2.086: Numerical Computation for Mechanical Engineers
Optimizing the Squat
2.086 Final Project: Benjamin Soria and Mark Moser
Learn About the Class
2.086 teaches programming concepts, including variable types, data structures, and flow control, through the use of case studies and real-world applications. The class provides an introduction to linear algebra, probability, and numerical methods relevant to MechE, including approximation (interpolation, least squares, and statistical regression), integration, solution of linear and nonlinear equations, and ordinary differential equations. The class covers deterministic and probabilistic approaches. Class examples are related to MechE, particularly robotics, dynamics, and structural analysis.
For the term project of 2.086, students conceive, implement, and use MATLAB to code a solution/analysis to an engineering purpose of their own choosing. This gives an opportunity to write longer, more ambitious code that allows students to dive deeper into topics that interest them and/or may benefit them professionally. Students present the problem they address to a community of technical professionals.
Learn About Our Project:
Project Description: The squat is widely considered the supreme barbell exercise for building up leg strength and athletic explosiveness. As it is a popular exercise, there exist many variations of the exercise. The high bar squat is most popular among the general public, the low bar squat is well-favored in powerlifting, and the front squat is fundamental among Olympic-style weightlifting. Each variation provides tradeoffs between flexibility, required effort, and achievable load. In each case, however, the athlete must be sure to 1) keep the weight of the bar over their midfoot (to prevent a torque about their midfoot and thus avoid spending energy resisting this motion) and achieve “depth” (70-90 degrees at the knee joint in general or get the crease of the hip below the plane of your knee for competitive powerlifting).
Barbell Forces: Levers, Moments, and Torque
By Jordan Feigenbaum, https://www.barbellmedicine.com/blog/barbell -forces-levers-moments-and-torque/
Numerical Analysis: We base our analysis on optimizing the squat for whatever the user is most interested in. There are a number of variables that a lifter can change in their squat that change their performance: knee width, heel height, and bar positioning on the back. Given one of two of these values, we aim to find values of the other variables to maximize the weight lifted. Additionally, we find the configuration that places the least stress on the athletes joints to help lifters avoid injury. We model muscles as springs, allowing us to introduces conditions regarding the speed of the squat and the strength of muscle groups.