Homework #2
import numpy as np
import matplotlib.pyplot as plt
plt.style.use('fivethirtyeight')
Homework #2¶
Consider the slider-crank shown above. Two links are connected by pins to the ground at \(A\) and the piston at \(C\). Link AB can rotate around \(A\) and link BC can rotate around \(C\) and the piston maintains contact with the ground.
Consider the following kinematic properties:
link AB \(L_1 = 1~m\)
link BC \(L_2 = 1~m\)
the angle of link AB rotates at a constant \(\dot{\theta}_1 = 1~rad/s\)
1. How many degrees of freedom does the slider-crank have? How many degrees of freedom and how many constraints?
2. The system begins to move with both links horizontal e.g. \(\theta_1 = \theta_2 = 0^o\) and \(\mathbf{r}_c = 2~m \hat{i}\). Find the positions of \(A,~B,~and~C\) for one full rotation, \(t = 0...2\pi\).
3. Plot the positions of \(B~and~C\) vs time.