Kinematics and Kinetics of Machines Report: Experiments and Analysis

This report presents three experiments focused on the kinematics and kinetics of machines. Experiment 1 aims to determine the mass moment of inertia of a connecting rod using the parallel axes theorem, detailing procedures for weight measurement, oscillation analysis, and calculations. Experiment 2 investigates the application of a torsional pendulum to measure the rotational inertia of a disk, including measurements of dimensions, oscillation times, and calculations for time, natural frequency, and mass moment of inertia, with error analysis. Experiment 3 explores the relationship between input and output angles of a 4-bar planar mechanism, comparing experimental and theoretical results using displacement approximation and polygon methods, and calculating velocity and acceleration at different points, providing a comprehensive analysis of the mechanism's behavior.

Kinematics and Kinetics of Machines Report
Experiment 1
Aim and objectives
The main aim of this experiment is to determine the mass of the inertial of connecting the rod
which is used in the combustion engine. Also, the project wants to illustrate how to make
application of the parallel axes theorem which is used to establish the mass of the inertial
about an axis passing through the centre of the mass which connects to the rod.
Procedures:
i. Determine the weight of the connecting rod
ii. Place the steel knife-edge in both of the two scales given, and determine the respective
weights
iii. Determine the distance between the edges of the two knifes through measurements
iv. Settle the connecting rod on the knife-edge and determine every mass balance
v. Compute the position of the centres of the mass by the use of the two measure
reactions , the distance between the supports and the weight of the connecting rod
measures which were measured in part 1
vi. Append but not fix the connecting rod on the knife-edge fixed to the wall (the connecting
rod has to be able to oscillate);
vii. From a an approximate angulation of 10 degrees release the connecting rod and count the
numbers of oscillations for 10, 20 ,30 seconds. Repeat this procedure three times for each
period (10, 20, 30 seconds). Calculate the period of oscillations, Tn in seconds per cycle.
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viii. The steps 7 and 9 have to be repeated with the connecting rod suspended by the inside of
its larger end.
Calculation
Experiment 1
Upper End Big Upper End Small
Oscillations Time (sec) Oscillations Time (sec)
10 7.40 8.1 0.81 10 9.30 9.27 0.927
8.60 9.10
8.30 9.4
20 16.44 16.51 0.826 20 18.75 18.53 0.926
17.02 18.40
16.07 18.44
30 25.11 25.09 0.836 30 27.55 27.55 0.918
24.85 27.63
25.31 27.47
Distancebig=12 cm => 0.12 m
Distancesmall =16 cm => 0.16 m
To calculate the weight of the connecting rode determine by:
W =m∗g
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W =1.677∗9.81=16.451 N
To calculate the time (sec) determine by:
T end big= 7.4+8.60+ 8.30
3 =8.1 sec
=>
8.1
10 =0.81
T end small = 9.30+9.10+9.4
3 =9.27 sec
=>
9.27
10 =0.927
To calculate the natural period determine by:
T nend big
= 0.81+ 0.826+0.836
3 =0.824 sec
T nend small
= 0.927+0.926+0.918
3 =0.925 sec
To calculate the natural frequency determine by:
Knend big
= 1
T nend big
= 1
0.824 =1.21
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Knend small
= 1
T nend small
= 1
0.925 =1.08
To calculate mass moment of inertia should be rearrange the equation determine by:
k n= 1
2 π √ wd
1o
 I o= w d
4 π2 Kn
2
I oend big
= 1.6451∗9.81∗0.12
4∗π2∗(1.21)2 =0.0335 kg . m2
I oend small
= 1.6451∗9.81∗0.16
4∗π2∗ ( 1.08 ) 2 =0.05607 kg . m2
To determine the total mass of the moment of inertial should be rearrange the equation
determined by:
I o=I c+md2
=>
I cend big
=0.0335−1.677∗( 0.12 ) 2=0.0093512 kg . m2
I cend small
=0.05607−1.677∗(0.16)2=0.0131388 kg . m2
Conclusion
In conclusion, the experiment which was carried out shows how to determine the mass of
the inertial of connecting rod with the use of different sizes. Also, procedures and formulas
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gives a clear example to how to use the parallel axes which is applied to determine the mass
of the moment of the inertial about an axis passing through the centres of the mass of the
connecting rod.
Kinematics and Kinetics of Machines Report
Experiment 2
Aim and objectives of the experiment
The aim of this experiment is to consider how to make application of the pendulum sprain
which was applied in measuring the rotational or the angular moment of the inertial of an
object. By turning an object suspended by a rod, the object will oscillate, with a simple harmonic
motion, around the spindle.
Procedures:
1. Measure the dimension of the shaft i.e. The length, radius and diameter
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2. Measure the dimensions of the disc i.e. The thickness, diameter and radius
3. Time the 40, 30 and 20 oscillations to find the period (T) of the pendulum oscillations.
Calculation
Oscillations Time(sec) T AV T n
20 17.81 18.12 0.91 0.9
18.35
18.21
30 28.87 27.19 0.91
26.47
26.22
40 35.37 35.08 0.88
35.06
34.81
ρ=7860 kg/m3
G = 77.2 GPa
Lshaft =111 cm => 1.11 m
Dshaft =0.67 cm => 0.0067m
Rshaft=0.335 cm => 0.00335m
Ddick=34.4 cm => 0.34 m
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Thieknessdick=2 cm => 0.02 m
To calculate the time (sec) determine by:
T sec= 17.81+18.35+18.21
3 =18.12 sec
To calculate the (T AV ) determine by:
T AV =18.12
20 =0.91 sec
To calculate (T n) determine by:
T n= 0.91+0.91+0.88
3 =0.9 sec
To calculate natural frequency (Kn) determine by:
k n= 1
T n
=¿ 1
0.9 =1.11
To calculate the polar moment of inertia (J) determine by:
J= 1
2∗π∗R4
J= 1
2∗π∗( 0.335 ) 4 =0.01978332=¿ 0.0198∗10−8 m4
To calculate the mass moment of inertia (I) determine by:
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I exp= J∗G
4∗π4∗k n
2∗L =¿ (0.0198∗10¿¿−8)∗(77.2∗10¿¿ 9)
4∗π4∗(1.11)2∗(1.11) =0.286849834 kg . m2 ¿ ¿
To calculate the mass (m) determine by:
m=V ∗ρ
V = π
4 ∗D2∗t
m= π
4 ∗D2∗t∗ρ => m= π
4 ∗¿
To calculate the mass moment of inertia ( I ) determine by:
I Theroy= 1
2∗m∗R2
I Theroy= 1
2 * 12.93089112 * ( 17.2
100 ¿2=0.1912737414 kg . m2
To calculate the error to find out the percentage between the expected and theoretical experiment
determine by:
E=theroy −exp
exp ∗100=> E=0.1912737414−0.286849834
0.286849834 ∗100=33.32 %
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Conclusion
In conclusion, all the objectives of this experiment were achieved. The experiment was able to
show how to determine the inertial moment of the disk by the use of the pendulum torsional.
Also, the high error rate does not give very accurate results. Additionally, the mass center of the
circle it might not co-inside with those hub of the bar. Throughout the oscillation, there could
make damping impacts because the oscillations might not make uniform. There could be kinks in
the bar due to the torsional coefficient increases.
EXPERIMENT 3
KINEMATICS AND KINERICS OF MACHINES
Aim
The main objective of this experiment is to determine the relationship which is between the
angler the input and the output of a 4-Bar planer mechanism by type the change of each angles
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increase to complete cycle of the crank input and identify each value. Some of the objectives
which were set to achieve the aims of the experiment include:
I. Compare the calculation result from displacement equation.
II. Identify the acceleration and velocity of the point.
III. Test the angler relationship between the input and output angler.
IV. Approximation method and polygon method
System
o 4-bar planar has four main components (couple, crank, grounds).
o Two protractors connected to the crank and joint and drawings sheet.
o Paper to note and pen, ruler.
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Procedures
a) Reading output angle for input angle by making increment starting from 10 degrees each
time until 360.
b) Note the recorded in table
c) By using mathematical equation, we calculate the value of the output angle for the input
angles
d) Compared the result with analytical result.
e) At 30 degrees the figure P been recorded as nominal. Remarkable the tow point with
5degree increment of the other side of the point P.
f) Using the ruler to measure the length of each increment. For this reading we find the
velocity and the equation velocity approximation.
g) From measured the X axis and Y axis of the point P we get the velocity by polynomial
approximation method.
h) Repeated step 7,6, and 5 for point P3 and P2 at 210 and 130 degrees.
i) By velocity polygon method we calculated the velocity of point P3, P2 and P1.
j) The end of this experiment we compere the result by obtained different method.
Equations used for calculations
a = 150mm b = 290mm c = 270mm d = 380mm
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To calculate output angle Ф
Displacement approximation method
Polynomial approximation Method
Calculation:
Form experiment A1 the calculation for theoretical angle output and error is obtained as follow:
A = 150mm B = 290mm C = 270mm D = 380mm
R1 cosθ−R2 cos ∅ + R3=cos (θ−∅ )
R1= d
c = 380/270 = 1.4074mm
R2= d
a = 380/ 150 = 2.5333mm
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