List No Grade
ME 302 THEORY OF MACHINES
Assignment Date : 11/03/2009
Due Date : 23/03/2009 @ 16:00 (Submit to C – 206)
Prepared by : Niyazi Ersan GÜRKAN, Hakan MENCEK (C – 206, 5271)
Section : …………………………………..
Name, Surname : …………………………………..
Student ID : …………………………………..
IMPORTANT NOTE: Please check your list number from the web site and write it on the top
left corner of this page. USE THIS PAGE AS A COVER PAGE FOR YOUR PROJECT.
Consider the hydraulic pump mechanism shown in Figure 1. The mechanism is driven via the
input shaft at point A0. Assume that the mechanism is loaded by a linear spring instead of
hydraulic fluid for simplicity. The schematic representation of the mechanism is shown in
Figure 1. Hydraulic pump mechanism 
 Figure P5.8, page 338, “Mechanisms”, Eres Söylemez, Middle East Technical University
(3) C k
B0, G4 +x
Figure 2. Schematic representation of the mechanism
Consider the motion of the mechanism corresponding to the full cycle rotation of the input
crank (link 2) i.e., 0° ≤ 12 ≤ 360°.
a) Perform a position analysis of the mechanism for input joint variable 12 and plot the
variations of 13 and s34 with respect to 12.
b) Perform velocity and acceleration analysis of the mechanism and plot the angular
velocity and acceleration of link 3 with respect to 12 (13 vs. 12 and 13 vs. 12).
c) Plot the x and y components of the linear velocity and acceleration of the mass
center of link 3 with respect to 12.
d) Derive the required torque relation (T), which is necessary to rotate the crank at a
constant rotational speed of 12, by using virtual work method. (Neglect frictional
effects on the system).
e) Plot the variation of the motor torque T with respect to 12 for different spring
stiffness values and comment on the results.
I) Dimensions of the mechanism:
|A0A| = 20 mm |A0B0| = 140 mm |AG3| = 80 mm |G3C| = 20 mm
II) Masses and radii of gyration:
m2 = 2 kg m3 = 1 kg m4 = 1.2 kg
r2 = 46 mm r3 = 46 mm r4 = 65 mm
III) Rotational speed of link 2
2 = 300 rpm (constant)
IV) Spring data:
k1 = 100 N/m k2 = 500 N/m k3 = 5000 N/m
Spring is unstretched when s34 is maximum.
This term project WILL be collected and graded. Therefore, please use the first as a cover
page for your project.
Please direct your questions to the assistants that prepared this assignment.
Late submissions will be penalized by severe percent reduction.
You can learn your list number from the course web site.
ABOUT THE PROJECT:
Give all of the references (books, papers, class notes etc) you use.
Present all of the calculations in full detail and in a neat form. Explain each step of your
Fully annotate the plots (i.e. state plot titles and axis labels in detail with corresponding
Provide units with your results.
You can use any software and/or programming language provided that you present full detail
about the tools you use, i.e. you must supply all the input/output evidences in printed form
as well as the source listings of your program, and the name of the program used.
Do not submit the print‐out of the tabulated data which is used for plotting the variations of
parameters with respect to others.
The solutions you submit must be the product of your own personal efforts. Any help which
you get from others in any form must not be beyond discussions on the solution methods
used and/or cross‐checking your findings. Otherwise, you will get a zero from the