Notes_08_02
1
of 3
Matrix Dynamic Analysis for Four Bar
The four bar linkage shown below operates in a vertical plane. Each link is a uniform bar with 2
cm by 2 cm square cross-section stainless steel. Assume that the masses of the bearings and the
effect
Notes_05_03
1 of 8
Three-Dimensional Experimental Kinematics
Digitize locations of landmarks on body i for points k=1 to n at given time t
All points must be on same body i
Use landmark weighting factor if point k is available at time t. Use if point k no
Notes_05_02
1 of 9
Two-Dimensional Experimental Kinematics
Digitize locations of landmarks on body i for points k=1 to n at given time t
All points must be attached to body i
Use landmark weighting factor if point k is available at time t. Use if point k
Notes_06_01
1
of 10
Static Force Analysis for Skid Loader - Scalar
A trunnion mount hydraulic cylinder actuates the arm of a skid steer loader as shown below. At
this position, e = 40 inches, = 61.131, = -12 ips, = -0.3625 rad/s.
Determine the force on th
Link 1
Link 2
Link 3
Link 4
Theta 2 (deg)
90
30
60
45
65
Theta 2 (rad)
alpha
gamma
beta
theta 4
theta 3
19.37
101.68
45.80
114.83
13.15
1.134464
System will lock when theta 2 is between + and Column J
Column J
# and between + and -
112.02 .
Column J
Notes_04_04
Two-Dimensional Constraints
General
1
of 6
Scleronomic constraints
independent of time such as mechanical joints
Revolute
Note: Haug uses
Double revolute
Parallel vectors (planar parallel-1)
parallel to
Notes_04_04
Pin-in-slot (planar parallel
Notes_04_06
page 1 of 9
D-mechanism
CONSTANT LOCAL BODY-FIXED LOCATIONS OF SPECIFIC POINTS
cfw_s1
A
cfw_
cfw_s2
,
T
cfw_
,
cfw_
,
,
T cfw_
,
T
cfw_
C
P
cfw_s4
cfw_
B
D
cfw_s3
T
,
T cfw_
,
T
cfw_
,
T
T
cfw_
,
T
cfw_q = cfw_ x2 y2 2 x3 y3 3 x4 y4 4 T
ESTI
Notes_04_01
page 1 of 4
Two-Dimensional Vector and Matrix Notation
global position of the origin of reference frame attached to body i
global position of point P attached to body i
example
global position of point B attached to body 4
global velocity of t
Notes_06_03
page 1 of 4
Static Force Analysis for Skid Loader Virtual Work
A trunnion mount hydraulic cylinder actuates the arm of a skid steer loader as shown below. At
this position, e = 40 inches, = 61.131, = -12 ips, = -0.3625 rad/s.
Determine the for
Notes_05_01
1 of 5
Numerical Derivatives Using Savitsky-Golay Floating Cubic Interpolants
measure position variable xi at times ti (note that the subscript i refers to time not body number)
for fixed time step h,
postulate
x = b 0 + b1 + b2 2 + b3 3
= ( b
Notes_07_04
Vehicle Inertial Measurements
SAE J182 - Motor Vehicle Fiducial Marks and Three-Dimensional Reference System
SAE J1100 - Motor Vehicle Dimensions
1
of 6
Scales Method
ISO 10392 - Road vehicles - Determination of centre of gravity
ISO 789-6 - A
Notes_08_03
page 1 of 5
dAlemberts Principle
An accelerating rigid body can be transformed into an equivalent quasi-static system by adding a
fictitious imaginary "inertial force" and "inertial moment". The inertial force and inertial moment may
be treate
Notes_08_05
Multiplanar Balancing
1 of 6
Notes_08_05
3 of 6
Notes_08_05
5 of 6
in-plane primary balancing (static balancing)
forces in X
Eq. 1
forces in Y
Eq. 2
secondary dynamic balancing to prevent shaking moments
moments in Y
Eq. 3
moments in X
Eq. 4
f
Notes_07_02
1
of 5
Area, Centroid and Area Moments for Polygonal Objects
Summations shown below are for closed CCW boundary sequences. CW boundary sequences will
produce negative values for area and moments. Closed boundaries require .
The term ai is twic
Notes_07_01
1
Mass Moment of Inertia Quiz
value
units
answer
mass m
_
_
_
length L
_
_
_
width w
_
_
_
thickness t
_
_
_
density
_
_
_
mass moment J
_
_
_
1 slug = 32.174 lbm
of 6
Mass Moment of Inertia Review
T=Fr
F=mr
F=ma
T = m r2
a=r
J
J = m r2
Note
Notes_07_03
1
Measuring Mass Moment of Inertia as a Simple Pendulum
m = mass
JG = mass moment about centroid
a = distance from pivot to centroid
g = acceleration of gravity
= time period for one oscillation
for small angles
assume
using
2 x 4 x 24 from No
Notes_08_01
page 1 of 3
Inverse Dynamics
Pin B at the end of crank link 2 forms a pin-in-slot joint with the horizontal slot in hammer link 4
as shown below. The mechanism is drawn approximately to scale. The weight of crank link 2 is
very small compared
Notes_06_02
page 1 of 2
Virtual Work
Rigid bar in horizontal plane
Newtonian
Infinitesimal kinematically consistent displacements
Virtual work
Virtual power
Virtual power for ground connections is zero because the velocity is zero. Virtual power across
in
Notes_08_04
Two-mass Equivalent Link
total mass
centroid location
check effective mass moment
(for slender rod )
1
of 17
Notes_08_04
2
Shaking Force for Slider Crank
assume crank is statically balanced G2 = A
split link 3 into m3B and m3C
constant crank s
Notes_04_03
Two-Dimensional Kinematics
Position
Velocity
Acceleration
Jerk
1
of 8
Snap
Partial derivatives
Notes_04_03
3
of 8
Although there are no formal definitions for terminology, higher derivatives of position are
often denoted as snap (fourth deriva
Notes_04_02
page 1 of 3
Two-Dimensional Coordinate Transformations
are unit vectors
[A] matrices are orthonormal
[A] -1 = [A] T
all columns are unit vectors
all columns are mutually orthogonal
all rows are unit vectors
all rows are mutually orthogonal
ME 481 Spring 2015 H12
Name _
Develop a Working Model (WM) simulation of a stick-slip drag-sled friction testing device.
Attach a screen shot of your WM device.
Your device should contain the following
a) a driver block that translates horizontally at 3.
ME 481 Spring 2015 H13
Name _
1) Develop a Working Model (WM) simulation of a simple pendulum as shown in Notes_07_03
with angular motion of 10 degrees of swing. Use m = 0.46 lbm, a = 3.7 inches and JG = 1.5
lbm.in2. Plot angular position, velocity and ac
ME 481 Spring 2015 H14
Name _
1) Download MATLAB files "ode_smd.m" and "ode_yd_smd.m" from our class web page. Run
"ode_smd.m" to provide a forward dynamic simulation of a spring-mass-damper. Provide a plot
of position and velocity as a function of time a
ME 481 Spring 2015 H15
Name _
1) Local coordinates for vertices on bodies 2 and 3 are provided below in CW boundary chains.
Time samples for position and attitude of each body are provided as data in the attached
MATLAB code. A sample plot of motion for b
ME 481 Spring 2015 H09
Name _
1) Modify your Working Model (WM) slider crank simulation as detailed below.
a) Change the motor that drives the crank to apply constant torque of 20 ft-lbf.
b) Place a large block so that the piston cannot move all the way t