GB2440510A

GB2440510A - Exercise article

Info

Publication number: GB2440510A
Application number: GB0615564A
Authority: GB
Inventors: Parm Sangha
Original assignee: Individual
Current assignee: Individual
Priority date: 2006-08-04
Filing date: 2006-08-04
Publication date: 2008-02-06
Also published as: WO2008015465A1; GB0615564D0

Abstract

A human propelled projectile 1, such as a ball, comprising one or more 3-axis accelerometers 10, 11, 12, 13, a signal processor 19 for analyzing an output of the accelerometers 10, 11, 12, 13, to provide information about a motion of the projectile 1 and a memory for storing said information about the motion of the projectile 1. The projectile 1 can provide a read-out of exercise parameters, such as height of throw or frequency of bounces, via a display 2. An alarm is preferably provided to be activated if a parameter of the motion falls below a certain limit. An input device may be provided for setting the limit and can be actuated by shaking, tapping or flipping the projectile.

Description

EXERCISE ARTICLE

The present invention relates to a human-propelled projectile, such as a ball, for use in human exercise and play.

It is widely recognised that obesity and lack of exercise are growing health problems.

The World Health Organisation has estimated that 60% of the world's population does not exercise enough, and that 2 million people die every year through inactivity.

Furthermore, it is estimated that more than 10% of children, and more than 20% of young adults in the United Kingdom are clinically obese. Therefore, a need exists for improved devices to promote physical exercise.

US-A-5779576 describes a throw-measuring football having an ellipsoidal shape and a tail fin to stabilise the flight of the ball. A single-axis accelerometer is provided inside 1 5 the football, and the distance travelled by the ball is determined by measuring the initial velocity and the time of flight of the ball. The primary purpose of this ball is to assist the training of American football players.

US-A -45 77865 describes an athletic ball containing a pressure sensor and a display device. The sensor detects the pressure pulse inside the ball when it strikes a surface.

The number of such impacts is displayed.

The present invention provides a human propelled projectile, comprising: one or more 3-axis accelerometers; a signal processor for analyzing an output of the accelerometer to provide information about a motion of the projectile; and a memory for storing said information about the motion of the projectile.

Preferably, the human-propelled projectile is a ball. The ball is preferably substantially spherical. The diameter of the ball is typically about 5cm to about 30cm. The weight of the projectile is typically from about lOOg to about 1kg. Suitably, the 3-axis accelerometers and the system controller are enclosed in cushioned pockets inside the projectile. For example, the projectile may be filled with a fibrous or foam cushioning material. The projectile may be tethered by a string, but more usually it is free to be thrown or struck in any direction.

The three-axis accelerometers may suitably be micro-electromechanical (MEMS) accelerometers These are solid-state devices that measure the changes in capacitance caused by the relative movement of moving and fixed structures created in a silicon substrate using wafer processing techniques. The accelerometers typically comprise an interface chip that generates a digital output, typically a serial digital output. The devices are commercially available, for example from SlMicroelectronjcs Preferably, there are at least two of the three-axis accelerometers, positioned at different locations within the projectile. The optimum location for the accelerometers is directly opposite each other on a line through the center of mass of the projectile. Suitably, the accelerometers in this configuration are equidistant from the center of mass. Whilst it can be shown that, even with two 3-axis accelerometers positioned at two locations with in the projectile it is not possible uniquely to determine the force and moment on the body. However, provided that the motion does not impart too much spin in relation to the sampling frequency of the accelerometers it is possible to calculate the trajectory parameters with reasonable accuracy using just two accelerometers. A larger number of accelerometers, for example four or six accelerometers, can be used for greater accuracy.

The orientation of the accelerometers is not important but the initial moment of inertia tensor of the object should be symmetrical To achieve this, small counterweights could be placed in the ball.

The sampling frequency is suitably from about 100Hz to about 2.5 kHz, which is the maximum frequency for the accelerometer's z-charmej. Sampling accuracy is typically 16-bits over the full-scale deflection of the accelerometers.

Suitably, the information about the motion of the projectile comprises one or more of the following parameters: maximum speed, mean speed, distance travelled (total distance and/or horizontal distance), position, maximum height attained, mean frequency of bounces, total number of bounces, spin frequency, kinetic energy expended, mean frequency of projections and total number of projections. The term "projections" refers to bounces, throws or strikes applied to the article. The use of 3-axis accelerometers allows all of these parameters to be calculated independently of the shape of the projectile or the path followed.

It will be appreciated that, for the calculation of these parameters, the signal processor must include a clock circuit so that acceleration can integrated over time to determine velocity and position values. Typically, the clock will be started and stopped (either automatically or by the user) at the start and end of an exercise program, and the parameters achieved can then be displayed.

Preferably, the projectile further comprises a display positioned to be visible from the exterior of the projectile. Typically, the display is adapted to display one or more of the said parameters of motion. The different parameters may displayed simultaneously, but more usually the different parameters are displayed individually in response to display commands entered through soft-key programming using one or more input keys associated with the display. In certain embodiments, the programming may be carried out wholly or in part by mechanical actuation of the projectile, for example the user could scroll through a menu by flipping or tapping the projectile.

In certain embodiments, for example where it is expected that the projectile may be struck or bounced hard enough to damage a display on the outside thereof, the display may be located inside the projectile, at a protected or cushioned location accessible by Opening the projectile (for example by Opening a reclosable fastener on the projectile) after the exercise program. In yet other embodiments, there may be no display in the projectile but simply a data port for downloading the measured parameters to an external display device after the exercise program. The same or different data port can be used for uploading exercise parameter thresholds as discussed below.

In certain embodiments, the projectile further comprises an alarm which may be activated by the system controller in the course of an exercise program when one or more of the parameters of motion falls below a respective predetermined threshold. The alarm may for example comprise a light (typically a light-emitting diode), or an audible alarm produced by a sound emitter. This enables the user to determine if they are achieving an exercise regime defined by the predetermined thresholds. For example, the alarm may be activated if the article is not being thrown high enough, or not being thrown, bounced or struck with sufficient frequency.

The predetermined thresholds may be fixed. However, preferably the user can define the threshold values of the parameters of motion so as to customise their exercise program.

Accordingly, the projectile preferably further comprises an input device for inputting said predetermined threshold in respect of one or more of said parameters. The input device may, for example, comprise one or more keys associated with the display and programmable in conventional soft-key programming fashion to customise the thresholds. The input device may be mechanically actuated by flipping, shaking or tapping the projectile as hereinbefore described.

In certain embodiments, the article further comprises automatic turn-on means, which are sensitive to motion, for turning on or re- setting the system controller. For example, in certain embodiments the device is reset by shaking it a predetermined number of times.

In certain embodiments, the article further comprises automatic shut-off means for turning off the display after a predetermined period of immobility.

An embodiment of the present invention will now be described further, by way of example, with reference to the accompanying drawings, in which: Figure 1 shows a top plan view of a ball according to the present invention; and Figure 2 shows a schematic cross-section through the ball of Fig. 1.

Referring to the drawings, the ball 1 has generally the appearance of a standard soccer ball. The outer diameter of the ball is about 15cm. On the outer surface of the ball is located a display (e.g. liquid crystal) 2 with input keys 3, 4, 5, 6, LED alarm light 7 and buzzer 8. (In alternative embodiments, some or all of the input keys could be omitted, and programming could be performed via the accelerometers by tapping, flipping or shaking the ball.) Referring to Fig. 2, the interior of the ball 1 is filled with packing material (e.g. a closed-cell polymer foam) to provide cushioning. Two three-axis accelerometers io, ii, are located opposite each other on a line through the center of the ball and equidistant therefrom each at a distance from the center of about 45mm. To validate the accuracy in this test projectile, two further three-axis accelerometers i 2,13 are located opposite each other on a perpendicular line through the center of the ball and equidistant therefrom. The accelerometers are mounted on respective, curved printed circuit boards 14,l5,16,17 The accelerometers are MEMS devices with serial digital output, available from STMicroelectronics under the designation LIS3LO2D. A rechargeable 9-volt battery 18 is located in a central pocket in the foam and can be recharged through socket (not Shown) in the side of the ball. A microprocessor based signal processor 19 is also embedded in the foam core of the ball, and is Connected through suitable connectors (not Shown) to the battery 18 and to the accelerometers.

In use, the ball may be activated by vigorous shaking, or by pressing any of the soft keys. This resets the display 2. The operator can then program exercise thresholds into the ball with the keys 3,4,5,6 using conventional soft-key programming techniques. For example, the display may prompt the user to select one or more of: minimum number of bounces, minimum frequency of bounces, minimum height of throw, and so forth.

When the program is complete, the display 2 prompts the user to start the exercise regime. If the user fails to achieve the programmed parameters during the exercise regime, then alarm light 7 and buzzer 8 will indicate failure. After exercise, the keys can again be manipulated to read out from the display parameters such as the average bounce frequency achieved, average height achieved, or any of the other parameters identified above.

The following is a discussion of the mathematical background for the signal processing program. Whilst this discussion is expressed in terms of the accelerometer configuration shown in the drawings, it will be appreciated that the principles of the method are applicable to different accelerometer configurations or projectile shapes.

Introduction

The equations of motion for a rigid body can be written mx=F (1) L=M (2) L=RIRT (3) R=QR (4) The variables are defined below. Equation 1 is the conservation of linear momentum and F = . F is the sum of all the forces acting on the ball. Equation 2 is the conservation of angular momentum and M = . (z -x) A F; is the total momenta acting on the body (z1 is the position force F; acts). The matrix is a function of the vector a defined by equation 23.

Equation 3 gives the relation between the angular velocity and angular momentum. The moment of inertia tensor is defined by: I = fJJp(rr -rrT)dr (5) There is a very important simplification if the ball is sufficiently symmetric so that I is proportional to the identity matrix. In this case RIRT = I and 1 can be treated as a scalar rather than a vector. If this is not the case the ball will wobble in fight. The electronics within the ball may make the ball asymmetric, but this can easily be countered by the positioning of internal weights. This is a very important simplification to the equations which will henceforth assume is true. L can then be eliminated as a variable and equations 2 and 3 combined to give: Ja=M (6) The simplification is because equations of motion no longer depend on the orientation R, which evolves according to equation 4.

Suppose in the reference configuration that x = 0 and y is some other point in the ball.

The position of this point later in time is given by x+Ry (7) and its velocity will be ---(x+Ry)=x+Ry=x+cjy (8) di Differentiating once more the acceleration is (9)

I

An accelerometer at position y experiences the difference between the acceleration at this point and gravity. So that the measured acceleration will be a=RTg_._M(1?YLQ2Ry] (10) The inertial guidance problem is then to estimate F and M from measurements of acceleration a. at different location y. and to use these to then integrate the equations of motion so as to know the position, and orientation of the ball at each moment in time.

Suppose we have two sensors at y1 and y2 measuring accelerations a1 and a2. After multiplying through by R and using Ri?T 1 we have (II) m I F MA(Ry2) 2 Ra2 = g----------Q Ry2 (12) m I Subtracting the two equations and defining R(y2 -y,) = b we get R(a, -a2) + MA [R(y, -y2)J+ 2R(y, -y2) = 0 (13) This equation only has a solution if [(a, ._a2)+RTc?R(y -y2)J.(y -y2)=0. This condition on the accelerations should always hold when the ball is behaving as a rigid body. This can be used to check correct functioning of the unit. During a tap or a bounce however when the body deforms and no longer behaves like a rigid body it may not be satisfied. However, this condition means that there are only five independent measurements of acceleration and it is impossible to determine all six unknown variables, 3 components each of F and M. This is clear in the general solution of equation 14 which is RTM fraj_a2)+RTcR(y1 -y2) JA(y -2(y1 -(14) I(Y1-y2) I where 2 can be any number. This uncertainty cannot be eliminated without the measurement of at least one component of acceleration at another location. If this solution is substituted back into equation 11 F can then be solved for, but this solution will also be arbitrary unless y1 is proportional to y2, that is they lie on the same line through the centre of the ball.

If we choose y1 y and y2 -y, that is opposite points on the sphere, when we add equations 11 and 12 we get R(a1-a2)/2=g! (15) Thus the moment force and centrifugal term exactly cancel and we get the force as F=mgmR(a1_a2)/2 (16) For our application the main requirement is an accurate estimation of F however and some uncertainty in M may not matter provided that the ball does not rotate too much in the throwing phase. That is provided we know R and we can assume it to be constant, we can estimate F accurately from this equation and centrifugal and moment forces cancel. The only errors coming from orientation changes during the throw. These can be partly compensated for and estimated since we can estimate M by using the minimum norm solution from equation 14 with A = 0.

Trajectory Phases The ball can be in different states that can be identified as follows. In each case the identification procedure operates by identifying a residual function e that must be small over a series of observations Stationary If the ball is stationary or only being moved slowly then F = 0, M = 0 and w = 0, so that a1 = RTg and a2 = RTg. The residual function is then e=jaj_RTg?+a2_RTg2 (17) R is calculated by minimising e over the sequence thus the orientation of the ball is known.

Free motion In free motion the ball moves along a ballistic trajectory and F = mg, M = 0 so that a1 + a2 = 0 and the residual test is e=ja1 +a2j2 (18) There is also a connection with the angular velocity (aj-a2)+2RT2Ry=O (19) which is the centrifugal acceleration. If the angular velocity is known from the throw phase this can be used as an additional check. Since co is constant in free motion for a symmetnc ball then RTf).R = so this simplifies to (a1 -a2)+2wA(wAy)=o (20) From this equation it is possible to calculate two components of co and this can be used to check or improve the calculation of the total force and moment in the throw phase.

Rolling In the rolling phase there is only a small retarding force and small moment. So this is the same as the stationary phase except that there are centrifugal terms. Thus a1 +a1 = 2RTg, However R is not constant and changes according to its equation of motion, and this must be included in calculating the residual.

e=I(a1 +a2)_2RTgf2 +I(a1 -a2)+2a.A(a)Ay)12 (21) There is another possible phase of motion corresponding to rolling with slipping where there will be a significant retarding force and moment. This could also be detected if necessary.

S

Tapping A tap is characterised by a rapid rise and fall in acceleration with total impulse zero (fa1dt = 0), after subtracting gravity. Precise characterisation is not possible in advance as it depends on how the ball deforms under impact. If the ball resonates this may provide a particularly easy way to detect taps using a filter tuned to the resonance frequency. This may be detected using equation 16, but rather than looking for small values of e a tap is identified with large values.

Bouncing This is similar to tapping except there will be a large residual impulse (fa1dt!= 0) that should be compatible with the impact speed.

Throwing This is the most important stage to accurately identify and track. For a motion to be identified as a throw it must follow the stationary phase and transition to the free motion phase. This distinguishes it from a bounce, which is between two free motion phases, or a tap, which is between to stationary phases. The phase is identified with large accelerations that do not match any of the other conditions. If the throwing motion is such that there is very little orientation change during the throw it is easy to integrate the accelerations directly, after removing gravity, to calculate the resultant linear velocity. If however the ball changes orientation during the throw, the evolution of the orientation must be integrated by estimating the moment and angular velocity. The resultant linear velocity will then be JR(a1 +a2)/2dt (22) Appendix If we define 0 -w -O) 0 -o (23) w 0 then Q is an antisymmetrjc matrix such that fx = (0 A X for all x. Rotation matrices can be parametensed in different ways. The best for our purposes is in terms of unit quatemions q1, q2, q3 and q4 such that q + q + q + q = 1. These require no trigonometric functions and do not suffer from gimbal lock. Then we write q +q -q -q 2q2q3 +2qq4 2q2q4 -2q1q3 R(q) = 2q2q3 -2q1q4 q12 +q -q -q 2q3q4 +2q1q2 (24) 2q2q4 +2q1q3 2q3q4 -2q1q2 q +q -q -q The equation of motion R(q) = =(tv)R(q) can then be written 0 co (O (O q1 =1/2 0 (25) q -a (0 0 a q3 -(0z Wy 0 For constant cv this can be integrated exactly as q' q; 0 (0 c0 0.) q1'=o = cos(ta./2) q2 + sin(t(o/2) x (26) q= U) -(0, W 0 - q - --cv 0 To increase speed the trig functions can be approximate using sin(sw/2) t/2 and cosQv/2) Ji (l2a2 /4). This preserves the normalisation of q.

Various identities hold if w is constant. Consider -(RTc =R) =(R)c =R +(R)Tc =R = RTQTc =R + RTcR RT(QT + =)R = 0 (27) di since is antisymmetric. Thus RTQR that is R and = commute and Rw = Table 1 -Definition of Terms x Centre of mass position x Centre of mass velocity x Centre of mass acceleration 0) Angular velocity L Angular momentum vector L Rate of change of angular momentum vector R Rotation matrix specifying orientation of the ball R Rate of change of rotation matrix Instantaneous rotation vector y General point within the ball a Acceleration measured by a transducer F Total force on the ball M Total moment on the ball m Mass of the ball I Moment of inertia tensor of the ball g Gravity q Quaternion coordinates parameterising R The above embodiment has been described by way of example only. Many other embodiments falling within the scope of the accompanying claims will be apparent to the skilled reader.

Claims

CLAIMS

I. A human propelled projectile, comprising: one or more 3-axis accelerometers; a signal processor for analyzing an output of the accelerometer to provide information about a motion of the projectile; and a memory for storing said information about the motion of the projectile.

2. A projectile according to claim 1, comprising two 3-axis accelerometers situated opposite each other on a line through the center of mass of the projectile.

3. A projectile according to claim 1 or 2, wherein the information about the motion of the projectile comprises one or more of the following parameters: maximum speed, mean speed, distance travelled, position, maximum height attained, mean frequency of bounces, total number of bounces, spin frequency, kinetic energy expended, mean frequency ofprojections and total number of projections.

4. A projectile according to any preceding claim, further comprising a display positioned to be visible from the exterior of the projectile and adapted to display one or more of the said parameters of motion.

5. A projectile according to any preceding claim, wherein the projectile further comprises an alarm which is activated when one or more of the parameters of motion falls below a respective predetermined threshold.

6. A projectile according to claim 5, further comprising a least one input device for inputting said predetermined threshold in respect of one or more of said parameters.

7. A projectile according to claim 6, wherein the input device is actuated by shaking, tapping or flipping the projectile.

8. A projectile according to any preceding claim, further comprising automatic turn-on means, which are sensitive to motion, for turning on the display.

9. A projectile according to any preceding claim, further comprising automatic shut-off means for turning off the display after a predetermined period of immobility.

10. A projectile according to any preceding claim, wherein the projectile is a substantially spherical ball.