
The angle Φ 501, also known as the club face approach angle, varies at least by 180 degrees throughout the backswing, downswing, and follow through. Ideally it is zero at maximum velocity, but a positive value will result in an “open” clubface and negative values will result in a “closed” face. The angle Φ 501 is at the control of the golfer and the resulting swing mechanics, and is not dependent on either a_{x }or a_{z}. However, it can not be known apriori, as it depends entirely on the initial angle of rotation around the shaft when the golfer grips the shaft handle and the angular rotational velocity of angle Φ 501 during the golfer'"'"'s swing.
The angle Ω 601, on the other hand, is dependent on a_{z}, where the radial acceleration causes a centrifugal force acting on the center of mass of the club head, rotating the club head down around the x_{f}axis into a “toe” down position of several degrees. Therefore, angle Ω 601 is a function of a_{z}. This function can be derived from a physics analysis to eliminate another unknown from the equations.
The angle η 401 results from both club shaft angle 702 lag/lead during the downswing and wrist cock angle 701. Wrist cock angle is due both to the mechanics and geometry relationships of the multi lever swing model as shown in
Before examining the specifics of these angles, it is worth looking at the general behavior of equations (4) through (6). If both angle Ω 601 and angle η 401 were always zero, which is equivalent to the model used by Hammond in U.S. Pat. No. 3,945,646, the swing mechanics reduces to a single lever constant radius model. For this case:
a_{sx}=a_{x }cos (Φ) 7.
a_{sy}=a_{x }sin (Φ) 8.
a_{sz}=a_{z} 9.
This has the simple solution for club face angle Φ of:
In Hammond'"'"'s U.S. Pat. No. 3,945,646 he states in column 4 starting in line 10 “By computing the vector angle from the acceleration measured by accelerometers 12 and 13, the position of the club face 11 at any instant in time during the swing can be determined.” As a result of Hammond using a single lever constant radius model which results in equation 10 above, it is obvious he failed to contemplate effects of the centrifugal force components on sensor 12 and sensor 13 of his patent. The large error effects of this can be understood by the fact that the a_{z }centrifugal acceleration force is typically 50 times or more greater than the measured acceleration forces of a_{sx }and a_{sy }for the last third of the down swing and first third of the follow through. Therefore, even a small angle Ω 601 causing an a_{z }component to be rotated onto the measured a_{sy }creates enormous errors in the single lever golf swing model.
In addition, the effect of the angle η 401 in the multi lever variable radius swing model is to introduce a_{z }components into a_{sx }and a_{sy}, and an a_{x }component into a_{sz}. The angle η 401 can vary from a large value at the start and midpoint of the down stroke when a_{z }is growing from zero. In later portion of the down stroke a_{z }becomes very large as angle η 401 tends towards zero at maximum velocity. Also, as mentioned above, the angle η 401 introduces an a_{x }component into a_{sz}. This component will be negligible at the point of maximum club head velocity where angle η 401 approaches zero, but will be significant in the earlier part of the swing where angle η 401 is large and the value of a_{x }is larger than that for a_{z}.
The cos (η) term in equations (4) and (5) is the projection of a_{x }onto the x_{f}y_{f }plane, which is then projected onto the x_{f }axis 104 and the y_{f }axis 106. These projections result in the a_{x }cos (Φ) cos (η) and a_{x }sin (Φ) cos (η) terms respectively in equations (4) and (5). The projection of a_{x }onto the z_{f}axis 105 is given by the a_{x }sin (η) term in equation (6).
The sin (η) terms in equations (4) and (5) are the projection of a_{z }onto the plane defined by x_{f }axis 104 and the y_{f }axis 106, which is then projected onto the x_{f }axis 104 and y_{f }axis 106 through the a_{z }cos (Φ) sin (η) and a_{z }sin (Φ) sin (η) terms respectively in equations (4) and (5). The projection of a_{z }onto the z_{f}axis 105 is given by the a_{z }cos (Φ) term in equation (6).
The angle Ω 601 introduces yet another component of a_{z }into a_{sy}. The angle Ω 601 reaches a maximum value of only a few degrees at the point of maximum club head velocity, so its main contribution will be at this point in the swing. Since angle Ω 601 is around the x_{f}axis 104, it makes no contribution to a_{sx}, so its main effect is the a_{z }sin (Ω) projection onto the y_{f}axis 106 of equation (5). Equations (4) and (5) can be simplified by rewriting as:
a_{sx}=(a_{x }cos (η)−a_{z }sin (η)) cos (Φ)=ƒ(η) cos (Φ) and 11.
a_{sy}=(a_{x }cos (η)−a_{z }sin (η)) sin (Φ)+a_{z }sin (Ω)=ƒ(Ω) sin (Φ)+a_{z }sin (Ω) where 12.
ƒ(η)=a_{x }cos (η)−a_{z }sin (η). From (11): 13.
which when inserted into (12) obtains:
a_{sy}=a_{sx }tan (Φ)+a_{z }sin (Ω) 15.
From equation (15) it is seen that the simple relationship between a_{sx }and a_{sy }of equation (10) is modified by the addition of the a_{z }term above. Equations (4) and (6) are rewritten as:
These equations are simply solved by substitution to yield:
Equation (19) can be used to find an equation for sin (η) by rearranging, squaring both sides, and using the identity, cos^{2 }(η)=1−sin^{2 }(η), to yield a quadratic equation for sin (η), with the solution:
To get any further for a solution of the three angles, it is necessary to examine the physical cause of each. As discussed above the angle η 401 can be found from an analysis of the angle α 403, which is the sum of the angles α_{wc }701, due to wrist cock and α_{sf }702 due to shaft flex lag or lead.
Angle α 403, and angle η 401 are shown in
R^{2}=A^{2}+C^{2}+2AC cos (α) 21.
A^{2}=R^{2}+C^{2}−2RC cos (η) 22.
Using R^{2 }from equation (21) in (22) yields a simple relationship between α and η:
α=cos^{−1 }((R cos (η)−C)/A) 23.
The swing radius, R 402, can be expressed either in terms of cos (α) or cos (η). Equation (21) provides R directly to be:
R=√{square root over (C^{2}+A^{2}+2AC cos (α))}. 24.
Equation (22) is a quadratic for R which is solved to be:
R=C cos (η)+√{square root over (C^{2}(cos (η)−1)+A^{2})}. 25.
Both α 403 and η 401 tend to zero at maximum velocity, for which R_{m}=A+C.
The solutions for the accelerations experienced by the club head as it travels with increasing velocity on this swing arc defined by equation (25) are:
The acceleration a_{z }is parallel with the direction of R 402, and a_{x }is perpendicular to it in the swing plane 308. The term V_{Γ} is the velocity perpendicular to R 402 in the swing plane 308, where Γ is the swing angle measured with respect to the value zero at maximum velocity. The term V_{R }is the velocity along the direction of R 402 and is given by dR/dt. The swing geometry makes it reasonably straightforward to solve for both V_{R }and its time derivative, and it will be shown that a_{z }can also be solved for which then allows a solution for V_{Γ}:
Now define:
so that:
V_{Γ}=√{square root over (Ra_{zradial})}, 30.
Next define:
Because (31) has the variable R 402 included as part of the time derivative equation (27) can be written:
Also equation (26) can be written:
The acceleration a_{v }805 is the vector sum of a_{x }804 and a_{z }803 with magnitude:
where
The resulting magnitude of the force acting on the club head is then:
F_{v}=m_{s}a_{v} 36.
β=η for no wrist torque. 37.
On the other hand, when force F_{wt }808 is applied due to wrist torque 802:
β=η+η_{et }where: 38.
F_{wt}=F_{v }sin (η_{wt}). 39.
The angle η_{wt }809 is due to wrist torque 802. From (38):
where C_{η}<1 is a curve fitting parameter to match the data, and is nominally around the range of 0.75 to 0.85. From the fitted value:
η_{wt}=(1−C_{η})β 41.
Using (41) in (39) determines the force F_{wt }808 due to wrist torque 802.
To solve for angle Ω 601 as previously defined in
It is worth noting that from equation (42) for increasing values of a_{z }there is a maximum angle Ω 601 that can be achieved of d C_{Ω}/C which for a typical large head driver is around 4 degrees. The term C_{Ω} is a curve fit parameter to account for variable shaft stiffness profiles for a given K. In other words different shafts can have an overall stiffness constant that is equal, however, the segmented stiffness profile of the shaft can vary along the taper of the shaft.
An equation for angle Φ 501 in terms of angle Ω 601 can now be found. This is done by first using equation (17) for a_{z }in equation (15):
Rearranging terms:
(a_{sy}−a_{sz }cos (η) sin (Ω)) cos (Φ)=a_{sx }sin (Φ)−a_{sx }sin (η) sin (Ω) 44.
Squaring both sides, and using the identity cos^{2 }(Φ)=1−sin^{2 }(Φ) yields a quadratic equation for sin (Ω):
sin^{2 }(Ω)[a_{sx}^{2}+(a_{sy}−a_{sz }cos (η) sin (Ω))^{2}]−2a_{sx}^{2 }sin (Ω) sin (η) sin (Ω)+a_{sx}^{2 }(sin (η) sin (Ω))^{2}−(a_{sy}−a_{sz }cos (η) sin (Ω))^{2}=0 45.
Equation (45) has the solution:
where the terms in (46) are:
b_{1}=a_{sx}^{2}+(a_{sy}−a_{sz }cos (η) sin (Ω))^{2 }
b_{2}=−2a_{sx}^{2 }sin (η) sin (Ω)
b_{3}=a_{sx}^{2}(sin (η) sin (Ω))^{2}−(a_{sy}−a_{sz }cos (η) sin (Ω))^{2 }
Equations (42) for Ω 601, (46) for Φ 501, and (20) for η 401 need to be solved either numerically or iteratively using equations (32) for a_{x}, (33) for a_{z}, and (25) for R 402. This task is extremely complex. However, some innovative approximations can yield excellent results with much reduced complexity. One such approach is to look at the end of the powerstroke segment of the swing where V_{R }and its time derivative go to zero, for which from equations (32), (33), (35) and (40):
In this part of the swing the a_{sx }term will be much smaller than the a_{sz }term and equation (18) can be approximated by:
a_{z}=a_{zradial}=a_{sz }cos (η). 48.
During the earlier part of the swing, the curve fit coefficient C_{η }would accommodate nonzero values of V_{R }and its time derivative as well as the force due to wrist torque 802.
The maximum value of η 401 is nominally around 40 degrees for which from (48) a_{ch}/a_{zradial}=1.34 with C_{η}=0.75. So equation (47) is valid for the range from a_{ch}=0 to a_{ch}=1.34 a_{zradial}, which is about a third of the way into the downstroke portion of the swing. At the maximum value of η 401 the vector a_{v }805 is 13 degrees, or 0.23 radians, off alignment with the z_{f }axis and its projection onto the z_{f }axis 105 is a_{sz}=a_{v }cos (0.23)=0.97a_{y}. Therefore, this results in a maximum error for the expression (48) for a_{z}=a_{zradial }of only 3%. This amount of error is the result of ignoring the a_{sx }term in equation (18). This physically means that for a_{z }in this part of the swing the a_{zradial }component value dominates that of the a_{sx }component value. Equation (47) can not be blindly applied without first considering the implications for the function ƒ(η) defined by equations (13) and (14), which has a functional dependence on cos (Φ) through the a_{sx }term, which will not be present when (47) is used in (13). Therefore, this cos (Φ) dependence must be explicitly included when using (47) to calculate (13) in equation (12) for a_{sy}, resulting in:
a_{sy}=(a_{x }cos (η)−a_{z }sin (η)) tan (Φ)+a_{z }sin (Ω). 49.
Equation (49) is applicable only when equation (47) is used for the angle η 401.
A preferred embodiment is next described that uses the simplifying equations of (47) through (49) to extract results for Φ 501 and η 401 using (42) as a model for Ω 601. It also demonstrates how the wrist cock angle α_{we }701 and shaft flex angle α_{sf }702 can be extracted, as well as the mounting angle errors of the accelerometer module. Although this is the preferred approach, other approaches fall under the scope of this invention.
The starting point is rewriting the equations in the following form using the approximations a_{z−}=a_{zradial }and a_{x}=a_{ch}. As discussed above these are excellent approximations in the later part of the swing. Rewriting the equations (4) and (49) with these terms yields:
a_{sx}=a_{ch }cos (Φ) cos (η)−a_{zradial }cos (Φ) sin (η) 50.
a_{sy}=a_{ch }tan (Φ) cos (η)+a_{zradial }sin (Ω)−a_{zradial }tan (Φ) sin (η) 51.
a_{zradial}=a_{sz }cos (η) 52.
Simplifying equation (31):
In this approximation V=V_{Γ }is the club head velocity and dt is the time increment between sensor data points. The instantaneous velocity of the club head traveling on an arc with radius R is from equation (29):
V=√{square root over (a_{zradial}R)}=a_{zradial}^{1/2}R^{1/2 }for which: 54.
Using equation (52) for a_{zradial }in (55):
During the early part of the downswing, all the derivative terms will contribute to a_{ch}, but in the later part of the downswing when R is reaching its maximum value, R_{Max}, and η is approaching zero, the dominant term by far is the da_{sz}/dt term, which allows the simplification for this part of the swing:
With discreet sensor data taken at time intervals Δt, the equivalent of the above is:
It is convenient to define the behavior for a_{ch }for the case where R=R_{Max }and η=0, so that from equation (52) a_{zradial}=a_{sz}, which defines:
Then the inertial spatial translation acceleration component of the club head is:
Substituting equation (52) and (60) back into equations (50) and (51) we have the equations containing all golf swing metric angles assuming no module mounting angle errors in terms of direct measured sensor outputs:
a_{sx}=a_{chsz}(√{square root over (R cos (η))}/√{square root over (R_{Max})}) cos (Ω) cos (η)−a_{sz }cos (η) cos (Φ) sin (η) 61.
a_{sy}=a_{chsz}(√{square root over (R cos (η))}/√{square root over (R_{Max})}) tan (Φ) cos (η)+a_{sz }cos (η) sin (Ω)−a_{sz }cos (η) tan (Ω) sin (η) 62.
Using equation (62) to solve for Φ, since this is the only equation that contains both η and Ω, yields:
Now there are two equations with three unknowns. However, one of the unknowns, η, has the curve fit parameter C_{η }that can be iteratively determined to give best results for continuity of the resulting time varying curves for each of the system variables. Also, there are boundary conditions from the multilever model of the swing that are applied, to specifics points and areas of the golf swing, such as the point of maximum club head velocity at the end of the downstroke, where:
 1. For a golf swing approaching max velocity the value of η approaches zero,
 2. Ω is at a maximum value when centrifugal force is highest, which occurs at maximum velocity.
 3. The club face angle, Φ, can vary greatly at maximum club head velocity. However, regardless of the angle at maximum velocity the angle is changing at a virtual constant rate just before and after the point of maximum club head velocity.
This knowledge allows for all equations to be solved, through an interactive process using starting points for the curve fit parameters.
The angle Ω 601 is a function of a_{sz }through equations (42), (48) and (52). The curve fit constant, C_{Ω}, is required since different shafts can have an overall stiffness constant that is equal, however, the segmented stiffness profile of the shaft can vary along the taper of the shaft. The value of C_{Ω} will be very close to one, typically less than 1/10 of a percent variation for the condition of no module mounting angle error from the intended alignment. Values of C_{Ω }greater or less than 1/10 of a percent indicates a module mounting error angle along the y_{cm}axis which will be discussed later. Rewriting equation (42) using (52):
The constants in equation (64) are:
 C_{Ω }Multiplying curve fit factor applied for iterative solution
 d Distance from housel to center of gravity (COG) of club head
 m_{s }mass of club head system, including club head and Club Head

 a_{sz }The measured z_{f}axis 105 acceleration force value
 K Stiffness coefficient of shaft supplied by the golfer or which can
Be determined in the calibration process associated with the user profile entry section of the analysis program
 C Club length
The angle η 401 is found from equation (47):
 C Club length
The curve fit parameter, C_{η}, has an initial value of 0.75.
An iterative solution process is used to solve equations (61), (63), and (64), using (65) for η 401, which has the following defined steps for the discreet data tables obtained by the sensors:
 1. Determine from sample points of a_{sz }the zero crossing position of a_{chsz}. This is the point where the club head acceleration is zero and therefore the maximum velocity is achieved. Because the samples are digitized quantities at discrete time increments there will be two sample points, where a_{chsz }has a positive value and an adjacent sample point where a_{chsz }has a negative value.
 2. Course tune of Ω 601: Use initial approximation values to solve for the numerator of tan (Φ) of equation (63) with respect to the sample point where a_{ch }passes through zero:
 a. Numerator of tan (Φ)={a_{sy}−a_{sz }cos (η) sin (Ω)}
 b. The numerator of tan (Ω) in equation 63 represents the measured value of a_{sy }minus a_{zradial }components resulting from angle Ω with the following conditions at maximum velocity:
 i. Toe down angle Ω, which is at its maximum value at maximum club head velocity, where maximum a_{sz }is achieved at η=0, for which a_{sz}=a_{zradial }From equation (52).
 ii. Angle η 401, which is a function of wrist cock and shaft flex lag/lead, is zero when maximum velocity is reached and a_{ch }is zero.
 c. Use the multiplying constant C_{Ω} to adjust the Ω 601 equation so that the tan (Φ) numerator function sample point value, equivalent to the first negative sample point value of a_{ch}, is set to the value zero.
 3. Use new course tune value for the Ω 601 function to calculate Φ 501 from equation (63) for all sample points.
 4. Next, fine tune the multiplying constant C_{Ω }of the Ω 601 function by evaluating the slope of Φ 501, for the point pairs before, through, and after maximum velocity.
 a. Examine sample point pairs of the total tan (Φ) function given by equation (63) before maximum velocity, through maximum velocity, and after maximum velocity, evaluating slope variation across sample pairs.
 b. Evaluate sequential slope point pairs comparing slopes to determine a variation metric.
 c. Tune multiplying constant C_{Ω} of Ω 601 function in very small increments until the slope of Φ 501 of all sample point pairs are equivalent.
 d. Now the value of the Ω function is defined but the value of η is still given with the initial value of C_{η}=0.75. Therefore, even though the value of Φ 501 is exact for values very near max velocity where η 401 approaches zero, values of Φ 501 are only approximations away from maximum velocity since Φ 501 is a function of η 401, which at this point is limited by the initial approximation.
 5. Calculate all sample points for the for the following functions:
 a. The fine tuned function Ω 601
 b. Approximate function η 401 with C_{η}=0.75.
 c. Function Φ 501 from equation (63)
 i. Which will be exact for sample points close to maximum velocity
 ii. Which will be an approximation for the sample points away from max velocity because the function η 401 is still an approximate function.
 6. Tune the multiplying curve fit constant C_{η }of the η 401 function using equation (61). This is done by rewriting equation (61) into a form which allows the comparison of a_{sx }minus the a_{sz }components which must be equal to a_{chsz}. The evaluation equation is from (61):
 a.
{a_{sx}+a_{sz }cos (η) cos (φ) sin (η)}/{cos (φ) cos (η)}=a_{chsz}(√{square root over (R cos (η))}/√{square root over (R_{Max}))}
 b. If everything were exact, the two sides of this equation would be equal. If not, they will differ by the variance:
Variance={a_{sx}+a_{sz }cos (η) cos (φ) sin (η)}/{cos (φ) cos (η)}−a_{chsz}(√{square root over (R cos(η))}/√{square root over (R_{Max}))}
 c. This variance metric is summed across a significant number of sample points before and after maximum velocity for each small increment that C_{η} is adjusted.
 d. The minimum summed variance metric set defines the value of the constant C_{η} for the η 401 function.
 7. Compare the value of C_{η }obtained at the conclusion of the above sequence with the starting value of C_{η} and if the difference is greater than 0.1 repeat steps 3 through 7 where the initial value for C_{η }in step 3 is the last iterated value from step 6.d. When the difference is less than 0.1, the final value of C_{η }has been obtained.
 8. Angle α 403 is now solved from equation (23) with η 401 across all sample points:
α=cos^{−1 }((R cos (η)−C)/A)
 a. α 403 represents the sum of wrist cock angle and shaft flex lag/lead angle as defined by α=α_{wc}+α_{sf}.
 b. In a standard golf swing the wrist cock angle is a decreasing angle at a constant rate during the down stroke to maximum club head velocity. Therefore, the angle can be approximated as a straight line from the point where wrist cock unwind is initiated.
 c. The slope of the angle α_{wc }701 is:
 i. [α_{wc }(at wrist cock unwind initiation)−α_{wc }(club head max Velocity)]/ΔT, where ΔT is the time duration for this occurrence.
 d. Since α_{wc }701 goes to zero at the point of maximum velocity and the time duration ΔT is known, the function of angle α_{wc }701 is now defined.
 9. The shaft flex angle α_{sf }702 is now defined as α_{sf}=α−α_{wc }for all sample points during down stroke. Any deviation from the straight line function of α_{wc }701 is due to shaft flex.
The iterative analysis solution described above is based on the club head module being mounted so that the x_{f}axis 104, y_{f}axis 106, and z_{f}axis 105 associated with the club head module 101 are aligned correctly with the golf club structural alignment elements as previously described inFIG. 2 .
Since the module 101 attaches to the top of the club head 201, which is a nonsymmetric complex domed surface, the mounting of the club head module 101 is prone to variation in alignment of the x_{f}axis 104, z_{f}axis 105, and y_{f}axis 106 with respect to the golf club reference structures described in
During mounting of the club head module 101, as shown in
 1. The module 101 being mounted a greater distance away or closer to the club face seam 1002 causing an angle rotation around the y_{f}axis 106 causing the x_{f}axis 104 and z_{f}axis 105 to be misaligned with their intended club structure references. The mathematical label that describes this angle of rotation is λ 1103 (as shown in
FIG. 11 ).  2. The module 101 being mounted closer to or farther away from the club shaft 202 causing an angle rotation around the x_{f}axis 104 causing the y_{f}axis 106 and the z_{f}axis 105 to be misaligned with the intended club structure references. The mathematical label that describes this angle of rotation is κ 1201 (as shown in
FIG. 12 ).
 1. The module 101 being mounted a greater distance away or closer to the club face seam 1002 causing an angle rotation around the y_{f}axis 106 causing the x_{f}axis 104 and z_{f}axis 105 to be misaligned with their intended club structure references. The mathematical label that describes this angle of rotation is λ 1103 (as shown in
The issue of mounting angle variation is most prevalent with the club head module 101 being rotated around the y_{f}axis. As shown in
For a linear acceleration path the relationship between true acceleration and that of the misaligned measured value of a_{sx }is given by the following equations where a_{sxtrue }is defined as what the measured data would be along the x_{f}axis 104 with α=0 1103 degrees. A similar definition holds for a_{sztrue }along the z_{f }axis 105. Then:
a_{sxtrue}=a_{sx}/cos (λ) 66.
a_{sztrue}=a_{sz}/cos (λ) 67.
However, the travel path 307 is not linear for a golf swing which creates a radial component due to the fixed orientation error between the offset module measurement coordinate system and the properly aligned module measurement coordinate system. As a result, any misalignment of the club head module axis by angle λ creates an a_{zradial }component as measured by the misaligned x_{f}axis 104. The a_{zradial }component contributes to the a_{sx }measurement in the following manner:
a_{sx}=a_{sxtrue}+a_{sz }sin (λ) 68.
The angle λ 1103 is constant in relation to the club structure, making the relationship above constant, or always true, for the entire swing. The detection and calibrating correction process of the mounting variation angle λ 1103 is determined by examining equations (50) and (53) at the point of maximum velocity where by definition:
 η goes to zero
 a_{ch }goes to zero
Therefore, at maximum velocity a_{sxtrue }must also go to zero. At maximum velocity:
a_{sxtrue}=a_{sx}−a_{sz }sin (λ)=0 69.
Now the measured data arrays for both the affected measurement axis x_{f}axis 104 and z_{f}axis 105 must be updated with calibrated data arrays.
a_{sxcal}=a_{sx}−a_{sz }sin λ 71.
a_{szcal}=a_{sz}/cos λ 72.
The new calibrated data arrays a_{sxcal }and a_{szcal }are now used and replaces all a_{sx }and a_{sz }values in previous equations which completes the detection and calibration of club head module mounting errors due to a error rotation around the y_{f}axis 106.
Now the final detection and calibration of the club head module 101 mounting error angle κ 1201 around the x_{f}axis 104 can be done. As shown in
The detection of mounting error angle κ 1201 is achieved by evaluating C_{Ω} resulting from the iterative solution steps 2 though 4 described earlier. If C_{Ω} is not very close or equal to one, then there is an additional a_{z}radial contribution to a_{sy }from mounting error angle κ 1201. The magnitude of mounting error angle κ 1201 is determined by evaluating Ω 601 at maximum velocity from equation (64) where for no mounting error C_{Ω}=1. Then the mounting angle κ 1201 is determined by:
κ=(C_{Ω}−1)(dm_{s}a_{sz }cos (η))/(C(KC+m_{s}a_{sz }cos (η))) 73.
As previously described for mounting angle error λ, the mounting error angle κ 1201 affects the two measurement sensors along the y_{f}axis 106 and the z_{f}axis 105. Consistent with the radial component errors resulting from the λ1201 mounting angle error, the κ 1201 mounting angle error is under the same constraints. Therefore:
a_{sycal}=a_{sy}−a_{sz }sin (κ) 74.
a_{szcal}=a_{sz}/cos λ 75.
The new calibrated data arrays a_{sycal }and a_{szcal }are now used and replaces all a_{sy }and a_{sz }values in previous equations which complete the detection and calibration of club head module mounting errors due to a mounting error rotation around the x_{f}axis 104.
Thereby, the preferred embodiment described above, is able to define the dynamic relationship between the module 101 measured axes coordinate system and the inertial acceleration force axes coordinate system using the multilever model and to define all related angle behaviors, including module 101 mounting errors.
All of the dynamically changing golf metrics described as angle and or amplitude values change with respect to time. To visually convey these metrics to the golfer, they are graphed in the form of value versus time. The graphing function can be a separate computer program that retrieves output data from the computational algorithm or the graphing function can be integrated in to a single program that includes the computational algorithm.
The standard golf swing can be broken into four basic interrelated swing segments that include the backswing, pause and reversal, down stroke, also called the powerstroke, and followthrough. With all angles between coordinate systems defined and the ability to separate centrifugal inertial component from inertial spatial translation components for each club head module measured axis, the relationships of the data component dynamics can now be evaluated to define trigger points that can indicate start points, end points, or transition points from one swing segment to another. These trigger points are related to specific samples with specific time relationships defined with all other points, allowing precise time durations for each swing segment to be defined. The logic function that is employed to define a trigger point can vary since there are many different conditional relationships that can be employed to conclude the same trigger point. As an example, the logic to define the trigger point that defines the transition between the back swing segment and the pause and reversal segment is:
By defining the exact time duration for each swing segment and understanding that each swing segment is related and continuous with an adjacent segment, the golfer can focus improvement strategies more precisely by examining swing segments separately.
By incorporating a low mass object that is used as a substitute strike target for an actual golf ball the time relationship between maximum club head velocity and contact with the strike target can be achieved. The low mass object, such as a golf waffle ball, can create a small perturbation which can be detected by at least one of the sensor measurements without substantially changing the characteristics of the overall measurements. In addition, the mass of the substitute strike object is small enough that it does not substantially change the inertial acceleration forces acting on the club head or the dynamically changing relationship of the inertial axes coordinate system in relation to the module measured axes coordinate system.
The data transfer from the club head module 101 to a user interface can take place in two different ways: 1) wirelessly to a receiver module plugged into a laptop or other smart device, or 2) a wired path to a user module that is attached to the golf club near the golf club grip.
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The approach developed above can also be applied for a golf club swing when the golf club head contacts the golf ball. For this case, the above analysis returns the values of the three angles and club head velocity just before impact. Using these values along with the sensor measurements after impact describing the change in momentum and the abrupt orientation change between the module'"'"'s measured sensor coordinate system and the inertial motional acceleration force coordinate system will enable the determination of where on the club head face the ball was hit, and the golf ball velocity.
The ability to correlate the acceleration measurements and resulting dynamics golf metrics time line to a spatial reference allows key dynamics swing metrics to be further evaluated in the contexts of space. This offers golfers great analytical benefit when evaluating a free golf swing that does not impact an object. The swing metrics can be analyzed in relation to key spatial reference locations, such as anticipated ball location, peak elevation of backswing, peak elevation of powerstroke, peak elevation of follow through and others such as club head travel path 90 degrees out from right or left shoulder. These spatial reference points all offer their own set of benefits when analyzing the varied dynamic swing metrics in reference to spatial locations near the club head travel path. True swing efficiency and effectiveness can now be evaluate without the motional perturbations that occur when the golf club strikes and object such as a golf ball. The benefit of analyzing a free swing as opposed to an impact swing can be demonstrated with a fundamental example of evaluating swing efficiency with respect to the dynamic swing metric of club head velocity which is directly related to achievable ball trajectory distance. In this example a golfer may want to improve and optimize their swing style for maximum distance. Using free swing measurements and analysis that provides dynamic club head velocity in relation to an anticipated ball location allows the golfer to evaluate if they are reaching maximum club head velocity before, at, or after the anticipated ball location. This is not possible with club/ball impact because of the abrupt velocity reduction resulting from impact eliminating the ability to determine where maximum velocity would have occurred after impact. Further, the swing style can be modified for maximum power and efficiency by aligning club head maximum velocity with anticipated ball location for maximum energy transfer at anticipated ball location. The same benefit themes demonstrated with the club head velocity example also can be applied to all dynamics swing metrics such as but not limited to, club head spatial acceleration and maximum club head spatial acceleration, club face angle and where the club face angle reached a square position, shaft flex lag/lead angle and many others.
These measurement and evaluation capabilities are not available with conventional swing analyzers that rely impacting with a golf ball, because the impact itself abruptly changes all swing metrics including club head orientation, club head motion and shaft actions and therefore eliminates the possibility of comprehensive analysis of true swing performance.
Several embodiments of correlation methods are demonstrated using the integration of conventional Receiver Signal Strength Indicator (also referred to as RSSI) functionality into the previously recited swing measurement and analysis system. The system uses RSSI to determine relative spatial relationships between the Club Head Module 101 (first module) and the USB Module 1301 (second module) during the entire swing. The spatial relationships, such as nearest together or farthest apart or equivalents or ratios are used to identify club head location(s) at a point or points in time that correspond to time location(s) on the acceleration measurement time line thereby correlating space an time.
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A software application of the first embodiment of the timespace correlation resides on User Interface 1302 computational engine and comprising all functions for user interface, display and data processing of measurements within software application. The data processing of measurements includes the previously recited algorithms for club head alignment calibration and acceleration data analysis. Further, software application implements a third algorithm that processes the receiver signal strength measurements in conjunction with synchronized acceleration measurements to determine time space correlation. The third algorithm processes steps of the first embodiment of the timespace correlation include the step of:
 1. Digitally low pass filter RSSI measured time line data to reduce effects of RF multipath fading
 2. Processes filtered RSSI data using peak detection and minimum detection methods to determine time points on time line of highest and lowest signal strength
 3. Flag and label time point of peak RSSI measurement defining the relationship of Club Head Module 101 and USB Module 1301 at minimum spatial separation.
 4. Flag and label time point of minimum RSSI measurement defining the spatial relationship of Club Head Module 101 and USB Module 1301 at maximum spatial separation.
 5. Label the correlated time points on the acceleration measurements and dynamics golf metrics results time line defining space time relationship.
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A software application of the second embodiment of the timespace correlation, resides on User Interface 1302 computational engine and comprising all functions for User Interface'"'"'s 1302, display and data processing of measurements within software application. The data processing of measurements includes the previously recited algorithms for Club Head Module 101 Alignment Calibration and Acceleration Data Analysis. Further, software application implements a third algorithm that processes the receiver signal strength measurements in conjunction with synchronized acceleration measurements to determine time space correlation. The third algorithm of the second embodiment of the timespace correlation includes the steps of:
 1. A means of calculating time delay between measurements made at Club Head Module 101 (first module) and measurements made at USB Module 1301 (second module) comprising the steps of:
 a. Define time duration of processing at Club Head Module 101 after acceleration signal is in a sample and hold state by multiplying the time duration of 1 instruction multiplied by number of instruction to complete the following tasks
 i. Data capture
 ii. Data formatting for wireless transmission protocol
 b. If wireless communication protocol uses Time Division Multiple Access (TDMA) structure, define the time duration between wireless packet transmissions based on that predefined structure.
 c. Define time duration of signal propagation=0
 d. Define time duration of processing at USB Module 1301 by multiplying the time duration of 1 instruction multiplied by number of instruction to complete the following tasks:
 i. receive and demodulate Club Head Module 101 transmitted signal
 ii. Receiver signal strength output from RSSI circuitry at a sample and hold state for measurement
 e. Sum steps (a.) and (b.) and (c.) and (d.) together to define time delay between measurements to define time delay between Club Head Module 101 measurements and USB Module 1302 measurements
 a. Define time duration of processing at Club Head Module 101 after acceleration signal is in a sample and hold state by multiplying the time duration of 1 instruction multiplied by number of instruction to complete the following tasks
 2. Time shift the measurement time line taken at the Club Head Module 101 (first module) in relation to measurements time line taken at USB Module 1301 (second module) by said time delay to define a single time line comprising all measurements synchronized and aligned in time.
 3. Digitally low pass filter RSSI measured time line data to reduce effects of RF multipath fading
 4. Processes filtered RSSI data using peak detection and minimum detection methods to determine time points on time line of highest and lowest signal strength
 5. Flag and label time point of peak RSSI measurement defining the relationship of Club Head Module 101 and USB Module 1301 at minimum spatial separation.
 6. Flag and label time point of minimum RSSI measurement defining the spatial relationship of Club Head Module 101 and USB Module 1301 at maximum spatial separation.
 7. Label the correlated time points with acceleration measurements and resulting dynamics golf metrics time line defining space time relationship.
 1. A means of calculating time delay between measurements made at Club Head Module 101 (first module) and measurements made at USB Module 1301 (second module) comprising the steps of:
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A software application of the third embodiment of the timespace correlation for this example, resides on User Interface 1302 computational engine and comprising all functions for User Interface, display and data processing of measurements within software application. The data processing of measurements includes the previously recited algorithms for Club Head Module 101 alignment calibration and acceleration data analysis. Further, software application implements a third algorithm that processes all receiver signal strength measurements from all antennas in conjunction with synchronized acceleration measurements to determine time space correlation. The third algorithm of the third embodiment of the timespace correlation include the steps of:
 1. A means of calculating time delay between measurements made at Club Head Module 101 (first module) and synchronized measurements made at USB Module 1301 (second module) for internal and remote antennas comprising the steps of:
 a. Define time duration of processing at Club Head Module 101 after acceleration signal is in a sample and hold state by multiplying the time duration of 1 instruction multiplied by number of instruction to complete the following tasks
 i. Data capture
 ii. Data formatting for wireless transmission protocol
 b. If wireless communication protocol uses Time Division Multiple Access (TDMA) structure, define the time duration between wireless packet transmissions based on that predefined structure.
 c. Define time duration of signal propagation=0
 d. Define time duration of processing at USB Module 1301 by multiplying the time duration of 1 instruction multiplied by number of instruction to complete the following tasks:
 i. receive and demodulate Club Head Module 101 transmitted signal
 ii. Receiver signal strength output from parallel RSSI circuitries at a sample and hold state for measurement
 e. Sum steps (a.) and (b.) and (c.) and (d.) together to define time delay between measurements to define time delay between Club Head Module 101 measurements and USB Module 1302 measurements
 a. Define time duration of processing at Club Head Module 101 after acceleration signal is in a sample and hold state by multiplying the time duration of 1 instruction multiplied by number of instruction to complete the following tasks
 2. Time shift the measurement time line taken at the Club Head Module 101 (first module) in relation to the synchronized group of received signal strength measurements time line taken at USB Module 1301 (second module) for internal and remote antennas 1803 and 1804 to define a single time line with calculated said time delay between measurements removed.
 3. Digitally low pass filter all RSSI measurements time lines separately to reduce effects of RF multipath fading.
 4. Processes each filtered RSSI data set separately using peak detection and minimum detection methods to determine time points on time line of highest and lowest signal strength for each predetermined location
 5. Process each filtered RSSI data set in relation to one another and evaluate for equivalent RSSI measurements at a single time point.
 6. Flag and label each time point of each peak RSSI measurement time line defining the relationship of Club Head Module 101 and USB Module 1301 at minimum spatial separation and further Club Head Module 101 and each remote antenna at minimum spatial separations.
 7. Flag and label each time point of each minimum RSSI measurement time line defining the relationship of Club Head Module 101 and USB Module 1301 at maximum spatial separation and further Club Head Module 101 and each remote antenna at maximum spatial separations.
 8. Flag and label each time point of each occurrence when two RSSI measurements time lines are equivalent at the same time point defining the relationship of Club Head Module 101 and any two antennas have equal spatial separation.
 9. Label the correlated time points with acceleration measurements and resulting dynamics golf metrics time line defining time space relationship.
 10. Use flagged time line points and predetermined locations of each antenna to map 3 dimension space club head travel on club head travel path.
 1. A means of calculating time delay between measurements made at Club Head Module 101 (first module) and synchronized measurements made at USB Module 1301 (second module) for internal and remote antennas comprising the steps of:
Invention anticipates that using three antenna located at any three predefined locations can map spatial club head travel in three dimension and correlate to acceleration measurement time line, however, portions of club head travel path can be more accurately represent spatially while reducing accuracy of other portions of the swing, with strategic predetermined locations focusing on providing more accuracy to a given portion or portions of a swing. In the example recited above the accuracy of the backswing and the powerstroke along with anticipated ball location have emphasis with regards to accuracy. In addition use of more than three antennas each with a predetermined location can increase three dimensional spatial accuracy of club head travel path over broader coverage of entire swing.
A forth embodiment of the time space correlation system provides for RSSI measurement capabilities at both the Club Head Module 101 (first module) as described in first embodiment and shown in
A software application of the fourth embodiment of the timespace correlation for this example, resides on User Interface 1302 computational engine and comprising all functions for User Interface, display and data processing of measurements within software application. The data processing of measurements includes the previously recited algorithms for Club Head Module 101 alignment calibration and acceleration data analysis. Further, software application implements a third algorithm that processes all receiver signal strength measurements from all antennas in conjunction with synchronized acceleration measurements to determine time space correlation. The third algorithm of the fourth embodiment of the timespace correlation includes the steps of:
 1. Digitally low pass filter Club Head Module 101 (first module) RSSI measured time line data to reduce effects of RF multipath fading
 2. Digitally low pass filter USB Module (second module) RSSI measured time line data to reduce effects of RF multipath fading
 3. Processes both filtered RSSI time line measurements separately using peak detection and minimum detection methods to determine time points on time line of highest and lowest signal strength
 4. Define time delay as time separation between RSSI measurements peaks taken at Club Head Module 101 (first module) and USB Module 1301 (second module)
 5. Time shift Club Head Module 101 (first module) measurement time line in relation to USB Module (101) measurement time line by said time delay to define a single time line comprising all measurements synchronized and aligned in time with respect to time of measurement.
 6. Flag and label time point of peak RSSI measurement defining the relationship of Club Head Module 101 and USB Module 1301 at minimum spatial separation.
 7. Flag and label time point of minimum RSSI measurement defining the spatial relationship of Club Head Module 101 and USB Module 1301 at maximum spatial separation.
 8. Label the correlated time points with acceleration measurements and resulting dynamics golf metrics time line defining time space correlation.
It is also anticipated that other embodiment arrangements of RSSI measurements exist and are covered by this invention. The may include a combination of embodiments 3 and 4 where RSSI is measure at Club Head Module 101 and USB Module 1301 connected further with remote antennas that transit signal and measure RSSI of received signals.
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Although specific embodiments of the invention have been disclosed, those having ordinary skill in the art will understand that changes can be made to the specific embodiments without departing form the spirit and scope of the invention. The scope of the invention is not to be restricted, therefore, to the specific embodiments. Furthermore, it is intended that the appended claims cover any and all such applications, modifications, and embodiments within the scope of the present invention.