Chapter 6, Problem 34P

Cam is a mechanical device that transforms rotary motion into linear motion. The shape of the disc is designed to produce a specified displacement profile. A displacement profile is a plot of the displacement of the follower as a function of the angle of rotation of the cam. The motion of a certain cam is given by the following equations.

$y=6\left[2\text{θ–0}\text{.5sinθ}\right]/\pi$ for $0\le \text{θ}\le \pi /2$

y = 6 for $\pi /2\le \text{θ}\le 2\pi /3$

$y=6-3\left[1-0.5\cos \left(3\left(\text{θ–2}\frac{\pi }{3}\right)\right)\right]$ for $2\pi /3\le \text{θ}\le \text{4}\pi \text{/3}$

y = 3 for $4\pi /3\le \text{θ}\le 3\pi /2$

$y=3–1.5{\left(\frac{\text{θ}-3\left(\pi /2\right)}{\pi /4}\right)}^2$ for $3\pi /2\le \text{θ}\le \text{7}\pi \text{/4}$

$y=0.75-0.75{\left(1-\frac{t-7\left(\pi /4\right)}{\pi /4}\right)}^2$ for $7\pi /4\le \text{θ}\le \text{7}\pi \text{/4}$

Write a MATLAB program that plots the displacement profile for one revolution. First create a 100 element vector for $\text{θ}$ , then by using a loop and conditional statements calculate the value of y for the corresponding values of $\text{θ}$ . Once y and $\text{θ}$ are known, plot y vs. $\text{θ}$ .