VALIDATION OF THE MEASUREMENT SYSTEM

RELIABILITY AND VALIDITY OF USING A ROTARY DIGITAL ENCODER FOR KINEMATIC MEASUREMENT DURING BALLISTIC MOVEMENTS

INTRODUCTION

Resistance training programs have traditionally involved the monitoring of weight lifted, repetitions and sets completed.  However, recent research has shown than volume of training is best quantified by the total work done (Kang, Martino, Russo, Ryder & Craig, 1996).  Further, in terms of maximal power performance, the velocity of movement, force, and power output are important factors which influence the resulting training adaptations (Wilson, Newton, Murphy & Humphries, 1993; Newton, Kraemer, Häkkinen, Humphries & Murphy, 1996).  Therefore, the accurate measurement of the displacement, velocity, and acceleration of the load moved during resistance training would provide further valuable information for the exercise scientist or strength and conditioning coach. 

Biomechanics terms these parameters the kinematics of the movement and such data can be used for performance assessment, technique analysis, and monitoring of training.  Kinematic analysis of the bench press (Wilson, Elliott & Kerr, 1989; McLaughlin & Madsen, 1984), Olympic lifting (Garhammer, 1978; Canavan, Garrett, & Armstrong, 1996), and squat (McLaughlin, Dillman & Lardner, 1984) have been reported all having used either cinematography or video for collection of displacement-time data.

Another approach has been to attach an accelerometer to the load (Ratliff & Bemben, 1995) and use a forward solution (Winter, 1990) to predict the velocity and acceleration data.  There is the advantage in predicting force applied based on the mass and a direct measurement of acceleration, however, accelerometers are sensitive to impacts, and the process of integration with time to produce velocity and displacement data can be prone to error.

A rotary encoder is a device which is used in numerous industrial applications and is available commercially from a number of manufacturers.  It consists of a light source and sensor located either side of a slotted disk.  As the disk rotates electrical pulses are generated with each pulse corresponding to a given angular displacement.  When attached to a sprocket and chain system, linear displacement of the chain can be measured.  Differentiation of the displacement with time produces velocity and acceleration data.  If the mass is known then force output can also be calculated.  Funato, Matsuo, and Fukunaga (1996) have used a rotary encoder to measure the displacement of a bar during various pull movements used in Olympic weightlifting.  They were also able to calculate velocity, work and power output.  Such a system offers considerable advantages by providing displacement, velocity, acceleration, force, and power data in real-time to be used in testing, training and rehabilitation.  

The purposes of this study were to: a) determine the reliability, accuracy and precision of a rotary encoder system for the measurement of displacement; b) compare the displacement, velocity and acceleration data derived from a rotary encoder system with that obtained from a high speed video motion measurement system; c) compare the acceleration measured for a free falling weight with that of the known acceleration due to gravity at sea level of -9.81 m.s-2.

METHODS

Equipment

Plyometric Power System (PPS)

The PPS (Plyopower Technologies, Lismore, Australia) allows traditional barbell weight training movements such as bench press and squat to be done in a dynamic, ballistic manner and has been described elsewhere (Wilson, et al., 1993; Newton et al., 1996).  The machine allows only vertical movement of the bar, and metal stops can be adjusted to limit the upper and lower travel of the bar in 0.01 m increments.  Linear bearings attached to either end of the bar allowed it to slide up and down two steel shafts with a minimum of friction.

As the bar was moved, the chain attached above and below, rotated a sprocket at the bottom of the PPS (Figure A.1). This sprocket in turn rotated a rotary encoder (Model E6B2-CWZ3E 600 pulse/rev, Omron Corporation, Japan). As a result, the encoder produced a 5 volt (TTL) pulse for approximately every 0.001 m of bar movement. These pulses along with a TTL signal indicating movement direction were fed into a counter timer board (Model CTM05, Computer Boards, Mansfield, MA) installed in a 80386DX computer running MSDOS (Microsoft Corporation, Redmond, WA). The counter timer card was capable of measuring pulse frequencies of up to 1MHz and time events with an accuracy of 10 microseconds.

High speed video motion measurement system

A high speed camera and recorder (Peak Performance Technologies, Denver CO) were used to record a video image of the bar movement during the jump squats.  The framing rate of the camera was 120 Hz.  A small reflective marker was placed on the bar to aid in the digitizing of the image.  The Peak Motion Measurement System Version 5.0 (Peak Performance Technologies, Denver CO) was used to determine the digital coordinates of the bar in each video frame.  This data was scaled according to the length of the scale rod and then stored as displacement time data for each trial.

Calibration

The distance encoder system was calibrated immediately prior to data collection by counting the total number of pulses produced as the bar was moved through a distance of 1.600 m.  The distance travelled per encoder pulse was determined and all subsequent displacement data was calculated by multiplying the number of pulses by this calibration factor.  The Peak Motion Measurement System was calibrated by recording the image of two markers separated by a vertical distance of 1.600 metres.  All coordinates were then scaled relative to this distance using the Peak Motion Measurement software.

Experiment A: Reliability of displacement measurement

Testing Procedures

During the first experiment, the bar was moved up and down manually through a set distance and the displacement of the bar in each direction calculated.  Steel stoppers attached above and below the bar ensured that the distance travelled was limited to the two measured distances of 0.700 m and 1.610 m.  The distance between the stoppers was measured using a steel tape measure.  During each repetition the number of pulses from the encoder since the last change in direction of movement were recorded and scaled to a displacement measure in metres for the up and down directions.  Two sets of 20 trials were completed on the first testing day, and a further 20 trials two days later to assess the intra-day and inter-day reliability respectively.

 

Figure A.1 Schematic diagram of the rotary digital encoder attached to the Plyometric Power System.

Statistical Analysis

Mean and standard deviation was calculated for each distance and direction. Accuracy was calculated as the difference between the mean measurement and the actual distance then divided by the actual distance and multiplied by 100. The precision of measurement was calculated as the standard deviation divided by the mean multiplied by 100.  A two-way (3 trials x 2 distances) repeated measures ANOVA with the trial as the within-subject factor was used to test for statistical differences using a criterion level of p0.05.  Inter-day and intra-day Technical Error of Measurement (TEM) and Intraclass Correlation Coefficients (ICC) were calculated according to the methods of Knapp (1992). 

Experiment B: Comparison of encoder system with high speed video system

Testing Procedures

A human subject performed counter movement jump squats with resistances of a light (bar weight = 17 kg), moderate (40 kg), and heavy (60 kg) load.  Three trials were completed at each load. Encoder pulses were counted from the rotary encoder and bar movement was recorded on high speed video throughout each jump. 

The  encoder pulses were converted to displacement data by multiplying the pulse count by the calibration factor and accounting for change in movement direction.  The video recording of the bar movement was digitised and actual bar displacement data calculated.  Both data sets were then optimally smoothed (Jackson, 1979) using a fourth order Butterworth digital filter then differentiated, first to obtain velocity time data, then again to obtain acceleration time data.  Maximum and minimum displacement, velocity, and acceleration were calculated as well as the time between each maxima and minima.  The results derived from the encoder system were then compared with the “standards” calculated from the video system by calculating the TEM, TEM%, and ICC (Knapp, 1992).

To compare the displacement, velocity and acceleration data from encoder and video systems at every time point throughout the movement, the encoder data was first reduced from the original 500Hz sampling frequency to 120Hz.  Linear interpolation was used to ensure that the data point derived from the encoder system was at exactly the same time as the corresponding data point from the video system.  The displacement data derived from the encoder and video recording was then compared by calculating the TEM and ICC between each data set at each time point.  This process was repeated for the velocity and acceleration data derived from each measurement system.

Statistical Analysis

Mean and standard deviation were calculated for each measured and derived variable.  Multivariate ANOVA with repeated measures was used to test for differences between the measurement system across all variables. A criterion level of p0.05 was used to determine statistical significance.

Experiment C: Comparison of acceleration due to gravity measured by the encoder system with the known value of –9.81 m.s-2

Testing Procedures

A 20kg load was dropped under free fall conditions for a distance of approximately 2 m landing on a mat of thick sponge rubber.  Ten trials were completed on one day and a further ten trials on another day.  Encoder pulses were counted from the rotary encoder and converted to displacement data by multiplying the pulse count by the calibration factor.  The displacement data for each trial was then smoothed using a fourth order Butterworth digital filter with a cut-off frequency of 12 Hz, then differentiated, first to obtain velocity time data, then again to obtain acceleration time data.  Measured acceleration due to gravity was then determined as the minimum acceleration achieved between the time of release and the time immediately before impact with the ground.  The results derived from the encoder system were then compared with the known value of ‘g’ at sea level of –9.81 m.s-2.  The error in measurement of ‘g’ was calculated as follows:

TEM and TEM% were calculated (Knapp, 1992) between the data collected on separate days to provide an indication of inter-day variability.  .

Statistical Analysis

Mean and standard deviation were calculated for measured acceleration due to gravity on days 1 and 2.  A paired t-test was used to test for differences between acceleration measured on different days. A criterion level of p0.05 was used to determine statistical significance.

DELIMITATIONS

The measurement of acceleration was limited to free-fall from a height of 2 m as this was the maximum permitted by the height of the PPS allowing for 0.75 m of padding to absorb the impact of landing.

The measurement of acceleration due to gravity was limited to a mass of 20kg as it was difficult and dangerous to drop higher masses in the laboratory setup, which was used.

LIMITATIONS

In addition to limitations arising from the above:

Direct measurement of acceleration was not possible because there was no accelerometer available in the laboratory where the experiment was conducted.

An indeterminable amount of resistance is present in the measurement system due to friction and rotary inertia of the sprockets, shafts and other rotating parts. 

RESULTS

Experiment A

The mean, standard deviation, percentage accuracy and percentage precision for the two distances measured are provided in Table A.1.  Best accuracy was obtained over the shorter distance (0.22%) and the worst during the upwards measurement of the 1.610 metres (0.51%).  Precision of measurement was highest for the 1.610 metres distance (0.10%) and lowest during the downwards movement over 0.700 metres (0.44%).  TEM was 0.9 mm and 0.8 mm intra-day and inter-day respectively, ICC was 0.9999 and 0.9999 intra-day and inter-day respectively.  There were no significant differences between measurement of either distance either within or between days.

Experiment B

Displacement, velocity, and acceleration data from a representative trial are presented in Figure A.2.  Comparisons of the summary variables of maxima, minima, and time between for displacment, velocity, and acceleration data appear in Table A.2.  TEM% ranged from 0.26% for the time between maximum and minimum displacement, and minimum acceleration; up to 5.23% for measurement of the time between maximum and minimum acceleration.  The ICC results varied considerably, ranging between 0.115 for minimum displacement up to 0.994 for measurement of the time between the maximum and minimum displacement. 

Table A.1 Accuracy and precision of distance measurement over 0.700 and 1.610 metres bar displacement for data pooled across all three trials.

Actual Bar

Displacement

Measured Distance

mean (s.d.) (metres)

Accuracy

(%)

Precision

(%)

 

Up

Down

Up

Down

Up

Down

0.700 m

0.7015(0.0019)

0.7016(0.0030)

0.22

0.22

0.26

0.44

1.610 m

1.6182(0.0016)

1.6176(0.0015)

0.51

0.47

0.10

0.09

 

Experiment C

Acceleration data for the ten trials on days 1 and 2 are presented in Table A4.  The mean measured acceleration was 9.713 m.s-2 for day 1 and 9.767 m.s-2 for day 2 representing differences with the known value of ‘g’ of –1.0% and –0.4% respectively.  The 0.56% difference between acceleration measured on days 1 and 2 was not statistically significant (t = -1.349, p two tailed = 0.210).  Inter-day TEM was 0.081 m.s-2 which equates to a TEM% of 0.83%.

 

 

 

Table A.2 Comparison of digital encoder and video systems for measurement of summary variables of bar kinematics during jump squats with light, medium, heavy loads. 

Variable

Encoder

Video

Difference

(%)

TEM

TEM%

(%)

ICC

max. displacement

0.220

0.213

3.2

0.014

1.61

0.860

min. displacement

-0.432

-0.422

2.3

0.021

1.21

0.115

total displacement

0.652

0.635

2.6

0.035

1.36

0.453

time max to min

0.747

0.751

-0.5

0.0078

0.26

0.994

max. velocity

1.737

1.684

*3.1

0.11

1.66

0.778

min. velocity

-0.947

-0.935

1.3

0.03

0.67

0.922

time max to min

0.980

0.986

-0.6

0.013

0.33

0.992

max. acceleration

4.879

5.070

-3.9

0.404

2.03

0.831

min. acceleration

-10.783

-10.729

0.5

0.114

0.26

0.978

time max to min

0.345

0.313

9.3

0.069

5.23

0.582

* indicates significant difference between encoder and video measures (p £ 0.05).

The results of comparing the displacement, velocity, and acceleration data derived from the encoder versus video systems at each time point throughout the movement are presented in Table A.3.  Averaged across the three loads, the TEM was 0.0054 m, 0.022 m.s-1, and 0.41 m.s-2; and ICC was 0.845, 0.992, and 0.998 for displacement, velocity, and acceleration respectively.

Table A.3 Comparison of the displacement, velocity, and acceleration data derived from the encoder versus video systems at each time point throughout the movement recorded at 120 Hz during jump squats with light, medium, heavy loads. 

Load

Displacement

Velocity

Acceleration

 

TEM

(m)

ICC

TEM

(m.s-1)

ICC

TEM

(m.s-2)

ICC

Light

0.0045

0.979

0.022

0.995

0.388

0.999

Medium

0.0053

0.907

0.024

0.990

0.44

0.999

Heavy

0.0065

0.648

0.019

0.991

0.42

0.996

Mean

0.0054

0.845

0.022

0.992

0.41

0.998

 


Table A.4 Accuracy and precision of distance measurement over 0.700 and 1.610 metres bar displacement for data pooled across all three trials.

 

Day 1

Day 2

Trial

Measured Acceleration (m.s-2)

Error (%)

Measured

Acceleration

(m.s-2)

Error (%)

1

9.615

-2.0%

9.868

0.6%

2

9.634

-1.8%

9.789

-0.2%

3

9.76

-0.5%

9.823

0.1%

4

9.764

-0.5%

9.726

-0.9%

5

9.638

-1.8%

9.805

-0.1%

6

9.783

-0.3%

9.695

-1.2%

7

9.806

0.0%

9.908

1.0%

8

9.656

-1.6%

9.767

-0.4%

9

9.768

-0.4%

9.621

-1.9%

10

9.705

-1.1%

9.669

-1.4%

Mean

9.713

-1.0%

9.767

-0.4%

S.D.

0.072

0.73%

0.090

0.92%

DISCUSSION

The aim of this study was to assess the validity and reliability of using a rotary digital encoder system to measure the kinematics of bar movement during a typical resistance training movement.  Further, this system was compared with a high speed video system which has been traditionally used for such analyses.  The system’s ability to measure acceleration was assessed by comparing measurement of acceleration of a freely falling object with the known value of ‘g’.

The encoder system could reliably measure bar displacement over the two distances tested.  This was evident from the mean distances measured being approximately 1.5 mm and 8 mm different from the actual distances of 0.700 m and 1.610 m respectively (Table A.1).  Accuracy and precision were also quite high being no worse than 0.5% with the majority of measures being 0.2% or better.  These results are comparable to those reported for distance measurement using video.  Shapiro, Blow, & Rash (1987) have reported an absolute mean error of 6.3 mm in measuring a distance of 2100 mm which is a precision of 0.3%.  Similarly, Smith, Risenhoover, Cheetham & Scheirman (1989) determined mean errors of 5.8 mm for their video measurement system.  A further evaluation of a video system for distance measurement reported mean errors of 2.8 mm in a 2 m field width (Newton & Neal, 1994).

The reliability of the encoder system in measuring the two test distances was very high.  TEM, which reflects the measurement error of the system, was less than 1 mm and did not increase even when determined between measurements on different days.  This consistency of measurement on repeat days is particularly notable and an important finding if the system is to be used for longitudinal testing of human performance.  Further, the very high ICC of 0.9999 for both intra-day and inter-day also attests to the very high reliability of this system in measuring displacement. 

When completing a kinematic analysis of a weight lifting or resistance training movement, the biomechanist will generally examine variables which summarise the overall performance, for example peak velocity and acceleration.  The encoder system produced results which were not significantly different from the video measures in all but maximum velocity.  The TEM% and ICC measures (Tables 2 & 3) showed that there was some variation between the two systems, however, it is suggested that this variation was a result of innaccuracies in the video measurement system rather than the encoder system.

It is known that the process of differentiation magnifies any random errors in the displacement data (Winter, 1990).  Examination of a representative trial (Figure A.2) reveals that although the displacement-time data collected from the two systems is very similar, the velocity, and in particular the acceleration-time data deviate much more for the video system.  The acceleration-time data collected from the video system shows random noise about a relatively smooth curve produced from the encoder data.  This random noise is the result of the video digitising process (Winter, 1990).  Thus, it would appear that more accurate results in terms of velocity and acceleration measures could be obtained from an encoder measurement system rather than video for recording the kinematics of the load during resistance training. 

Jump squats were used in this study because the movement involves relatively high displacement, velocity and acceleration values.  It would be expected that similar results would be obtained for more traditional resistance training movements such as squat and bench press which involve slower velocities and much lower peak accelerations.

The system measured acceleration due to gravity with an error of 1.0% or less.  Therefore, it can be concluded that the measurement of acceleration around 1g is accurate.  Further, there was only 0.56% difference between measurement of ‘g’ on consecutive days indicating good repeatability in acceleration measurement inter-day.  The low TEM and TEM% values comparing measurement on days 1 and 2 confirmed this.  It was interesting that the system consistently tened to under-estimate the value of ‘g’.  Although it was not determined, it is suggested that the deficit was due to slight resistive forces in the measurement system.  Sources of this resistance may include friction in the bearings and chains as well as rotary inertia in the sprockets and shafts of the PPS.   

The Plyometric Power System as used in this study is a specialised piece of equipment which limits movement to a single plane.  However, a digital encoder system could also be applied to other resistance testing and training devices, which incorporate a pulley system or involved rotation about a central axis.  The data produced from such a system would enhance performance testing and resistance training programs by providing 1) instantaneous feedback to the athlete or patient, and 2) automatic recording of repetitions, sets, volume, velocity, power, and work completed.   

CONCLUSIONS

Valid and reliable kinematic data can be derived from a digital rotary encoder interfaced with a counter timer card in a computer for measuring and recording human movements which maximise power production.  This system is more accurate, precise and repeatable than using a high-speed video system for this purpose.