Emily WeimerBiomechanics Laboratory DAngular KinematicsMaxAngularPosition(deg)MinAngularPosition(deg)AngularDisplacement(deg)AverageAngularPosition (deg)AverageAngularVelocity(deg/sec)MaximumAngularVelocity(deg/sec)AverageAngularAcceleration(deg/sec^2)MaximumAngularAcceleration(deg/sec^2)40 RPM121.82 76.208 .109667 99.78587801-19.1871347590.636660.700921986653.6833380 RPM120.36 76.904 .677 98.7587957 -0.30713978 166.809326.2849462 1691.89660 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5758595105115125Angular Position v. Time40 position80 positionTime (s)Angular Position (deg)0 1 2 3 4 5-200-1000100Angular Velocit y v. Time40 RPM velocity80 RPMTime (s)Velocity0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1500-1000-500050010001500Angular Accelerat ion v. Time40 RPM accel80 RPMTime (s)AccelerationDiscussion:In the above figures, both the 40 RPM and 80 RPM pedaling speeds have a similar sinusoidal curve for their angular kinematics at the knee joint. The main difference between the different pedaling speeds is the frequency, with the 80 RPM frequency being higher, meaning thatmore complete pedal cycles happen during the 5 second periods, which in the graph can be seen as having more peaks. Overall, both the 40 RPM and 80 RPM pedaling speeds followed similar trends but the 80 RPM speed happened more frequently, and had higher and lower positive and negative values. The values for the 80 RPM speed had a much bigger range from peak to minimalposition whereas the 40 RPM speed tended to be closer to zero with a smaller range between peakand minimal position. The angular position vs. time graph is the only graph that doesn’t have negative values, as the position being measured was the knee while pedaling, which was continuously moving in the positive direction, both velocity and acceleration vs. time graphs haveboth positive and negative values.In the angular position vs. time graph, the 40 RPM and 80 RPM maximum, minimum, andaverage values were very close. For example, there was only a 1.46-degree difference in the maximum angular position, with the 40 RPM having a slightly greater maximum position at 121.82 degrees, as well as only a 0.696-degree difference in the minimum angular position, this time with 80 RPM having a slightly greater minimum position at 76.904 degrees. Just by looking at the angular position graph values, you can tell that there isn’t much variance between the 40 RPM and 80 RPM maximum and minimum values, which can be inferred that the averages are about the same as well, which can then be confirmed by looking at the data points to see that 40 the averages are very similar with 40 RPM having a 1.02708-degree higher average angular position. In contrast with the angular position data, the angular velocity and angular acceleration saw greater differences between data values. An example of this can be seen in the 76.1726-degree difference between the maximum angular velocity values for 40 RPM and 80 RPM with 40 RPM having a maximum velocity of 90.63666 degrees and 80 RPM having a maximum velocity of 166.8093 degrees. The average angular velocity, average angular acceleration, and maximum angular acceleration also vary greatly between the 40 RPM and 80 RPM speeds. We obtained these results by using a bicycle ergometer, which has a fixed system. The participant’s data was recorded while pedaling through a fixed system. If the participant were to walk or run, their data would be much different because neither of those involve a fixed system, rather a system that would yield extremely variant results from person to person. Using a bicycle ergometer for the purpose of this lab allows us to analyze the data of a fixed system, which yields similar results for all participants. The average values for both angular velocity and angular acceleration were also a source of difference in the data for this lab. The maximum value for angular velocity and angular acceleration was much greater than the average velocity and average acceleration, in both 40 RPM and 80 RPM. Due to the fixed system of the bicycle ergometer, the values go from high to low, passing through zero each time. Ignoring positive and negatives, the values above zero were similar to the values below zero, which would lead to an average value somewhere around zero. When pedaling at 80 RPM, the participant is pedaling at a faster speed, so the average values for velocity and acceleration were larger in the 80 RPM trial than the 40 RPM trial. The data was pretty much to be expected because of the fixed system, the participant would have averages coming out somewhere around zero because the maximum and minimum values would basically cancel each other