Emily WeimerBiomechanics Laboratory BLinear KinematicsIntroduction:The purpose of this laboratory was to analyze the relationships between various kinematic variables, including linear position, displacement, and velocity. These variableswere all studied during steady-state human locomotion. By looking at the linear position, using a marker placed near the participant’s body center of mass, we were able to calculate and analyze the displacement, velocity, and acceleration. We looked at the two different human locomotion patterns; walking and running. After obtaining the data we were able to calculate the velocity values during difference formulas including First Central Difference Method, Forward Difference Method, and Backward Difference Method. Methods:Participants placed a position marker near their center of mass, presumably around the sacrum, and then were asked to walk and run at their comfortable speed acrossthe force platform. Using the force platform ensured that the movements were captured by the motion analysis system, Qualysis. Participants were instructed to maintain a steadyspeed while walking or running through the camera’s field of view. The video cameras used in our laboratory recorded the participant’s motion at 240 Hz. Throughout motion, the Qualysis system was able to determine the 3D position of the position marker placed on the sacrum throughout the duration of movement. Following the in lab portion, the data for complete stride of both walking and running was extracted. We were able to differentiate this data to analyze an estimate of the instantaneous velocity over the full stride cycle for both walking and running. Using the velocity data that we calculated we could then create an estimate of the instantaneous acceleration again for the full stride of both walking and running. The formulas that were used were:1. First Central Difference Methodv = ᵢ xᵢ ₊ ₁ + xᵢ ₋ ₁ 2Δt 2. Forward Difference Methodv₁= x ₂ - x ₁ Δt 3. Backward Difference Methodvn = xn – xn-1 Δtv = velocity at time iᵢxᵢ₊₁ = position at time i+1xᵢ₋₁ = position at time i-1Δt = change in time (time interval)n = number of data pointsSample Calculations:Here we were able to use the different equations to solve for horizontal velocity values:- Forward Difference Method = (-0.884 - -0.887) / (1/240) = 1.550- First Central Difference Method = (-0.871- -0.884) / (2 * (1/240)) = 1.549- Backward Difference Method = (.492 - .486) / (1/240) = 1.499 ResultsWalking:RunningTime CMHorizontalCMVerticalHorizontalVelocityVerticalVelocityHorizontalAccelerationVerticalAcceleration0.000 -1.160 0.938 2.63754 1.0943 2.25719 0.42250.004 -1.149 0.934 2.62814 1.0926 -3.33601 1.12020.008 -1.138 0.929 2.60974 1.0850 4.30259 2.78120.013 -1.127 0.924 2.59228 1.0694 4.05234 4.68190.017 -1.116 0.920 2.57597 1.0460 3.75003 6.51890.692 0.816 0.956 2.69830 -1.0018 -4.58446 -7.36040.696 0.827 0.952 2.67914 -1.0289 -4.59642 -5.63610.700 0.838 0.948 2.66000 -1.0488 -4.57194 -3.85080.704 0.849 0.943 2.64104 -1.0610 -3.40380 -1.98010.708 0.860 0.939 2.63163 -1.0653 -2.25803 -1.0148Time CMHorizontalCMVerticalHorizontalVelocityVerticalVelocityHorizontalAccelerationVerticalAcceleration0 -0.884 0.911 1.550 -0.048 -0.266 2.2590.004166 -0.877 0.911 1.549 -0.038 -0.468 3.3700.008333 -0.871 0.911 1.546 -0.020 -0.809 4.4300.0125 -0.865 0.911 1.542 -0.001 -1.082 4.3050.016666 -0.858 0.911 1.537 0.016 -1.344 4.1331.0125 0.467 0.910 1.488 -0.130 1.089 3.8981.016666 0.473 0.909 1.493 -0.113 0.894 4.0191.020833 0.480 0.909 1.496 -0.097 0.676 4.0931.025 0.486 0.908 1.498 -0.079 0.392 3.0921.029166 0.492 0.908 1.499 -0.071 0.222 2.0650 0.2 0.4 0.6 0.8 1-0.300-0.200-0.1000.0000.1000.2000.300Walking Vertical Velocity vs. Time Time (s econds )Ve locity (me te r s /se cond)0.000 0.200 0.400 0.600-1.5-1-0.500.51Running Vertical Velocity vs. Time Time (se conds)Ve locity (me te rs/se cond)0 0.2 0.4 0.6 0.8 1-1.000-0.800-0.600-0.400-0.2000.0000.2000.4000.600Walking Horizontal Displacement vs. Time Time (se conds)Displa ce me nt (me te rs)0.000 0.200 0.400 0.600-1.500-1.000-0.5000.0000.5001.000Running Horizontal Displacement vs. Time Time (seconds)Displacement (meters)0 0.2 0.4 0.6 0.8 10.8800.8900.9000.9100.9200.9300.9400.950Walking Vertical Displacement vs. Time Time (seconds)Displa ce me nt (me te rs)0.000 0.200 0.400 0.6000.8000.8500.9000.9501.0001.050Running Vertical Displacement vs. Time Time (s e conds)Displa ce me nt (me te rs)Discussion0 0.2 0.4 0.6 0.8 10.0000.5001.0001.5002.000Walking Horizontal Velocity vs. Time Time (se conds)Ve locity (me te r s /se cond)0.000 0.200 0.400 0.60000.511.522.533.5Running Horizontal Velocity vs. Time Time (se conds)Ve locity (me te r s /se cond)0 0.2 0.4 0.6 0.8 1-4.000-2.0000.0002.0004.0006.000Walking Vertical Acceleration vs. Time Time (se conds)Acce le ration (m/s e cond squa re d)0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700-30-20-1001020Running Vertical Acceleration vs. Time Time (s e conds)Acce le ration (m/s e cond squa re d)0 0.2 0.4 0.6 0.8 1-6.000-4.000-2.0000.0002.0004.000Walking Horizontal Acceleration vs. Time Time (se conds)Acce le ration (m/s e cond squa re d)0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700-10-50510Running Horizontal Acceleration vs. Time Time (se conds)Acce le ration (m/s e co nd squa re d)When looking at the vertical displacement of the center of mass for both walking and running, a similar trend can be noticed. Both graphs have similar curves, which suggests that there are similarities between the vertical displacements of the center of mass when walking and when running. These results can be broken down further to notice that in the walking portion, the vertical heights are lower than the running vertical heights. This is due to walking having less of a bounce and a shorter flight phase than running. The downward curve on the running graph also happens sooner than the downward curve of the walking graph, which can be explained by the faster step/land pattern of the foot hitting the ground that happens when running. Lastly, it is noticeable that both graphs appear to go through similar curve patterns. When looking more closely, it is noted that the walking curve goes through two up and down patterns in the 1.03-second period while the running curve goes through almost 2.5 up and down patterns in only .708 seconds. This is because the participant is able to complete more