NEWTONS LAWS OF MOTION, EQUATIONS OF MOTION, &
EQUATIONS OF MOTION FOR A SYSTEM OF PARTICLES
Todays Objectives:
Students will be able to:
1. Write the equation of motion
for an accelerating body.
2. Draw the free-body and kinetic
diagrams for an accelerat
EQUATIONS OF MOTION:
NORMAL AND TANGENTIAL COORDINATES
Todays Objectives:
Students will be able to:
1. Apply the equation of motion
using normal and tangential
coordinates.
In-Class Activities:
Reading Quiz
Applications
Equation of Motion using
n-t Coo
EQUATIONS OF MOTION:
RECTANGULAR COORDINATES
Todays Objectives:
Students will be able to:
1. Apply Newtons second law
to determine forces and
accelerations for particles in
rectilinear motion.
In-Class Activities:
Reading Quiz
Applications
Equations of
EQUATIONS OF MOTION:
CYLINDRICAL COORDINATES
Todays Objectives:
Students will be able to:
1. Analyze the kinetics of a
particle using cylindrical
coordinates.
In-Class Activities:
Reading Quiz
Applications
Equations of Motion using
Cylindrical Coordina
Due date: 04/08
Hand-writing answer sheets will be only accepted. Please, leave the sheets at the Engineering bldg. 5,
#217 or give them to me in the beginning of the class on the due date. If you have any question, please,
contact Jeong Hyeon Kim (wce728
Due date: 04/05
Hand-writing answer sheets will be only accepted. Please, leave the sheets at the Engineering bldg. 5,
#217 or give them to me in the beginning of the class on the due date. If you have any question, please,
contact Jeong Hyeon Kim (wce728
Due date: 03/22
Hand-writing answer sheets will be only accepted. Please, leave the sheets at the Engineering bldg. 5,
#217 or give them to me in the beginning of the class on the due date. If you have any question, please,
contact Jeong Hyeon Kim (wce728
CURVILINEAR MOTION:
GENERAL & RECTANGULAR COMPONENTS
Todays Objectives:
Students will be able to:
1. Describe the motion of a
particle traveling along a
curved path.
2. Relate kinematic quantities
in terms of the rectangular
components of the vectors.
In-
CURVILINEAR MOTION:
NORMAL AND TANGENTIAL COMPONENTS
Todays Objectives:
Students will be able to:
1. Determine the normal and
tangential components of
velocity and acceleration of a
particle traveling along a
curved path.
In-Class Activities:
Reading Qui
ABSOLUTE DEPENDENT MOTION ANALYSIS
OF TWO PARTICLES
Todays Objectives:
Students will be able to:
1. Relate positions, velocities, and
accelerations of particles
undergoing dependent motion.
In-Class Activities:
Reading Quiz
Applications
Define Dependent M
CURVILINEAR MOTION: CYLINDRICAL
COMPONENTS
Todays Objectives:
Students will be able to:
1. Determine velocity and
acceleration components
using cylindrical
coordinates.
In-Class Activities:
Reading Quiz
Applications
Velocity Components
Acceleration Co
RELATIVE-MOTION ANALYSIS OF TWO PARTICLES
USING TRANSLATING AXES
Todays Objectives:
Students will be able to:
1. Understand translating
frames of reference.
2. Use translating frames of
reference to analyze relative
motion.
In-Class Activities:
Reading Q
RECTILINEAR KINEMATICS: ERRATIC MOTION
Todays Objectives:
Students will be able to:
1. Determine position,
velocity, and acceleration of
a particle using graphs.
In-Class Activities:
Reading Quiz
Applications
s-t, v-t, a-t, v-s, and a-s diagrams
Conce
INTRODUCTION &
RECTILINEAR KINEMATICS: CONTINUOUS MOTION
Todays Objectives:
Students will be able to:
1. Find the kinematic quantities
(position, displacement, velocity,
and acceleration) of a particle
traveling along a straight path.
In-Class Activities:
Engineering vibration (PME302) HW # 3. Due: Oct. 17
1. A wave consisting of the wave from a passing boat impacts a seawall. It is desired to calculate the resulting vibration.
Figure P3.15 illustrates the situation and suggests a model. This force in Figu
Plot the response x(t) of an underdamped system with
n 2
rad/s, = 0.1,
and
and v0=0 for the following initial displacements: x0= 1 mm, x0= 5 mm, x0= 10
for the following initial displacements:
mm
mm
10
mm, and x0= 100 mm.
t=linspace(0,30,500);
for k=1:len
(: PME302) # 2. : 10 9
1. m kx 0
x
n 2
rad/s, x0 = 1 mm, v0 =
5 mm/s
. (2 )
2. 1 mm , (phase shift at t=0) 2 rad 5 rad/s .
. (2 )
3. An undamped system vibrates with a frequency of 10 Hz and amplitude 1 mm. Calculate the maximum amplitude of the
sys
Engineering vibration (PME302) HW # 1. Due: Sep. 28
x
x
f
f
k1
m
k1
k2
m
k2
(a)
x1
x2
(b)
x3
x1
f
f
f
k3
x3
x2
k5
f
f
f
c5
k1
c1
k3
k2
m1
c2
m2
c3
k4
m3
k1
c4
c1
m1
(c)
1. Derive the equation of motion for the above systems.
k2
k3
m2
k4
m3
c4
(d)
2. Using
107
Chapter 11
Synthesis of Linkages
11.1
A function varies from 0 to 10. Find the Chebychev spacing for two, three, four, five,
and six precision positions.
With x0 = 0.0 and xn +1 = 10.0 , Eq. (11.5) becomes:
x j = 5.0 5.0 cos
j\n
1
2
3
4
5
6
11.2
2
1.4
107
Chapter 10
Mechanism Trains
10.1
Find the speed and direction of gear 8 in the figure. What is the kinematic coefficient of
the train?
N 2 N 4 N 5 N 7 18 15 33 16
5
=
=+
N 3 N 5 N 6 N 8 44 33 36 48
88
8 = 8/ 2 2 = ( +5 88 ) ( 1 200 rev/min ccw ) = 68.
105
Chapter 9
Worms and Worm Gears
9.1
A worm having 4 teeth and a lead of 1.0 in drives a worm gear at a velocity ratio of 7.5.
Determine the pitch diameters of the worm and worm gear for a center distance of 1.75
in.
px = l N 2 = 1 in 4 teeth = 0.25 in/
103
Chapter 8
Bevel Gears
8.1
A pair of straight-tooth bevel gears is to be manufactured for a shaft angle of 90. If the
driver is to have 18 teeth and the velocity ratio is to be 3:1, what are the pitch angles?
N 2 = 18 teeth ,
2 = tan 1 ( N 2 N 3 ) = 1
99
Chapter 7
Helical Gears
7.1
A pair of parallel-axis helical gears has 14 normal pressure angle, diametral pitch of
6 teeth/in, and 45 helix angle. The pinion has 15 teeth, and the gear has 24 teeth.
Calculate the transverse and normal circular pitch, t
81
Chapter 6
Spur Gears
6.1
Find the diametral pitch of a pair of gears having 32 and 84 teeth, respectively, whose
center distance is 3.625 in.
N 2 N 3 32 + 84
+
=
= 3.625 in
2P 2P
2P
116 teeth
P=
= 16 teeth/in
2 ( 3.625 in )
R2 + R3 =
6.2
Find the numbe
67
PART II
DESIGN OF MECHANISMS
68
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69
Chapter 5
Cam Design
5.1
The reciprocating radial roller follower of a plate cam is to rise 2 in with simple
harmonic motion in 180o of cam rotation and return with simple harmonic motion i