MN5562/ME5047 – Computer-Aided Engineering 2020-21
Assignment: Synthesis and Dynamic Simulation of a six-bar linkage
Lecturer: Dr Yohan Noh (email: [email protected])

Question 1:
Given a six-bar linkage with the link lengths L1 = 0.1 m, L2 = 0. 04 m, L3 = 0. 12
m, and L4 = 0. 08 m, L5 = 0.06 m, L6 = 0.04 m, find the values for θ3, θ4, θ5, θ6,
ω3, ω4, ω5, ω6, α3, α4, α5, and α6 as shown in Figures 1, 2, and 3 for the open
circuit of the linkage assuming θ2 = 40°, ω2 = 25 rad/sec, and α2 = 15 rad/sec2.
The mass density is ρ=100000kg/m3, the link thickness T is 0.005 m, the joint
shaft and hole radius (R1) is 0.005 m, the link radius (R2) is 0.01 m, and the two
holes on the links are cut with a diameter d5 and d6 (l5, and l6) away from the
joints, respectively).
There is an external torque on the link 4 of τ4 N·m, applied at the centre of
mass (lg4) on link 4, and at the same time an external force of Fp @θf acts on
link 3, applied at point p and lf away from point A.

The different parameter values as shown below will be provided individually to
students.


Taking gravity acceleration as 9.81m/sec2, find F12, F32, F43, F14, F45, F65, and F16
at the joints and the driving torque τ12 needed to maintain motion with the
given angular velocity ω2 = 25 rad/sec and acceleration α2 = 15 rad/sec2 for this
instantaneous position of the link (Figures 1 to 3).
1) Find the values of θ3, θ4, θ5, θ6, ω3, ω4, ω5, ω6, α3, α4, α5, and α6
2) Find the accelerations of AA (m/sec2), ABA (m/sec2), AB (m/sec2), AC
(m/sec2), ADC (m/sec2), and AD (m/sec2).
3) Find the centre of mass values lg2 lg3 lg4 lg5 lg6 of links 2, 3, 4, 5, and 6.
4) Find the mass moment of inertia (kg·m2) about the centre of mass of
links 2, 3, 4, 5, and 6.
5) Find the values of Ag2 Ag3 Ag4 Ag5 Ag6 of links 2, 3, 4, 5, and 6 (see Figure
3).
6) Find the force and moment equations for dynamic force analysis on links
2, 3, 4, 5, and 6, and cast the equations in the matrix form.
7) Find the values for F12 (F12x and F12y), F32 (F32x and F32y), F43 (F43x and F43y),
F14 (F14x and F14y), F45 (F45x and F45y), F65 (F65x and F65y), and F16 (F16x and
F16y) at the joints and the driving torque τ12 needed to maintain motion
with the given angular velocity and acceleration of ω2 = 25 rad/sec and
α2 =15 rad/sec2, respectively, for this instantaneous position of the link.
Regarding question 1, you have to write down the complete derivation of 1) to
7) rather than the final equation.


Figure 1 Dynamic force analysis of a six-bar linkage (front view)

Figure 2 Dynamic force analysis of a six-bar linkage (top view)

Figure 3 Dynamic force analysis of a six-bar linkage (free-body diagrams)

Question 2:
For the six-bar mechanism described in Problem 1, simulate the mechanism for
the case in which the motion begins with a crank angular velocity of ω2 = 25
rad/sec and a constant angular acceleration of α2 =15 rad/sec2.
The matrix equation (matrix form in Problem 1) is solved using an m-file
function that will take all of the integrator outputs as input arguments (Figure
4).
1) Plot the values of θ2, θ3, θ4, θ5, and θ6 for the first 2 seconds.
2) Plot the values of ω2, ω3, ω4, ω5, and ω6 for the first 2 seconds.
3) Plot the values of α2, α3, α4, α5, and α6, for the first 2 seconds.
4) Plot the values of Ag2 Ag3, Ag4, Ag5, and Ag6 of links 2, 3, 4, 5, and 6 for the
first 2 seconds.
5) Plot F12 (F12x and F12y), F32 (F32x and F32y), F43 (F43x and F43y), F14 (F14x and
F14y), F45 (F45x and F45y), F65 (F65x and F65y), and F16 (F16x and F16y) at the
joints and the driving torque τ12 needed to maintain motion for the first
2 seconds.
6) Plot the coupler curve (plot x positions versus y positions) at the point of
the centre of mass in Link 5.
Regarding question 2, you have to show the graphs of 1) to 6), paste the m-file
codes (you have to add comments to explain why you used the MATLAB
commands in the code) on the assignment, and upload the simulink file (.slx)
on WISEflow.

Figure 4 Simulink realisation of full dynamics simulation of a six-bar mechanism

Question 3:
For the six-bar mechanism described in Problem 1, simulate the mechanism
using Simscape for the case in which the motion begins with a crank angular
velocity of ω2 = 25 rad/sec and a constant angular acceleration of α2 =15
rad/sec2.
Regarding question 3, you have to show the graphs of 1) to 5), paste the
Simscape design (front view and top view) on the assignment, and upload the
simulink file (.slx) on WISEflow.
1) Plot the values of θ2, θ3, θ4, θ5, and θ6 for the first 2 seconds.
2) Plot the values of ω2, ω3, ω4, ω5, and ω6 for the first 2 seconds.
3) the values of α2, α3, α4, α5, and α6, for the first 2 seconds.
4) Plot the values of Ag2 Ag3, Ag4, Ag5, and Ag6 of links 2, 3, 4, 5, and 6 for the
first 2 seconds.
5) Plot F12 (F12x and F12y), F32 (F32x and F32y), F43 (F43x and F43y), F14 (F14x and
F14y), F45 (F45x and F45y), F65 (F65x and F65y), and F16 (F16x and F16y) at the
joints and the driving torque τ12 needed to maintain motion for the first
2 seconds.
6) Plot the coupler curve (plot x positions versus y positions) at the point of
the centre of mass in Link 5.


Question 4:
Compare the two simulation results obtained from questions 2 and 3.
1) Show the comparison of Ag2 (Ag2x and Ag2y), Ag3 (Ag3x and Ag3y), Ag4 (Ag4x
and Ag4y), Ag5 (Ag5x and Ag5y), and Ag6 (Ag6x and Ag6y) on links 2, 3, 4, 5, and
6 obtained from the two simulations (questions 2 and 3).
2) Show the comparison of the force and torque components (F12x, F12y,
F32x, F32y, F43x, F43y, F14x, F14y, F45x, F45y, F65x, F65y, F16x, F16y, and τ12) at all link
joints obtained from the two simulation results (questions 2 and 3).
Regarding question 4, you have to show the comparison graphs between the
two simulation results on the assignment.

Question 5:
The two simulation results are not exactly the same. Express your opinion as to
why that is, also describe what factors should be considered to improve the
simulation results obtained from question 2 in comparison with the simulation
results obtained from question 3.




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