Allen Salama - End of 3rd MP Update

I was initially tasked with calculating the kinetic energy output of gait motion, which I approached in 6 parts. I dealt with two segments, the thigh and the leg (separated by the knee), each with three energy values to obtain: translational energy, rotational kinetic energy, and potential energy. I actually started with the second type first, as I knew it would prove to be the most difficult to calculate of three.
I started with the RKE of the leg. Since the hip has very little movement throughout the walking motion, I assigned it as a fixed point in order to find the rate of angle change. I separated the motion into several cycles, and worked with each one individually. Using trigonometry, I created an "isosceles" triangle by taking the frame with the widest stance (since the two legs of the triangle are actually the length of the leg segment) and assumed that angle to be the total angle change. I did this for each cycle, plugged it into RKE after finding each trial's moment of inertia, and found the average of all the trials. The value ended up being below 1 J, which discouraged me (even though RKE is supposed to be smaller), and because of this, I decided to neglect the RKE of the thigh since it would have been much more difficult to calculate.
The next-most difficult energy to calculate was potential energy of each segment. I found the coordinates of the center of mass of each segment, and measured its potential energy at each time frame by finding the distance (or height) from the position of the COM at that time frame from the absolute minimum location of the entire motion. I took the sums of these values to obtain my total PE results for each segment.
Lastly, translational energy. This was simply mv^2, and I found the velocities of each segment by putting their distances traveled over time. This too, surprisingly, yielded pretty low values.

Looking back I definitely would have approached the calculations differently. I averaged all the RKE values from the start, when in hind sight should have done it like with the PE values: calculating the RKE at each time frame and taking the sum of all those energy values. I think that's why I may have gotten very small energy amount for RKE and TE.

After the math, I attempted to use the coordinates and values I had from using the Kinovea video analysis software in order to build a walking model on the computer. I went with Wolfram's Systemmodeler, but after a couple unsuccessful weeks, I got no where with the program. Simply put, Systemmodeler was just out of my and Max's reach and it required a very comprehensive foundation of mechanical engineering and modeling.

Luckily, Mr. Lin sent me a link to an OpenSim model developed by a Stanford researcher.  I have been playing around with it for the past two days, and it is certainly far more complex and intricate than what I had envisioned. But adding parameters could allow me and Max to observe the effects which adding mass of the knee has on the gait motion and energy output.

The biggest problem is, obviously, time. Personally, I would rather just get straight into the building and wiring of the generator rather than work with computer models, and with the end of the year approaching quickly, that made be what needs to happen.

Potential Energy Calculations
Rotational Kinetic Energy Calculations
Translation Energy/Final Calculations

Week 15-17 Progress Report

We have both made considerable progress in their respective areas of focus in relation to the project.

Max:

Through an initial multimeter test of the first prototype of the generator, I found that the generator was producing voltage with alternating current. I also discovered through this test that there was a negligible amount of current being produced by the generator. To solve the first problem, converting the ac current to dc, I researched a component provided to us by Mr. Lin called a DC Rectifier. By utilizing the information I found I was able to construct a circuit that successfully converted the current to DC. The next step was to analyze this electricity with a oscilloscope. The graphs of the scope showed a large amount of interference which we will try and filter out on the next attempt at getting a data reading. With the information I was able to extract I came to the conclusion that the amount of wire we have wrapped around the doughnut provides us with 100 millivolts. A quick estimation revealed that we could fit four to five of these sections of wire on the doughnut. By adding these and doubling the thickness of each section we could potentially generate a full volt of electricity.

At this point two main problems are where we will focus our attention. The first is that even with the DC rectifier the multimeter was still not able to read any current in the generator. The second is that to maintain the amount of voltage I was achieving in the test, the ball would move much faster than a walking leg would be able to rotate it. We have not discussed a solution to the first problem because it is probably due to a low power generation. The second problem however is our main concern. In order to solve this we will use a program which I am still trying to obtain call maplesim. This program will allow us to implement the formula that Allen has been working on to create a model that will optimize the generator shape to cater to the motion of the leg. We will also construct a robot leg that we can use to uniformly test every new generator prototype we make.

Allen:

I have been working with the Kinovea video analysis software to acquire a rough estimate of the amount of kinetic energy yielded by the human walking motion, which could then be converted to power. The approach to determining rotational kinetic energy has varied; originally, I had been attempting to take the angle change of the entire leg to calculate angular velocity, but after conferring with Max and Mr. Lin, a better approach would be dividing the walking motion into two segments: one from hip to knee and the second from knee to ankle. This week, I have been honing in on the first segment. Although there is an angle tool in Kinovea with tracking capabilities, the data wouldn’t export to Excel. So, I has resorted to simple trigonometry; assuming that the length of each segment is fixed, the walking motion can be described in the form of an isosceles triangle, with two of the legs being equal (the length of the measured segment) and the base being that actual path of the knee marker.

Using that method of thinking, I divided the walking motion of a video clip (which he and Max had taken earlier on a treadmill, using neon green stickers as trackers) into 9 walking cycles. To find the third side, I found the slope of the tangent line for the path of the knee marker. This slope will be used to calculate the distance between the absolute extrema for each cycle graph, which will essentially be the third side of the triangle. Now, with three sides of a triangle, I can use the Law of Cosine to find the angle of each cycle’s triangle at its widest point. Using the Intermediate Value Theorem, because the motion of the knee is a continuous function, I can assume that there is a point in that function in which the angle is 0 radians - that is why finding the third side with the absolute extrema can be used to find the angle change, as the “longest” triangle will essentially describe the largest angle and consequently the total angle change.

I will find the average angular velocity for each cycle, and use that value - along with the moment of inertia for the hip-knee segment - to calculate a rough estimate of the rotational kinetic energy for that segment. I then will repeat the process for the second segment (knee to ankle). Since the motion of the knee isn’t purely rotational, I will also use Kinovea to calculate the translational kinetic energy for each segment, which should be a lot easier and require much less trigonometry. I will then send this out to Dr. Philip Martin of the Department of Kinesiology at Iowa State for an expert opinion, and if all bodes well, I will move on to working alongside Max with the MapleSim (or a similar tool) software, as well attempt to build a simple robot that uses segments to mimic gait motion to use during the testing phase of the project. A robot should yield more consistent results than a human, but first, a more optimally-shaped generator will need to be created, which will be the next phase.

Week 14 Progress Report

This week, Max brought a multimeter and wire with him in  order to begin electrical testing. He coiled a segment of the doughnut (the two halves held with basic tape for the moment) tightly with wire, hooked the ends to the voltmeter and started whipping the ball around within. We were pleased to find that voltage was generated (roughly 200-300 millivolts), but disappointed to see no value for current arise. Perhaps the value was too small to be picked up on the multimeter, but that will be our next step moving forward.
Allen continued to sift through the documents he had received and found another flaw in his earlier calculations, this time with the angular velocity. Originally, he had used Kinovea to use the point on his knee joint to generate values of angular velocity. However, this now seems to be inaccurate; rather than acquiring the angular velocity of the knee joint, what needs to be found is the angular velocity of the entire leg. Dr. Martin says this can be found by measuring the rate of change of the angle at which the leg moves. So, Allen re-recorded video snippets, this time placing green rather orange orange dots (the orange didn't provide enough contrast against his skin accompanied with the poor lighting in the gym) along the entire leg. He will continue to fidget with the angle tool in Kinovea in order to extract data to Excel like he had before in order to garner the correct yield for angular velocity.

Week 13 Progress Report

This week we ran into some speed bumps with our project. When attempting to print the second half of the "doughnut" plastic model for the track, Max saw that the printing was all jumbled up. Plastic would print out haywired and linear rods would stick through the track. We were puzzled as to why these problems didn't arise with the first print, but Max solved this issue but reconfiguring the actual shape of the track on SketchUp into one that included much more hidden geometry. Now, the prints are huge successes; the track has just enough thickness and space for the neodymium ball to roll around fluidly. However, our "doughnut" shape may not be optimal after all; while walking around with it on the side of our knees, we noticed that the ball didn't really swing around as we had envisioned it would. Instead, the ball would just roll back and forth along the bottom of the track. We will see to this shape-issue later, as Max wants to get a start on testing this device for actual electric conductivity next week.
Allen reached out to two professors, Dr. Phillip Martin of the Department of Kinesiology at Iowa State university and Dr. Todd Royer of the Department of Kinesiology and Applied Physiology at the University of Deleware, to seek guidance regarding the calculation of the moment of inertia. What he got was far more than expected: a revsed vision of human walking entirely. Walking isn't one body of movement, but rather the compilation of several segments at work. Dr. Martin in particular provided Allen with some excellent resources in two chapters from Dr. David A. Winter's Biomechanics and Motor Control of Human Movement, 5th edition.  Instead of calculating the rotational kinetic energy (RKE) of the knee joint, Allen needs to calculate the RKE the entire leg ("leg"in this case is referred to as the lower shank, aka from the knee to the ankle). The moment of inertia is found by the formula: I_{leg cm} = [m_leg  * (length_leg * radius of gyration_leg)²]. The length of my lower shank is approximately .413m. Since my mass is 65.7709kg and the leg takes up roughly 4.65% of the body mass (based off Winter's findings), the mass of my leg is 3.06kg. Finally, the radius of gyration is a given ratio of 0.302, so after plugging in all these values into the formula above, the moment of inertia in my leg equates to roughly 0.0476kg*m^2.