1Lecture 3Review Lab #2Data NormalizationPresenting Angular Kinematic DataEXS 587Dr. MoranFall 2007Lecture Outline• Further explanation of Lab #2• Data Manipulation» Normalization» Missing Data Points• Angular Kinematic Data Presentation2Jump HeightTouch DownMax Y-CoordLab #2: Summarized Data• Vertical Jump Analysis• Without Arms» Maximum Knee Flexion = 110.9 ± 4.4°» Hip Marker Vertical Displacement = 0.35m• With Arms» Maximum Knee Flexion = 97.6 ± 3.5°» Hip Marker Vertical Displacement = 0.40m*» * = went off viewing screen (projectile motion)3Lab #2: (con’t)• Why did the “With Arms” trials produce the greater vertical displacement of the COM with a smaller countermovement?– Hara et al. (2006) The effect of arm swing on lower extremities in vertical jumping– Journal of Biomechanics – 39: 2503-2511– Increase in total body work (34% came from upper extremity)– Work at the knee was REDUCED Lab #2: Why does a countermovement help the VJ?• Stretch Reflex• Propioceptors: sensory organs» Located within:1.) joint capsules (Ruffini endings, pacinian corpuscles)2.) Muscles (spindles)3.) Tendon (GTO – golgi tendon organs)» Muscle Spindles: report the relative change in muscle length, afferent (IIa) endings are located between the muscle fibers and monitor and speed and magnitude of stretch» If the stretch is quick enough, then motor neurons will also be stimulated  STRETCH REFLEX4Lab #2: Why does a countermovement help the VJ?• Inhibitory Action:» Sensory fibers also synapse with the motor neurons of the antagonist muscle fibers providing an inhibitoryresponse (RECIPROCAL INHIBITION)Other Factors Why a counter-movement improves VJ performance• A counter-movement jump has been found to increase stored potential elastic energy within the tendons by 26 ± 3% » Voight et al. (J. of Biomech, 1995)» Only a minimal amount of stored energy is the result of muscle fiber (Alexander et al., 1977)Increased control of the direction of movement with a countermovement action5Data Manipulation• How does a researcher average data across numerous trials?» Problem: each trial does not take the same amount of time so computing the mean for each frame would not be correct» Solution: an ENSEMBLE AVERAGE can be computed• Steps to Compute Ensemble Average1.) Normalize: this means that a given portion of each trial is identified as 100% and rescaling the sampling rate as a percentage of that durationEx (Gait): from right-foot toe-off to right-foot toe-off is considered one full cycle2.) Data Interpolation: in order to compute an average a researcher needs data of a kinematic variable at the SAME point in time. What data frames could we use to match trials from the vertical jump kinematicanalysis?Normalizing DataPicking Out Event MarkersFind these same event markers in every trial!Marker #1Maximum Knee FlexionMarker #2Touch Down6Normalizing Data(Continued)11037Trial #210445Trial #1Event #2Event #1Sampling Frequency = 60 Hz (60 frames/second)1.22 s0.98 sLinear Interpolation• Assumption: that the data between collected data points is linear. That may be acceptable when a high sampling frequency is utilized.» Ex: Data Point #1 (x,y) 0.310s 1.185mData Point #2(x,y) 0.315s 1.190mLinear Equation: m = (1.190-1.185)/(0.315-0.310)m = (0.005)/(0.005) = 1y – 1.185 = 1*(x – 0.310)f(x) = x + 0.875So:f(3.11) = 0.311 + 0.875 = 1.186f(3.12) = 0.312 + 0.875 = 1.187…7Linear Interpolation(continued)• For movements that occur rapidly and the sampling rate is not high, a splineinterpolation is warranted. • MS Excel Add-In: cubic spline interpolationThese methods would also be used to deal with missing data points. Missing data points can occur in kinematic analysis when markers are blocked during a movement sequence. Angular KinematicsPresentation• Presentation Form• Joint Angle vs. Time» Most common• Angle-Angle Diagram» Aids visual understanding of a movement sequence• Phase Plot» Motor Control Field  viewed as an expression of the control of that system8Angle-Angle PlotsInterpretation• Decoupled Coordination: one joint angle changes while the other remains constant• A trajectory line with a slope means both angles are changing at a constant ratio– Positive Slope = in phase (ex. Extension in both)– Negative Slope = out of phase (Flexion in one, Extension in the other)• Turning Points = both points reach maximum and then start in opposite “joint direction”; synchronization• Rounded Trajectory = phase offset; decoupled coordinationAngle-Angle PlotsApplication: Sprinting DrillsRunning A DrillRunning B DrillSprintingOnline