MEMB2044 Theory of Machines Semester 2 Assignment Malaysia

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.

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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


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