Four$-$Bar Analysis Using Numerical Methods

For the mechanism shown, find the angular velocity and angular acceleration of the follower link over the course of an entire rotation of the crank link, which spins at $60$ RPM$.$

Set up a vector of ${}_2$ values that sweep from $0$ degrees to $360$ degrees

Set up a vector of time steps, $t$ and a step size, $dt,$ that correspond to how long it takes for the crank link to make a full rotation and how many discrete steps it takes to make that rotation

I chose to analyze the linkage over $100$ steps, so $dt=\frac{1}{100}$ seconds

Set up a for loop to analyze ${}_4$ at each time step $($index should be from $1$ to the length of jour time vector$)$

Inside of this for loop, you need to find

Length of line BD

Gamma

Follower angle, ${}_4$

Using your vector of ${}_4$ values and your time step dt

Numerically estimate the angular velocity for each pair of ${}_4$ values $-$ this will result in a vector of $4$ values

${}_4(t_i)$~~$\frac{{}_4(t_{i+1})-{}_4(t_i)}{dt}$

Numerically estimate the angular acceleration for each pair of ${}_4$ values $-$ this will result in a vector of ${}_4$ values

${}_4(t_i)$~~$\frac{{}_4(t_{i+1})-{}_4(t_i)}{dt}$

Plot ${}_4$ and ${}_4$ vs time