4-Bar Linkage Optimization

Project Overview

The purpose of this project was to build off of the Habitat’s Air-Lock Linkage System project by optimizing the link lengths for a maximum button depression time. My partner and I decided on two main methods to accomplish this optimization: Brute Force and a multi-dimensional Newton-Raphson method.

The brute force method consisted of a MATLAB program that calculated the button depression time based off of the input linkage lengths. Using this program, we were able to gather an initial range of optimal link lengths and narrow down our focus. Since this took a long time to complete, we decided just to use the program more for checking the solution from the Newton-Raphson method.

For the multi-dimensional Newton-Raphson method, we used a set of 5 equations and 5 unknowns and a known button depression time to solve for link lengths that satisfied these requirements. These 5 equations were mainly implemented to help constrain the geometry of the link lengths. In addition, the known button depression time was just a proportion of the maximum allowable button depression time of 2 minutes.

Position graph of each joint as it moves through one complete rotation of the crank-shaft

Position graph of each joint as it moves through one complete rotation of the crank-shaft

Brute force data from initial link length inputs with the color corresponding to button depression time

Brute force data from initial link length inputs with the color corresponding to button depression time

Brute force data from narrowed link length inputs showing a clearer maximum area

Brute force data from narrowed link length inputs showing a clearer maximum area

First condition used for developing the Newton-Raphson equations demonstrating the point in time at which the button is initially pressed

First condition used for developing the Newton-Raphson equations demonstrating the point in time at which the button is initially pressed

Second condition used for developing the Newton-Raphson equations representing the point in time at which the button stops being pressed

Second condition used for developing the Newton-Raphson equations representing the point in time at which the button stops being pressed

Third condition used for developing the Newton-Raphson equations depicting the lowest height that the coupler-rocker joint reaches in its rotation cycle

Third condition used for developing the Newton-Raphson equations depicting the lowest height that the coupler-rocker joint reaches in its rotation cycle

Graph of coupler-rocker joint as a function of time showing more clearly what is being optimized

Graph of coupler-rocker joint as a function of time showing more clearly what is being optimized