DETECTION OF THE HITTING POINT

Abstract

The present invention is directed to a method for determining at least one first coordinate of the hitting point of an object on the surface of an article.

Claims

1. A method for determining at least one first coordinate of the hitting point of an object on the surface of an article, wherein the longitudinal axis of the article defines an x-coordinate, the transverse axis of the article along its width defines a y-coordinate and the perpendicular to the x-coordinate and the y-coordinate defines a z-coordinate, comprising the following steps: (a) measuring at least one first kinematic variable in a first direction at a first point of the article as a function of time; (b) transforming the measured first kinematic variable into the frequency space; and (c) determining the first coordinate of the hitting point on the basis of the transformed kinematic variable in the frequency space.

2. A method for determining a first and a second coordinate of the hitting point of an object on the surface of an article, wherein the longitudinal axis of the article defines an x-coordinate, the transverse axis of the article along its width defines a y-coordinate and the perpendicular to the x-coordinate and the y-coordinate defines a z-coordinate, comprising the following steps: (a) measuring a first kinematic variable in a first direction at a first point of the article as a function of time; (b) measuring a second kinematic variable in a second direction at a second point of the article as a function of time; (c) transforming the measured first kinematic variable and the measured second kinematic variable and/or a linear combination of the measured first and second kinematic variables into the frequency space; and (d) determining the first and second coordinates of the hitting point on the basis of the transformed kinematic variable(s) in the frequency space.

3. The method according to claim 2, wherein the first direction is substantially identical to the second direction.

4. The method according to claim 2, wherein the first point differs from the second point.

5. The method according to claim 1, wherein the determination of the first and/or the second coordinate of the hitting point on the basis of the transformed kinematic variable(s) in the frequency space comprises: (a) determining a characteristic frequency interval; (b) determining at least one characteristic value of the first and/or the second kinematic variable with respect to the characteristic frequency interval; and (c) determining the first and/or the second coordinate of the hitting point on the basis of the at least one characteristic value.

6. The method according to claim 5, wherein the lower limit of the characteristic frequency interval is between 0 Hz and 100 Hz.

7. The method according to claim 5, wherein the upper limit of the characteristic frequency interval is between 20 Hz and 500 Hz.

8. The method according to claim 5, wherein the characteristic value comprises one or a combination of the following values: local or absolute minimum of the first and/or the second kinematic variable in the characteristic frequency interval, local or absolute maximum of the first and/or the second kinematic variable in the characteristic frequency interval, mean value of the first and/or the second kinematic variable in the characteristic frequency interval, mean value of the first and/or the second kinematic variable in a partial interval of the characteristic frequency interval.

9. The method according to claim 5, wherein the first and/or the second coordinate is a function of the characteristic value.

10. The method according to claim 1, wherein the first and/or the second kinematic variable is the acceleration.

11. The method according to claim 2, wherein the determination of the first and/or the second coordinate of the hitting point on the basis of the transformed kinematic variable(s) in the frequency space comprises: (a) determining a characteristic frequency interval; (b) determining at least one characteristic value of the first and/or the second kinematic variable with respect to the characteristic frequency interval; and (c) determining the first and/or the second coordinate of the hitting point on the basis of the at least one characteristic value.

13. The method according to claim 11, wherein the lower limit of the characteristic frequency interval is between 0 Hz and 100 Hz.

13. The method according to claim 11, wherein the upper limit of the characteristic frequency interval is between 20 Hz and 500 Hz.

14. The method according to claim 11, wherein the characteristic value comprises one or a combination of the following values: local or absolute minimum of the first and/or the second kinematic variable in the characteristic frequency interval, local or absolute maximum of the first and/or the second kinematic variable in the characteristic frequency interval, mean value of the first and/or the second kinematic variable in the characteristic frequency interval, mean value of the first and/or the second kinematic variable in a partial interval of the characteristic frequency interval.

15. The method according to claim 11, wherein the first and/or the second coordinate is a function of the characteristic value.

16. The method according to claim 11, wherein the lower limit of the characteristic frequency interval is between 5 Hz and 80 Hz.

17. The method according to claim 11, wherein the lower limit of the characteristic frequency interval is between 10 Hz and 50 Hz.

18. The method according to claim 11, wherein the upper limit of the characteristic frequency interval is between 25 Hz and 400 Hz.

19. The method according to claim 11, wherein the upper limit of the characteristic frequency interval is between 30 Hz and 300 Hz.

20. The method according to claim 5, wherein the lower limit of the characteristic frequency interval is between 5 Hz and 80 Hz.

Description

[0017] In the following, preferred embodiments of the present invention are described in more detail with reference to the Figures, in which

[0018] FIGS. 1a-c show the measuring result of an experiment;

[0019] FIG. 2 shows a flow chart for an exemplary algorithm for the determination of the y-coordinate; and

[0020] FIG. 3 shows a flow chart for an exemplary algorithm for the determination of the x-coordinate.

[0021] FIGS. 1a to 1c illustrate the result of an experiment by means of which it is meant to exemplarily explain the basic idea on which the present invention is based. Even if the following description refers to the example of a tennis racket, the method explained by means of this example basically can be applied to any objects and articles whatsoever.

[0022] The diagrams respectively shown in FIGS. 1a and 1b schematically illustrate a tennis racket (in the experiment discussed here, the Extreme MP model of Head was used) at the racket head of which two sensors are attached whose positions are schematically indicated by respective crosses and the designations HP1 and HP2. The sensors are acceleration sensors of the type Bruel & Kjoer 4501. The string bed of the tennis racket was hit by means of a hammer at defined points, wherein the power of impact is irrelevant since it can be scaled out. The hitting points of the hammer HP11 to HP19 are denoted by crosses in each of the diagrams shown in FIGS. 1a and 1b. The respective acceleration was measured by the sensors at the positions HP1 and HP2 during the hitting moment and subsequently thereto. In FIGS. 1a, the Fourier-transformed signal of the sensor at the position HP1 is illustrated as a function of frequency for the hitting points HP11 to HP15. The corresponding signal for the hitting points HP13, HP 17 and HP18 is illustrated in FIG. 1b. As can be clearly seen, the different curves clearly differ in their shapes from each other depending on the respective hitting point. The curves exhibit, for example, respective minima that occur at clearly different frequencies depending on the respective hitting points. In the case of logarithmic scaling as depicted for the curves of FIG. 1a in FIG. 1c, these minima are even more clearly pronounced and it can be clearly seen how the minima are shifted towards the greater frequencies with increasing distance d of the hitting points from the racket handle.

[0023] The idea of the present invention is based on generating a correlation between the specific curve shape in the frequency space and the actual hitting point of the ball (i.e., the object) on the string bed (i.e., the surface of the article). Once such a correlation has been established empirically, the hitting point of the ball can be determined in a simple way by measuring the acceleration and transforming the measuring signal into the frequency space. This approach can analogously be applied, for example, to the situation of a bird hitting on the wing of an airplane. If the typical hitting speed and the typical weight of such a bird are known, a correlation between the specific curve shape of the measuring signal in the frequency space and the actual hitting point of the bird on the wing can be determined empirically.

[0024] As apparent from the example of FIG. 1, it is generally possible for this purpose to define different characteristic values on the basis of which the correlation can be made. The curves in FIG. 1, for example, differ not only in the positions of their minima but also, for example, in differently pronounced maxima or in different amplitudes at, for example, 120 Hz. Therefore, it is emphasized that the exemplary embodiments of specific algorithms for the determination of the x-coordinate and/or the y-coordinate of the hitting point as described in more detail in the following are only preferred embodiments which, however, are not to be understood as being limiting. In fact, other characteristics of the different curves in the frequency space can be determined by means of which conclusions with respect to the position of the hitting point can be drawn.

[0025] FIGS. 2 and 3 illustrate a specific embodiment of a method for determining an x-coordinate as well as a y-coordinate according to the invention. The diagram shown in FIG. 2 schematically illustrates an article with a definition of the x-coordinate and the y-coordinate, wherein the origin of the coordinate system is formed by the centroid of the string bed. One acceleration sensor each can be arranged at one or more of the positions S.sub.1, S.sub.2 and S.sub.3. The acceleration sensor S.sub.3, however, is not necessary for the embodiment discussed here. The only acceleration sensors required are the two acceleration sensors S.sub.1 and S.sub.2, which are preferably attached at the two arms or rather are respectively arranged at the transition of each of the arms into the bridge. Preferably, the acceleration sensors S.sub.1 and S.sub.2 measure the acceleration along the z-direction, i.e. perpendicular to the x-coordinate and the y-coordinate, over a period of preferably 2 s at a sampling rate of preferably 10,000 s.sup.1.

[0026] Each of FIGS. 2 and 3 schematically depicts the measuring signals of the acceleration as functions of time of the two sensors S.sub.1 and S.sub.2 as S.sub.1(t) and S.sub.2(t), respectively. FIG. 2 depicts a preferred flow chart for determining the y-coordinate, while FIG. 3 depicts a preferred flow chart for determining the x-coordinate.

[0027] In the case of the determination of the y-coordinate as exemplarily illustrated in FIG. 2, firstly the power spectral density (psd) of the measured signals S.sub.1(t) and S.sub.2(t) is determined. In other words, the measured kinematic variable is transformed into the frequency space. To this end, for example, a discrete Fourier transformation, such as, e.g., FFT (fast Fourier transformation) may be used. Each of the transformed signals is subsequently filtered. The filtering step can be performed by means of known techniques, such as, for example, a digital bandpass filter (e.g. the third order Butterworth filter). Subsequently, a characteristic value of the transformed signal is determined on the basis of a characteristic frequency interval. In the illustrated embodiment, the characteristic frequency interval is [50 Hz, 100 Hz] and the characteristic value is the mean value of the transformed function in this frequency interval. In the case of, for example, a wing of an airplane instead of a tennis racket, the characteristic frequency interval may be at considerably lower frequencies and for example be [0 Hz, 20 Hz] or [5 Hz, 25 Hz]. If the mean values of the sensors S.sub.1 and S.sub.2 thus determined are denoted by S.sub.1y and S.sub.2y, respectively, the y-coordinate of the hitting point can be determined by means of the following formula, wherein the values of S.sub.1y and S.sub.2y are to be indicated in the unit m/s.sup.2 and the result provides the y-coordinate in cm:

y=(S.sub.2yS.sub.1y)2.39

[0028] This formula was heuristically determined for a specific tennis racket. In the case of another type of racket and in particular in the case of another article or body, such as, for example, a wing of an airplane, the individual numerical values of the above formula may considerably deviate from the embodiment discussed here. Furthermore, as already mentioned, it may be advantageous in the case of another article to determine another characteristic frequency interval and/or another characteristic value.

[0029] FIG. 3 depicts the corresponding algorithm for the exemplary determination of the x-coordinate in a flow chart. In the present embodiment, firstly the two measuring signals S.sub.1(t) and S.sub.2(t) of the sensors S.sub.1 and S.sub.2 are added and the thus obtained signal S(t) is converted into a power spectral density S(f) by means of, for example, a discrete Fourier transformation (DFT). Subsequently, an upper limit frequency f.sub.og as well as a lower limit frequency f.sub.ug of the characteristic frequency interval [f.sub.ug, f.sub.og] is determined. Preferably, the interval is [10 Hz, 200 Hz]. The minimum of S(f) and the respective frequency f.sub.min are then determined on the basis of this characteristic frequency interval. The x-coordinate is then a function of the respective minimum frequency f.sub.min:x=x(f.sub.min). In a preferred embodiment, the x-coordinate of the hitting point can be determined by means of the following formula, wherein the frequency values are to be indicated in the unit Hz and the result provides the x-coordinate in cm:

x=(f.sub.min150)/5.7, if f.sub.min<170

x=(f.sub.min210)/10, if f.sub.min<170

[0030] Alternatively, the x-coordinate can also be a function of the minimum frequency as well as the two frequencies of the characteristic frequency interval:

x=x(f.sub.min, f.sub.ug, f.sub.og)

[0031] As has been explained several times, these two exemplary embodiments are specific examples which by no means should be considered to be limiting. Rather, this example is only intended to explain that the finding of a precise algorithm correlating a kinematic variable in the frequency space with a coordinate of the hitting point actually works. However, this algorithm can generally be modified in various ways and empirically adapted to the geometries and vibration behaviors of many different articles. However, on the basis of the above explained example, the knowledge of the specific vibration behavior of a specific article will enable the person skilled in the art to determine a characteristic frequency interval corresponding to this vibration behavior as well as an appropriate characteristic value. The determination of equations corresponding to the equations indicated above for the case of the tennis racket is then possible to the person skilled in the art by simple experiments.