Homework #2

import numpy as np
import matplotlib.pyplot as plt
plt.style.use('fivethirtyeight')

Homework #2

slider crank diagram: two links connected to a piston and the ground

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 L1=1 m

  • link BC L2=1 m

  • the angle of link AB rotates at a constant ˙θ1=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. θ1=θ2=0o and rc=2 mˆi. Find the positions of A, B, and C for one full rotation, t=0...2π.

3. Plot the positions of B and C vs time.