Question in Mechanical Engineering (Dynamics)

EXTRA CREDIT ASSIGNMENT (7.5% of the overall grade BONUS)

DUE DECEMBER 14TH, THURSDAY BY 5 PM TO SLOAN 221

The real-life mechanism shown above can be found in the play area of the Kruegel Park in Pullman. It consists of 4 rigid bodies:

• Link AD rotates about a fixed axis going through A, with a known angular speed ω1=2 rad/s at a given instant under the effect of a horizontal force F1=1 N . θ1 is the angle between this link and the horizontal and it’s equal to 30o at this particular instant. The relevant lengths for this link are: |AD|=0.5 m, |AC|=0.2 m and the center mass of this link is at the mid-point of of A and D. The mass of this link is 3 kg and mass moment of inertia of this link about point A is 0.25kg.m2.

• The links EB and BF are rigidly connected to each other and the entire structure rotates about a fixed axis passing through point B, with a known angular speed ω2=1 rad/s at a given instant under the effect of a horizontal force F2=0.5 N. θ2 is the angle between EB and the horizontal and it’s equal to 90o at this particular instant. The relevant lengths for these links are:

|EB|=0.5 m, |BF|=0.5 m, center of mass of BF is at the mid point of B and F and, center of mass of EB is at the mid point of E and B. The masses of EB and BF are both 3 kg. The mass moment of inertia of EB and BF about point B are both 0.25 kg.m2.

• The link CG undergoes general plane motion, and is connected to the other links at points C and G through pin connections. θ3 is the angle between this link and the horizontal and it’s equal to 15o at this particular instant. The length |CG|=0.5 m and the center of mass is located at the mid point of C and G. The mass of this link is 3 kg and mass moment of inertia of this link about its center of mass is 0.0625 kg.m2.

• The scoop GF is connected to the other links at points G and F through pin connections and undergoes general plane motion. θ4 is the angle between the scoop and the horizontal and it’s equal to 60o at this particular instant. The center of mass of the scoop is located at point H which is collinear with G and F. The length |GF|=0.1m, |FH|=0.2 m. The mass of the scoop is 2 kg and its mass moment of inertia about its center of mass is 0.1 kg.m2. Assume there are no forces acting on the scoop by the ground.

Given this information, write down all the equations that are necessary to determine the following at the given instant:

1. Angular speeds of link BF and the scoop. 2. Angular accelerations of all the links.

You don’t need to solve these equations. You can leave vector equations as is, namely you don’t have to convert them to two scalar equations. You are advised to draw the free body diagrams of each link and apply Newton’s second law. You are looking at 30 scalar equations (vector equations count as 2 scalar equations).