Data Acquisition Not covered in detail he Hamill text, nor in most texts on reserve. The best text to read if the lecture and slides are not clear to you is: Winter, D. Biomechanics of Human Movement. John Wiley & Sons, New York, 1979. Photographs Ø If taken in the correct plane photographs can allow for later evaluation of angles and hence for a static kinetic analysis. Ø In dynamic situations how do you know you have the extreme posture? Where am I? Ø The accurate and complete answer to this question is not as simple as it may seem. Video Systems Ø There is a limited amount of quantitative data that can be gleaned from a full-motion video system. Ø Stop frame capability does however allow for a reasonably accurate assessment of posture. Ø 60 frames/sec is more than adequate for most movements but the real problem is identifying joint centres of rotation and calibration. 1
Opto-Electronic Systems The location of the joint centres of rotation is entered directly into the computer. Systems usually come with software that will calculate velocity and acceleration. Q-Track and Force Plate Data Q-trac markers Previous Data Acquisition System in Dr. Robinovitch s Lab 2
Injury Prevention and Mobility Laboratory http://www.sfu.ca/ipml/ Position & Displacement Ø Position defines an object s location in space. Ø Displacement defines the change in position that occurs over a given period of time. Ø Displacement is a vector Ø Distance is a scalar Movements Occur Over Time Speed Knowledge of the temporal patterns of a movement is critical in a kinematic analysis since changes in position occur over time. Speed is a scalar (m/s) Speed = distance Δtime Δ = change in 3
Velocity is a vector (m/s) Velocity Velocity = Δposition(displacement) Δtime Velocity is designated by lowercase v Time is designated by lowercase t Dimensions (fundamental units in brackets) Ø Mass (M) Ø Length (L) Ø Time (T) Ø Other fundamental units like temperature is not a focus of Kin 201 Velocity Fundamental units = LT -1 Displacement => Velocity B If we plot our displacement data on a graph we are calculating the slope of the line when we calculate velocity. Displ. A Δt = run Δx = rise Time 4
Displacement => Velocity Finite Differentiation v = position final - position initial time at final displ. - time at initial displ. v = x f - x i t f - t i = x f - x i Δt Δx x 1 x 2 x 3 x 4 x 5 Δt As (t f - t i ) is usually constant we just use Δt. t 1 t 2 t 3 t 4 t 5 Displ. Finite Differentiation B (x 2, y 2 ) A (x 1, y 1 ) Time Finite Differentiation Vx Vy 1.5 1.5 x2 " x1 =! t y 2 " y =! t 1 5
Sample Data Video Ø Full frame video is 60 Hz (60 frames per second). Ø So strictly speaking ΔT (time interval) is 0.01666666666 recurring. Ø The values will be acceptable if you use 0.0167, 0.0333, 0.0500, etc. (0.15-0.00) / 0.0167 = 8.98 Finite Differentiation (0.22-0.15) / 0.0167 = 4.19 Finite Differentiation Ø But at what time do the velocities on the previous table occur? Ø In other words: What is instantaneous velocity? Ø Clearly the value you get from differentiation is the average velocity of the time period used. There in no such thing as instanaeous velocity when dealing with digital displacement data. 6
Finite Differentiation x!1.5! 1.5 y = = x2 " x1! t y 2 " y! t 1 Finite Differentiation What is instantaneous velocity? x 1 x 2 Δt x 3 x 4 x 5 V 2-3 V 3 x 1 x 2 x 3 x 4 x 5 2Δt Finite Differentiation First Central Difference Method! 2 x x " x 3 1 = 2! t You do loose sensitivity in this method, but you can discuss velocities at the same time frame as displacements and acceleration. And if Δt is small enough you will avoid sensitivity problems. Finite Differentiation First central difference method (0.22-0.00) / 0.0333 = 6.61 7
Acceleration Acceleration Acceleration = Δvelocity Δtime Acceleration is designated by lowercase a It is used for both scalar and vector quantities. Ø Again if we are using coordinate systems we use the following convention. Horizontal " acceleration!!! x Vertical " acceleration!!! y Acceleration Ø If my velocity in the x-direction goes from 3 m/s to 2 m/s in 0.05 seconds what would my acceleration be? Ø Answer: -20 m/s 2 Ø Be careful of the term deceleration Ø Deceleration means slowing down (it is in effect a scalar term ). It does not mean negative acceleration (vector). Ø You can have negative acceleration and speed up! 8
Sample Problem Time (s) Displ. (m) 0.0 0.000 0.5 0.857 1.0 3.160 1.5 6.484 2.0 10.564 2.5 15.210 10.5 105.514! Time Displ.!! 0.0!0.000!! 0.5!0.857!! 1.0!3.160!! 1.5!6.484!! 2.0!10.56!! 2.5!15.21!! 3.0!20.26!! 3.5!25.60!! 4.0!31.130! 4.5!36.77!! 5.0!42.480! Time Displ.! 5.5!48.21!! 6.0!53.95!! 6.5!59.68!! 7.0!65.42!! 7.5!71.16!! 8.0!76.89!! 8.5!82.63!! 9.0!88.37!! 9.5!94.11!! 10.0!99.84!! 10.5 105.51!! Draw the following graphs (do not use first central difference method du to large Δt) d vs t v vs t a vs t Sampling Theory Winter, 1979 (page 22-39) 9
Instantaneous Velocity How small should Δt be? Tangent Displ. Δt => 0 This line would be a poor estimate of the tangent for this section of the curve. Time Δt Analogue to Digital Ø Obviously the smaller Δt is the more accurate you estimate of instantaneous velocity. Ø However, the smaller you try to get Δt the more expensive it is going to be! Ø Regular video at 60 frames/sec is good for most applications. 10
Synchronization (A to D) Ø If you have force platform, video and EMG data there can be a problem in synchronizing the data. Ø This is not a problem if all data is collected by computer. However, if some data is collected on video and some on the computer how do you know the time frames on the video match those collected by the computer? Ø One possibility is to turn a light on in the video view once the computer starts data collection. Signal 2 Aliasing Error (Δt is too large to sample signal 2) Signal 1 Aliasing Error Proper sampling rate Sampling rate too low Error (Noise) Ø In one study researchers actually drilled markers into bone. Ø However, markers are almost always placed on the skin and are therefore vulnerable to movement that is not due to movement of the skeleton. Ø When landing from a jump or the impact of foot strike the markers will vibrate. Ø If not very well isolated the sensors will also vibrate. Ø The 60 Hz AC electrical current could also affect the recorded data. Ø Any source of error like these is referred to as noise. Filtering Raw Data Sampling Theory Filtering attenuates (reduces) noise 11
Differentiation is Sensitive to Noise Signal vs Noise The differentials (slopes) calculated between these markers is much larger than the difference in their locations. Red stars = true location of bony landmark Yellow stars = location of marker due to noise Integration Ø Differentiating positional data to get velocity and acceleration has been covered. Ø However, acceleration may be collected in a biomechanical analysis. Ø In this case, you may want to calculate velocity and displacement data. Ø This is the opposite of differentiation and is known as integration. Accelerometer 12
Tri-Axial Accelerometers Ø Accelerometers vary considerably in resolution and max. acceleration. Ø Must be sure of planar acceleration if using uniaxial accelerometers. Ø Tri-axial accelerometers are bulkier and much more expensive. Ø These can be rented rather than purchased. Vibration (seat pan accelerometer) Ø Vibration is measured using accelerometers and then various mathematical and statistical techniques are used to quantify and interpret the signal. Force Platform Data If you have force and obviously F = ma, then you can easily calculate the acceleration of the body s centre of gravity. Finite Integration Ø We have seen that finite differentiation methods are used with digital data. Ø Similarly, finite integration methods are used with digital data. Ø We saw that with finite differentiation you are calculating the slope of the curve. Ø Finite integration calculates the area under the curve. Ø Most often used with force-time curves area under the curve is mechanical impulse (Ft = Δmv) Ø Integration of an acceleration curve (from force plate data divided by body mass) will allow you to calculate velocity of the body s centre of gravity. Ø Integration again will calculate displacement of the whole body centre of gravity. 13
7 acc. 3 A Example B 0 6 8 Time Ø Area A equals 3m/s 2 x 6s = 18 m/s Ø Units! LT -2 x T = LT -1 Ø This is change in velocity from 0-6 s. Ø Area B is 14 m/s. Ø Total change in velocity from 0-8 s is 32 m/s. If :" a = #v #t Then :" #v = a#t Finite Integration Acceleration Hence area under curve = a"t Δt # Approximated as = a 1 + a & 2 % ("t $ 2 ' Time a 1 a a 2 Riemann Sum Ø Finite integration approximates the area under curves as a series of rectangles Ø This is called the Riemann sum (see equation opposite) Ø If Δt is small enough this is an accurate approximation t30 vxi! dt t1 ds = 30 " i= 1 = ds (v xi *dt) Example above: Horizontal velocity time curve with 30 time intervals. Integral equals change in displacement. Integration is less sensitive to errors due to noise High frequency noise present A B The slope of curve A varies greatly but the area under the curve is not that different from curve B. 14
Stride Rate vs Stride Length Kinematics of Running Reserve text: Hamill & Knutzen, Chapter 8 (pages 319-323) Running Kinematics Ø Stride length (SL) and stride frequency (SF) are very commonly studied kinematic parameters. Ø Both SR & SL increase linearly (approx.) from a slow jog up until 7 m/s. Ø After this SR increases much more than SL. Ø Support and non-support phases are also of interest. Ø Support Phase: Jogging 68%, moderate sprint 54%, full-sprint 47% Mechanical Efficiency (Figure 8-27) 0 2 consumption PSF = preferred stride frequency -20% -10% PSF +10% +20% 15
110.000 100.000 90.000 Displacement - Time Answer to Running Kinematics Problem Displacement-Time Graph Answer to Running Velocity - Kinematics Time Problem 14.000 12.000 Velocity-Time Graph Displ. (m) 80.000 70.000 60.000 50.000 40.000 30.000 20.000 10.000 0.000 0 1 2 3 4 5 6 7 8 9 10 Time (s) Vel. (m/s) 10.000 8.000 6.000 4.000 2.000 Female high school sprinters reached max. speed between 23-37 m. Lost an average of 7.3% during final 10 m. Chow, 1987 0.000 0 1 2 3 4 5 6 7 8 9 10 11 Time (s) Ø The world record for the 100m is? Ø The world record for the 200m is? 100 m vs 200 m Accel. (m/s2) Answer to Running Acceleration Kinematics - Time Problem 8.000 7.000 6.000 5.000 4.000 3.000 2.000 Acceleration-Time Graph 1.000 0.000 0 2 4 6 8 10 12-1.000 Time (s) 16