measurement errors in kinematics and kinetics assignment

Ben Greenwood Evaluation of Biomechanical Measuring Techniques Word Count: 4051

Measurement Errors in Kinematics and Kinetics Assignment

Introduction

The progression of video analysis along with advances in computer processing speeds and capacities

has transformed biomechanical analysis almost beyond recognition in the past decade (Lee, 2011;

Hughes & Franks, 2008). The developments in video analysis have given biomechanists greater

interactive control of the image quality during the recording process (Angulo & Dapena, 1992). The

additional interactive control helps to prevent any major errors in exposure, as well as permitting the

start of the analysis during the recording process itself. A study by Chu et al (2012) revealed that

video analysis is multi-dimensional, non-invasive, and can effectively process dynamic motion with

only a small degree of movement restriction. Therefore, it is clear that video analysis has become a

major contributor in the field of sport biomechanics and motion simulation.

Unlike video analysis, a force plate provides objective data by describing an aspect of locomotion

that cannot be assessed by visual observation (Clayton, 2005). Force plates are considered to be the

‘gold standard’ for vertical jump measurements because of their ability to observe numerous kinetic

variables in relation to sports performance (Buckthorpe et al, 2012; Hood et al, 2012). A study by De

Lisa (1998) found that force plates enable one to measure, not only the ground reaction forces (GRF)

but also the centre of pressure during gait. Therefore, force plates are an important piece of

equipment in biomechanical research, particularly when measuring force applied during movement.

Numerous studies have revealed that video analysis and force plates are well established pieces of

equipment in the field of sport biomechanics and motion simulation (Morris & Lawson, 2010; Barrey,

1999). However, few studies have revealed which of these two methods provides the greater

analysis on vertical jump performance. Therefore, it may be useful to look at individual studies on

both video analysis and force plates and analyse their validity accordingly. A study by Linthorne

(2001) found that the segmentation method associated with video analysis is often time consuming

due to the computer-assisted digitising, calibration, and calculation processes. Whereas, the

dynamic method (force plates) has been found to be considerably easier to use (Paredes et al, 2015;

Golriz et al, 2012).

The study by Golriz et al (2012) contained a number of limitations in regards to the validity of their

Midot posture Scale Analyser (MPSA) force plate. however, the study failed to assess the validity of

the MPSA prior to the onset of the experiment. In addition, the MPSA is a lower cost force plate with

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a low-technology design. Therefore, it is difficult to compare the functionality of the MPSA with the

far more technologically advanced Kistler force plate (9287ca). In spite of these limitations,

Linthorne et al (2001) used the same force plate and video analysis methods as the present study

and therefore comparisons can be made between the studies.

One particular study that focuses on vertical jump height using both video analysis and force plates

is that of Palazzi et al (2012). This particular study utilised a 14-camera Vicon 3D motion analysis

system and a Kistler multi-component force plate simultaneously to obtain vertical trajectories of

the centre of mass (COM). The findings of Palazzi’s (2012) study reveal that video analysis and force

plates are effective in measuring vertical jump performance. Although this study did not compare

video analysis and force plates directly, it demonstrated that the two methods can be used

concurrently to produce valid and reliable data.

There is a severe lack of research regarding the comparison between video analysis and force plates

in vertical jump performance. Therefore, it is apparent that further research is needed to verify

which of these two methods produces the fewest measurement errors. Numerous studies have

shown that advanced video analysis and force plates are expensive and therefore researchers or

institutes may select the optimum method based on their available budget (Roos & Surujlal, 2014;

Cross, 1998).The quality of video analysis and force plates means that any potential findings could

have significant practical applications as the vertical jump is used frequently in a variety of different

sports (Psycharakis, 2011).

The aim of the present study is to provide conclusive evidence regarding the optimum method of

vertical jump analysis. The study procedure will compare a number of variables relating to each

systems ability to calculate jump height, flight time, vertical displacement, the velocity of the COM at

take-off (TO) and the peak concentric velocity and acceleration statistics. The error variables utilised

in the study includes the level of agreement (LOA), mean error (ME), bias and the full scale output

(FSO), as these accuracy measures have been found to be particularly effective in determining the

validity of data (Bratu, 2013).

The implications of verifying the most effective method of vertical jump analysis are considerable.

Although both video analysis and force plates have been shown to be highly effective in producing

and analysing kinetic data (Buckthorpe et al, 2012; Hood et al, 2012; Angulo & Dapena, 1992), few

studies have produced conclusions as to which method is indeed superior. Therefore, the findings of

the present study focus on uncovering this information.

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Methods

Force Plate Testing

Initially, the validity and reliability of the 60cm x 90cm force plate (Kistler 9287ca) was tested by

weighing the mass (N) of an assumed 5kg weight against an electronic scale (Seca 813). Seca

electronic scales are considered to be the ‘gold standard’ due to their high precision and reliability

(Darmstadt et al, 2007). The mass of the weight was weighed five times each by the force plate

(central) and column scale. Following this, the weight was placed on the outer four segments

(bottom left, top left, bottom right, top right) of the force plate and weighed once more per

segment.

The error variables including LOA were recorded and analysed by placing the 5kg weight on the

centre of the force plate. LOA is the defined as the mean difference plus and minus 1.96 times the

SD of the differences (Bland & Altman, 1986). A study by Olsen et al (2013) noted that an effective

LOA is useful in assessing whether an experimental method is sufficiently precise. The additional

error variables produced during force plate testing, included bias, % bias, absolute random error,

and the % random error. In addition, SD and CV variables for 68% and 95% of the LOA have also

been calculated for analysis. The 68% and 95% LOA are visual judgements of how well two methods

of measurement agree (British Journal of Anaesthesia, 2007). Specifically, the 68% or 95% illustrates

the magnitude of the systematic difference (Giavarina, 2015).

The testing of the force plate will analyse a number of common variables including mass (N), average

mass (N), average SD, grand mean, differences, differences squared and the absolute differences

between the force plate and the electronic scale. In addition, SD and CV will be analysed for each

mass to display how extensive the data is.. The selected error measures have been commonly used

by researchers to evaluate the degree of error in a wide range of studies (Altman & Bland, 2005;

Armstrong & Collopy, 1992). In addition, Chai and Draxler (2014) found that mean absolute error

were useful error measures, particularly when used alongside other metrics. Therefore, it seemed

logical to include previously used error measures for association purposes.

Following the initial testing of the force plates, the subject performed fifteen 5m and 10m walks per

distance. The subject walked over the centre of the force plates for both distances. Walking was

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selected in the present study as it is the most commonly used exercise for testing force plate

functionality (Zeni et al, 2008; Cross, 1998).

The testing of the force plate during the 5m and 10m walks produced several common variables

including the time (s) to walk the selected distance, the average velocity (m/s), contact time on the

force plate (s) and the active, passive and impact peaks for the Y axis. The SD, CV and the average

mean will also be analysed for the 5m and 10m walks respectively. These variables have been used

in a number of studies, and have found to be most useful within a sample or comparing samples

with normal distribution and equal means (Felix & Barkoulas, 2015).

The drift of the force plate was measured at 20s intervals for a total of 300s (5 minutes). Drift is

defined as “an undesirable change in output signal over time, which is not a function of the

measured variable” (Caldwell et al, 2004). Studies have revealed that drift significantly affects the

signals in piezoelectric force plates, and is caused by leakage currents and poor insulation

resistances (Quagliarella, 2008; Caldwell et al, 2004). Therefore, it was important that the study

measured the drift prior to the experimental procedure. Testing the force plates for levels of drift

produced a number of common variables including average force of the Y axis, maximum and drift

measurements, and subsequent percentage (%) changes.

The hysteresis of the force plate was tested using five up values and five down values. Hysteresis is

defined as “a system which has multiple stable equilibrium points and dynamics that are

considerably faster than the time scale at which inputs are varied” (Morris, 2011). Testing the force

plate for hysteresis produced a number of error variables for analysis, including the differences

between the up and the down values, the correlation coefficient and the %FSO.

The cross-talk of the force plate was tested using five measurements. Cross-talk is defined as “the

incomplete isolation of the left and right image channels so that one image leaks into the other”

(Woods, 2011). A study by Woods (2011) found that high levels of cross-talk can lack data fidelity.

Therefore, it is important to make sure that there are not excessive levels of disturbance from either

drift, hysteresis or crosstalk. Testing the force plate for cross-talk produced several common

variables including absolute mass (N), average force and absolute mass % of the X, Y and Z co-

ordinates.

The force testing procedure took place over two different sessions, approximately a week apart.

Both sessions included the same operators and force plate. In addition, the two sessions produced

the same variables (common and error), that were later used for analysis. Finally, the data was

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transported to the Bioware computer software program for analysis and Microsoft Excel for

presentation purposes.

Video Analysis Testing

The error variables produced during force plate testing were also used during video analysis testing. The validity and reliability of a high speed camera (Fastec TS3 – 100hz)

and its software was tested by digitising a 1m stick 20 times (10 times each for system one and

system two) per frame. The test utilised an intra-frame and inter-frame during the testing process.

Chitradevi & Vijayalakshmi (2014) noted that Intra-frames are usually performed relative to

information that is contained only within the current frame and not relative to any other frames

whereas the Inter-frame prediction technique only focuses on changes in the image from the

previous subpages.

The testing of video analysis equipment produced a number of common variables for the intra-frame

and inter-frame including the industrial length of the 1m stick, grand mean, differences, differences

squared, the absolute differences between the systems and the other error variables.

The video analysis testing procedure took place over two different sessions, approximately a week

apart. Both sessions included the same operators, equipment and analyst. In addition, the two

sessions produced the same variables (common and error), that were later used for analysis. The

data was then transported to the Simi Motion computer software program for analysis and

Microsoft Excel for presentation purposes.

Experimentation

The experiment involved a validity and reliability comparison between video analysis and force

plates during vertical jump performance, as previous studies have failed to uncover the optimum

method of kinetic analysis. The subject performed seven maximum vertical jumps on the force plate,

whilst being monitored by video analysis. The jump height (flight time), jump height (TO velocity),

vertical displacement, the velocity of the COM at TO and the peak concentric velocity and

acceleration of the COM were all measured using either Bioware (force plates) or Simi Motion (video

analysis).

The jump height, vertical displacement, velocity and data was analysed alongside the error variables

for both force plates and video analysis. These results were transferred onto their respective

5


software and analysed according, before being transferred to Microsoft Excel for presentation

purposes.

Results

Figure 1: The calculated mass (N) of the 5kg weight by the force plate and electronic scale in week one (W1) and week two (W2)

Figure 1. compares the ability of the force plate to calculate the mass (N) of a 5kg weight against the

electronic measuring scale in week one and week two.

Figure 2: The drift produced by the force plate over a 300s period

6

Attempt 1 Attempt 2 Attempt 3 Attempt 4 Attempt 547.00

47.50

48.00

48.50

49.00

49.50

50.00

W1 Force Plate W1 Electronic Scale W2 Force Plate W2 Electronic Scale

Mas

s (N)


Figure 2. displays the amount of drift affecting the validity of the force plate whilst weighing of the

5kg weight over fifteen, 20 second time intervals (total time = 300s). The orange line refers to the

percentage change (%), which is considered to be a strong indicator of drift.

Figure 3: The hysteresis produced by the force plate *Figures displayed in Newtons (N)

Figure 3. displays the amount of hysteresis affecting the validity of the force plate whilst weighing

five 2.5kg weights. The up values signify the placing of a weight whereas the down values refer to

the removal of a weight.

7

0-20 20-40 40-60 60-80 80-100

100-120

120-140

140-160

160-180

180-200

200-220

220-240

240-260

260-280

280-300

46.4

46.6

46.8

47

47.2

47.4

47.6

47.8

48

-0.004

-0.003

-0.002

-0.001

0

0.001

0.002

Average Fy (N) % Change

Time Intervals (s)

Aver

age

Fy (N

)

Perc

enta

ge C

hang

e (%

)


Figure 4: The % absolute mass (cross-talk) Fz in week 1 (W1) and week 2 (W2).

Figure 4. displays the amount of cross-talk affecting the validity of the force plate in the Z axis, whilst

weighing the 5kg weight. The two lines refer to the % absolute mass (N) in week one and week two.

Figure 5: The % absolute mass (cross-talk) Fx in week 1 (W1) and week 2 (W2).

Figure 5. displays the amount of cross-talk affecting the validity of the force plate in the Z axis, whilst

weighing the 5kg weight. The two lines refer to the % absolute mass (N) in week one and week two.

Attempts Intra S1 Intra S2 Inter S1 Inter S2

Attempt 1 0.99 0.99 1.00 0.99

8


0.020

0.040

0.060

0.080

0.100

0.120

0.140

0.160

0.180

0.200

W1 %Absolute Mass Fz (N) W2 % Absolute Mass Fz (N)

New

tons

(N)


0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

0.16

Average Fx (N) Average Fx (N)

New

tons

(N)


Attempt 2 0.99 0.98 1.00 0.99

Attempt 3 1.00 0.99 1.00 1.00

Attempt 4 0.99 0.99 0.99 0.99

Attempt 5 0.99 0.99 1.00 0.99

Attempt 6 0.99 0.99 1.00 0.99

Attempt 7 1.00 0.99 1.00 1.00

Attempt 8 1.00 1.00 0.99 1.00

Attempt 9 1.00 0.99 1.00 1.00

Attempt 10 1.00 0.99 1.00 1.00

Mean 1.00 0.99 1.00 1.00

SD 0.01 0.00 0.00 0.01

CV 0.53 0.48 0.42 0.53

Table 1: The length (M) calculated by the video digitisation of a 1m stick for intra-frames (intra) and inter-frames (inter) in

system 1 (S1) and system 2 (S2)

Table 1. displays the digitised lengths of the 1m stick by inter-frame and outer-frame video analysis

in system one and system two. Table 1. also includes the mean, SD and CV values produced by video

analysis.

Figure 6: The jump height calculated by the flight time equation for force plates and video analysis

9

Attempts 1 Attempts 2 Attempts 3 Attempts 4 Attempts 5 Attempts 6 Attempts 70.20

0.21

0.22

0.23

0.24

0.25

0.26

0.27

0.28

0.29

0.30

Force Plate Video Analysis

Heig

ht (M

)


Figure 6. compares the force plate and video analysis results for jump height (flight time equation).

The blue line signifies the seven Y displacement measures calculated by the force plate and the

orange line signifies those calculated by video analysis.

Figure 7: The jump height calculated by TO velocity equation for force plates and video analysis

Figure 7. compares the force plate and video analysis results for jump height (TO velocity equation).

The blue line signifies the seven jump height measures calculated by the force plate and the orange

line signifies those calculated by video analysis.

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Attepmt 1 Attepmt 2 Attepmt 3 Attepmt 4 Attepmt 5 Attepmt 6 Attepmt 70.42

0.44

0.46

0.48

0.50

0.52


Tim

e (S

)

Attempt 1 Attempt 2 Attempt 3 Attempt 4 Attempt 5 Attempt 6 Attempt 70.20

0.21

0.22

0.23

0.24

0.25

0.26

0.27

0.28

0.29

0.30


Heig

ht (M

)


Figure 8: The flight time (S) calculated by force plates and video analysis

Figure 8. compares the force plate and video analysis results for flight time (S). The blue line signifies

the seven flight time measures calculated by the force plate and the orange line signifies those

calculated by video analysis.

Figure 9: The Y displacement (M) of the centre of mass (COM) during the contact phase calculated by force plates and

video analysis

Figure 9. compares the force plate and video analysis results for displacement in the Y axis (M). The

blue line signifies the seven Y displacement measures calculated by the force plate and the orange

line signifies those calculated by video analysis.

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0.37

0.38

0.39

0.40

0.41

0.42

0.43

0.44

0.45

0.46


Disp

lace

men

t (M

)


Figure 10: The calculated concentric velocity (M/S) of the COM by force plates and video analysis

Figure 10. compares the force plate and video analysis results for concentric velocity of the COM

(m/s). The blue line signifies the seven velocity measures calculated by the force plate and the


Figure 11: The calculated peak concentric acceleration (M/S2) of the COM by force plates and video analysis

Figure 11. compares the force plate and video analysis results for concentric acceleration of the COM

(m/s2). The blue line signifies the seven acceleration measures calculated by the force plate and the


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10.20

10.40

10.60

10.80

11.00

11.20

11.40

11.60

11.80

12.00

Force Plate Video

Acce

lera

tion

(M/S

2)


2.25

2.30

2.35

2.40

2.45

2.50

Force Plate Video

Velo

city

(M/S

)


Figure 12: The calculated take-off velocity (M/S) of the COM by force plates and video analysis

Figure 12. compares the force plate and video analysis results for the TO velocity of the COM (m/s).

The blue line signifies the seven velocity measures calculated by the force plate and the orange line

signifies those calculated by video analysis.

Figure 13: The calculated take-off acceleration (M/S2) of the COM by force plates and video analysis

Figure 12. compares the force plate and video analysis results for the TO acceleration of the COM

(m/s). The blue line signifies the seven acceleration measures calculated by the force plate and the


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Attempt 1 Attempt 2 Attempt 3 Attempt 4 Attempt 5 Attempt 6 Attempt 7

-12.00

-10.00

-8.00

-6.00

-4.00

-2.00

0.00


Acce

lera

tion

(M/S

2)


1.95

2.00

2.05

2.10

2.15

2.20

2.25

2.30

2.35

2.40


Velo

city

(M/S

)


Variable Bias Bias (%) Absolute

Random

Error

Random

Error (%)

LOA (-) LOAD (+)

Force Plate

Testing

-0.38 (W1)

-0.82 (W2)

-0.79 (W1)

-1.67 (W2)

0.13 (W1)

0.11 (W2)

0.26 (W1)

0.23 (W2)

-0.51 (W1)

-0.92 (W2)

-0.26 (W1)

-0.51 (W1)

Video Analysis

Testing

0.01 (W1)

0.00 (W2)

0.5 (W1)

0.3 (W2)

0.01 (W1)

0.01 (W2)

1.04 (W1)

1.33 (W2)

-0.01 (W1)

-0.01 (W2)

0.02 (W1)

0.02 (W1)

Jump Height

(Flight Time)

-0.01 -2.59 0.02 5.85 -0.02 0.01

Jump Height

(TO Velocity)

-0.04 -15.01 0.01 5.41 -0.05 -0.02

Flight Time -0.01 -1.32 0.01 2.95 -0.02 0.01

Y Displacement

of the COM

0.01 3.37 0.02 5.84 -0.01 0.04

Concentric

Velocity of

COM

-0.08 -3.47 0.07 3.09 -0.15 -0.01

Concentric

Acceleration of

COM

-0.21 -1.89 1.11 10.22 -1.32 0.91

TO Velocity of

COM

-0.16 -7.53 0.06 2.80 -0.23 -0.10

TO Acceleration

of COM

-2.02 23.49 3.27 -37.98 -5.30 1.25

Table 2: The error variables of each aspect of the study

Table 2. displays the error variables during the force plate testing, video analysis testing and the

experimental procedures.

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Discussion

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The force plate tests were utilised to assess the validity and reliability of the individual plate, as

regular checks are essential in identifying any systematic errors (Bartlett, 2007). One major

inconsistency during the force plate tests was the considerable difference between the results

produced in week one and week two. Although the same experimental procedure was used in both

weeks, there were large discrepancies in the amount of cross-talk detected in the Z axis of the force

plate (Figure 4.). These discrepancies are concerning as cross-talk can propagate to the accuracy of

quantities such as joint forces and moments, which are often estimated from an individual’s COM

(Cappello et al, 2004; Cappozzo, 1984). However, Numerous studies have found that Kistler force

plates, in particular, the 9287ca model are reliable (Hansen et al, 2011; Rogind et al, 2013).

Therefore, the discrepancies may have occurred due to human error or a methodological limitation.

The force plate tests relating to drift exhibited unexpected results, as there was a sharp rise at the

160-180s interval. A study found by Quagliarella et al (2008) found that high levels of drift can affect

the GRF and pressure components of piezoelectric force plates. Consequently, the affected GRF can

inhibit outcome measures including sagittal joint forces, moments and powers (Sinitski et al, 2015).

In spite of this, the results in Figure 2. revealed that the percentage change had decreased

considerably by the 260-280s interval. A major limitation of the present study was that the drift was

only tested for 300s (5 minutes). A study by Sinitski et al, (2015) revealed that drift should be tested

over a greater time interval in order to be effective. Therefore, it is difficult to quantify drift unless a

greater time interval is implemented into the study.

The testing of hysteresis provided no clear discrepancies however the results from Figure. 3 and the

subsequent %FSO did reveal slight error. A study by Bartlett (2007) revealed that the %FSO in a study

(0.02%) should be 0.5% of the full-scale deflection or less. Therefore, it can be assumed that the

level of hysteresis in the present study was considered sufficient. However, it is important that

hysteresis is monitored for use in further study, particularly as it can cause major disturbances in the

performance of piezoelectric force plates (Vojtko, 2006).

The video analysis tests were employed to determine the level of digitising accuracy of the 1m stick.

The results displayed in Table 1. show precise digitisation of both intra-frame and inter-frame in

systems one and two. A study by Bartlett (2007) revealed that the importance of using multiple

digitisations of the same sequence, in order to reduce systematic error. Furthermore, Bartlett (2007)

noted that a second operator should be employed to digitise at least one sequence so that

systematic errors can be connected to one of the operators. However, the present study precluded

any systematic errors from occurring by utilising these submissions. Therefore, the video analysis

testing was considered to be methodologically sound.

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The main discrepancies between force plates and video analysis was observed in data focusing on

the COM (Figure. 9, 10, 11, 12, 13). The reason for such discrepancies may be due to the

inconsistencies in predicting the participants COM. Studies have found that the segmental approach

for calculating the COM produced errors from unrecorded dynamics of segment masses (Maus et al,

2011; Schmitt & Gunther, 2010) and unexpected motion of the viscera (Minetti and Belli, 1994).

Correspondingly, the accuracy of the dynamic method is limited by the precision of the measured

forces and the precision of the integration constants (Maus et al, 2011; Cavagna, 1975).

A study by Cotton et al (2008) revealed that incorporating methods that predict the COM would

result in systematic errors. This theory is emphasised by the error variables for the COM-related data

in Table 2. In particular, the random error % for the concentric acceleration of the COM (10.22%) and

the TO acceleration of the COM (-37.98%) was far greater than the none-COM data. Furthermore,

the bias % for the TO velocity of the COM (-7.53%) and the LOA (-) (-5.30) and LOAD (+) (1.25) for the

TO acceleration of the COM was also significantly higher than the none-COM data. In spite of these

results, the LOA is the only error variable to be commonly approved in modern research (Atkinson &

Nevill, 1998).

One of the main limitations found in the present study was that drift was only tested for 300s

whereas research has demonstrated that performing a more extensive test would produce more

accurate results (Sinitski et al, 2015). The importance of implementing effective equipment testing

should not be understated as drift can significantly affect the signals in piezoelectric force plates

(Quagliarella, 2008). A second limitation of the study was that both the dynamic and kinematic

methods for calculating COM had major faults, and therefore it may be beneficial to sought

alternative methods, as well as investigate more accurate error variables to assess such methods.

Conclusion

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The results of previous studies and the accuracy of the data produced in Table 1. revealed that the

video analysis tests were more effective than the force plate tests because of the reduced probably

of obtaining systematic errors including drift, hysteresis and cross-talk. However, the lack of research

regarding the optimum method of analysing vertical jump performance means that further research

is required. Therefore, the only major finding of the study was that both dynamic and kinematic

methods of predicting the position of the COM had significant faults. Consequently, it may be

beneficial to sought alternative methods for future study.

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measurement errors in kinematics and kinetics assignment

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