Computational Assignment 5

Due Wednesday 10 November 2004

Consider the slider-crank mechanism (Figure 1) consisting of two rigid links and a piston that are connected by frictionless revolute joints and constrained to move in the vertical plane. The piston, connected to bar AB at the center of mass B, slides on a frictionless horizontal plane. The bars and the piston, all made of steel (density: 7.8´10³ kg/m³), have an identical thickness of 20 mm (measured along the joint axes). A constant torque of 100 N×mm is applied to the crank OA, which initially is at rest with = 30°. Perform the following simulations for 0 £ t £ 0.5 s (using the coordinate frame as shown, whose origin is at O).

1. Submit a printout of your model (front view, with all joints and the torque shown, at t = 0).
2. Compute and plot the crank’s angular position , velocity and acceleration as a function of time.
3. Compute and plot the piston’s position , velocity and acceleration as a function of time.
4. Compute and plot the x- and y-components of the reaction force at joint O as a function of time.

Figure 1. A crank-slider mechanism

Solution:

1. The print of the model is shown in Figure 2

Figure 2. The model printout of the slider-crank mechanism

2. The crank’s angular position, theta_OA, angular velocity theta_dot_OA and angular acceleration thetha_double_dot_OA are plotted in Figures 3~5 respectively.

Figure 3. The crank’s angular position theta_OA as a function of time	Figure 4. The crank’s angular velocity theta_dot_OA as a function of time
Figure 5. The crank’s angular acceleration theta_double_dot_OA

3. The the piston’s position x_B , velocity x_dot_B and acceleration x_double_dot_B as a function of time.

Figure 6. The piston’s translational position x_B as a function of time	Figure 7. The piston’s translational velocity x_dot_B as a function of time
Figure 8. The piston’s translational acceleration x_double_dot_B as a function of time

4. The x- and y-components of the reaction force at joint O as a function of time are plotted in Figures 9 and 10.

Figure 9. x-component of the reaction force at joint O as a function of time

Figure 10. y-component of the reaction force at joint O as a function of time

I also provide the link to the solution model. Click here (crank-slider mechanism), you can download it.

To check the solution model, right click any part (such as link, joint, torque or even the figure) that you are interested in and choose “info”. A window will pop up showing you its setting information.

Created by Yi Wang, Mechanical Engineering, Carnegie Mellon University, 11/10/2004