| University | Universiti Teknologi MARA (UiTM) |
| Subject | MEMB2044 Theory of Machines |
QUESTION 1: Analysis of a Four-Bar Linkage [30 Marks]
The crank O2A of the four-bar linkage shown in Figure 1 is rotating with:
- Angular velocity (ω): 3 rad/s (clockwise)
- Angular acceleration (α): 2.5 rad/s2 (counterclockwise)
The dimensions of the linkage are as follows:
- O2A = 100 mm
- AB = 200 mm
- O4B = 75 mm
- AC = 100 mm
- BC = 150 mm
- AD = 50 mm
- Crank angle θ2 = 45°
Using the information provided, complete the tasks below:
(a) Space Diagram and Output Angles [5 Marks]
- Sketch the space diagram of the given configuration, focusing on the O2-A-B-O4 linkage lengths only.
- Estimate the coupler angle and the rocker output angle for the linkage.
(b) Velocity Analysis [10 Marks]
- Using the values obtained in part (a), graphically estimate the following for the current configuration:
- Linear velocity of the coupler and rocker.
- Angular velocity of the coupler and rocker.
(c) Acceleration Analysis [12 Marks]
- Using the values from parts (a) and (b), graphically estimate the angular accelerations of the:
- Rocker
- Coupler
(d) Impact of Constant Input Angular Velocity [3 Marks]
- Discuss how the acceleration would change if a constant input angular velocity is applied instead of the given conditions.
- Explore all possible outcomes and scenarios.
QUESTION 2: Analysis of a Non-Typical Four-Bar Linkage [7 Marks]
Figure 2 shows a non-typical four-bar linkage mechanism where:
- Link a is the input link.
- An external force is applied at the handlebar.
- The input angle is represented as θa.
- The handlebar rotates with:
- Angular velocity (ωa):
- Angular acceleration (αa):
Complete the tasks below:
(a) Vector Loop Diagram [3 Marks]
- Draw a vector loop diagram for the mechanism. Ensure that:
- The diagram is clearly labeled.
- Use the given letters and symbols.
(b) Velocity Equations [4 Marks]
- Using the vector loop method, derive the equations that can be solved to determine the velocity of the output variables (ω).
- Note: Do not attempt to solve the equations. Simply derive them.
Units: All dimensions are in millimeters unless otherwise stated.
Semester: MEMB2044, Semester 2, 2023/2024
