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MIET2510 Mechanical Design

Week 1 Tutorial - Kinematics Fundamentals and Analysis of Mechanisms

Steps to Find the Mobility of a Mechanism

  1. Identify the Links and Joints:
    • Count the total number of links ($L$) in the mechanism.
    • Count the total number of 1 DOF joints ($J_1$).
    • Count the total number of 2 DOF joints ($J_2$).
  2. Use Gruebler’s Equation:
    • Substitute the values of $L$, $J_1$, and $J_2$ into Gruebler’s equation, $ M = 3(L-1) - 2J_1 - J_2$ and do the calculation to find the mobility $M$.
  3. Interpret the Result:
    • A positive value of $M$ indicates the number of degrees of freedom (mobility) the mechanism has.
    • An $M$ value of 0 indicates a structure with no mobility.
    • A negative $M$ value indicates an over-constrained system or a structure under pre-load.

Question 1

Draw a kinematic diagram of the following machine. Your diagram should be roughly to scale and each link should be numbered.

Question 2

Draw a kinematic diagram of the following device. Your diagram should be roughly to scale and each link should be numbered.

Question 3

Calculate the mobility of the linkages

Question 4

Calculate the mobility of the linkages

Question 5

Calculate the mobility of the linkages

Question 6

Calculate the mobility of the linkages

Question 7

Calculate the mobility of the linkages

Question 8

Calculate the mobility of the mechanism shown below.

Question 9

Calculate the mobility of the mechanism shown below.

Question 10

Calculate the mobility of the mechanism shown below.

Question 11

Calculate the mobility of the mechanism shown below.

Question 12

Find the mobility of the ice tongs before and after grabbing

Question 13

Find the mobility of the gas pedal mechanism

Question 14

Using the kinematic diagram you drew in Question 2 calculate the mobility of the mechanism using Gruebler’s equation.