MEMB2044 Theory of Machines Semester 2 Assignment Malaysia

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 θ_a.
• The handlebar rotates with:
  • Angular velocity (ω_a):
  • Angular acceleration (α_a):

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

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