1
week 9
1
Week 9
MECH226
Phil Commins
Overview
Week 9 – Kinetic analysis, analytical method
Week 10 – Virtual work method
Week 11 – Energy distribution method
Week 12 – Balance of rotors and mechanisms
week 9
2
Week 9
Kinetic Analysis
Analytical Method
Based on notes developed by Dr Oliver Kennedy – Presented by Phil Commins
(Chapter 11, Norton)
week 9
3
A
O
O
B
g
g
g
2
2
3
4
4
73.9
16.7
60
200 mm
Superposition  Analytical
Method Example
Same
example
from
Week 7
week 9
4
A
O
O
B
g
g
g
2
2
3
4
4
73.9
16.7
60
200 mm
Superposition example
Mechanism
specs and
problem
outline.
link
length (mm)
mass (kg)
I
(kg m
)
2
100
0.5
0.0005
3
200
1.0
0.004
4
150
0.75
0.002
Link 2 is driven at a constant speed of 100 rad/s
in a cw direction.
The centre of gravity of each link is at its
geometric centre.
Find the forces acting at the pin joints between
each of the links, and the torque required to
maintain the rotation of
link 2 at this point in
the mechanism's motion.
The c.g. of each link is at its geometric centre.
A
= 1000 m/s
A
2
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week 9
5
Steps in the analysis .
..
1. Carry out a motion analysis of the mechanism to
determine the acceleration (linear and angular) of each
link.
2. Determine the inertia forces and torques acting on each
link.
(NB these act to oppose the actual accelerations  the
inertia force acts through the centre of gravity of the
link, but may be offset to also provide the inertia torque.
The offset approach is used when a graphical solution is
being applied. If an analytical method is adopted, take
moments about one of the joints {
Σ
M
A
= 0} .)
week 9
6
Steps in the analysis .
..
3. Take one of the links  draw a free body diagram
showing all the forces and torques acting on it (inertia
and external, and forces acting from the other links at
the joints).
4. Solve for any unknown forces (using 3 force and 2 force
principles as appropriate). When complete this means
that the forces acting on this link from the other links
will be known
.
5. Carry out a force balance at each of the remaining
joints through the mechanism (NB during this stage of
the solution, the remaining links are considered to be
rigid massless connectors
)
week 9
7
Steps in the analysis .
..
6. The forces and torques required throughout the
mechanism to support the external and inertial loads on
the link that is the subject of the analysis have now
been determined.
7. Now put those results aside, and consider
another
link
to be the subject of the analysis. Consider the external
and inertial loads on this link, carry out force & torque
balances as before.
8. Do this for each link  then collect all the results and
superimpose the results to determine the combined
loads (the force at each joint can be determined by a
vector addition).
week 9
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 Three '09
 WeihuaLi
 Force, Inertia, analytical approach, Kinetic Analysis Analytical Method, Analytical Method Example

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