Calculating the Mass of a Prosthetic Limb

by Riley Monaghan

Submitted : Fall 2012

In this project, the goal was to calculate the mass of a prosthetic limb within given parameters. Two functions, a(z) and b(z), were given, along with a set of three constraints, to help calculate the Greek constants; two graphs, one of a single cross section and the other of a sketch of the prosthetic, densities of plastic foam and titanium, and a radius of 1 cm for the titanium rod, along with the total length of the prosthetic of 45 cm.

The researcher first found the Greek constants of a(z) and b(z). This left the researcher with two equations that would help determine the (x, y) coordinates based on the position of z on the prosthetic. This allowed the researcher to set up a triple integral to find the total area, using the parameters of the two equations and the length of the prosthetic (45 cm).

The researcher found the total area of the prosthetic, then subtracted the area of the titanium rod, and multiplied it by the density of plastic foam that was given, to find the mass of the plastic foam. The researcher then found the mass of the titanium rod by multiplying the area of the titanium rod by the density of titanium. These two masses added together gave the researcher the total mass of the prosthetic limb.

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