Analyzing Experimental Data and Identifying Errors
Updated: Oct 13, 2020
Ok, so either something in our math was incorrect, or in our experiment. After checking my math with a mentor and my brother, I realized in the shower that my experiment had been poorly setup and had a large error. The diagram below best displays what was assumed on the right in our math calculations vs. the setup that we used which is on the left. It also shows that we can fix this error by attaching the springs around the pulley using a toothed belt instead of screwing it down to holes in the pulley as we did earlier (images in previous article).
It appears that at smaller angles that this error may not measure that much, but to make sure I decided to calculate the error in force that came as a result of the bend in the direction of the spring's pull. It is important to note that the bend only occurs on one side, while on the other a string simply rolls around the pulley, and the direction of the spring's pull remains the same.
After doing some geometry and using laws of sines and cosines, I came up with two funcitons. f(x) shows the effective extension of the bent spring when the angle of the joint (z) is set to a certain value. g(x) shows how this will effect the force at the end using a set of springs that have a resting length of 3. What we can see in this graph is that changing the initial value of the extension will have a linear relationship to the force when the joint is rotated 45 degrees. This agrees with our experimental data, and shows that our error was calculated.
Now, we must fix this experimental error, measure data again, and test whether we can achieve variable stiffness accurately using this spring system.