The center of mass of a rigid body is a unique point that represents the mean position of all matter that composes it. Allowing representing complex bodies as a single point, this concept is underlying the basis of all essential mechanical calculations, and is therefore a crucial consideration in engineering. The paper shows how to devise a fast and convenient way of locating the centroid of planar objects of different shapes. For several shapes that can be represented as regions bounded by graphs of functions, this point can be found by using integral calculus. However, solving for the center of mass by hand is not only quite tedious, but also inapplicable to objects of arbitrary shape. Thus, it is decided to write a Python-based program that would implement computer vision techniques to scan through images depicting different objects and locate their centroids. For geometric bodies, the results produced by the program are aligned with those predicted by integral calculations. Moreover, the program is also able to successfully mark the centroids of arbitrary shapes, meaning that it is applicable to any possible planar object. The results are then proven experimentally by balancing the analyzed objects about the identified point.
"Locating Centers of Mass with Image Processing,"
Undergraduate Journal of Mathematical Modeling: One + Two:
1, Article 1.
DOI: https://doi.org/10.5038/2326-36184.108.40.20606 Available at: https://scholarcommons.usf.edu/ujmm/vol10/iss1/1
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Arcadii Grinshpan, Mathematics and Statistics
Jeffrey Golabek, Mechanical Engineering
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