PROBLEM 1
Rod AB is made of a mild steel that is assumed to be elastoplastic
with E 29 106 psi and Y 36 ksi. After the rod has been attached
to the rigid lever CD, it is found that end C is 83 in. too high. A vertical
force Q is then applied at C until th
Homework #5 Mech III
1) With reference to a rectangular Cartesian coordinate system, the state of strain E at a
point is given by the matrix
5 3 0
E = 3 4 1 x10-4.
0 1 2
(a) What is the unit elongation in the direction of 2i + 2j + k?
(b) What is the chan
A beam of the cross section shown, made of steel that is assumed to be elastoplastic with
a yield strength 01, and a modulus of elasticity E, is bent about the x axis.
(a) Write a matlab code that calculates the bending moment M and the curvature rc
for v
MATLAB PROBLEM TORSION
A SOLID HOMOGENOUS CYLINDRICAL SHAFT HAS A LENGTH L, A DIAMETER D, A MODULUS
OF RIGIDITY G, AND A YIELD STRENGTH Y . IT IS SUBJECT TO A TORQUE T THAT IS
GRAUALLY INCREASED FROM ZERO UNTIL THE ANGLE OF TWIST OF THE SHAFT HAS
REACHED
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Electrical components and circuits
19
where V is the potential difference between the surfaces and Q is the
magnitude of the charge distributed on either surface. In terms of current,
I dQ/dt implies
dV 1 dQ
dt
C dt
2:8
In electronics, we take I ID (displ
Electrical components and circuits
35
Notice that we have now switched to lowercase symbols. Lowercase is generally
used for a.c. quantities while uppercase is reserved for d.c. values. Now is the time
to get into complex notation, often used in electrica
Digital electronics
139
Count
enable
J
Clock
input
Q
J
C
Q
J
C
K
Q
C
K
K
Q1
Q2
Q3
Figure 4.43 Circuit for Example 4.6.
Figure 4.44 Timing diagram for Example 4.6.
R
(a)
Q
CLK
Q
S
D
(c)
Q
CLK
Q
J
Q
(b)
CLK
K
Q
Q
T
Q
(d)
Figure 4.45 Flip-flops: (a) R-S; (b)
84
Mechatronics
VCC
Ic
Rc
+
RB
IB
Vin
+
Vout
VCE
VBE
Figure 3.44 The BJT inverter.
A simple BJT switch (an inverter, shown in Figure 3.44) is analyzed by
superimposing the load line equation on the IV characteristic curves shown in
Figure 3.45.
The base e
Digital electronics
103
integer result. Then the process is repeated with the remainder. The number in the
new base is the result of the divides, lined up in order of exponent from left to
right, while we make sure to remember to put zeros in places where
132
Mechatronics
A
B
Glitch
Q
(a)
t
A
B
NA
t1 Inverter delay
NB
t2 Inverter delay + Wire
difference delay
Expanded glitch
Q
(b)
Figure 4.33 Exclusive OR gate: (a) timing diagram; (b) expanded view of a glitch caused by signal
racing.
4.7.1 Latches and fli
Digital electronics
129
To use the device as a combinational logic circuit implementing a Boolean
expression, the address inputs of the memory become the Boolean input variables
and the data outputs become the required functions. The functions need to be
204
Mechatronics
window on top of the EPROM IC. Then new data can be stored on
the EPROM. Another type of EPROM is electrically erasable (EEPROM).
Data in EEPROM can be erased electrically and rewritten through its
data lines without the need for ultravio
46
Mechatronics
Electronic energy level
Increase
in
Energy
conduction band level
valence band level
em
el
ek
zero (nucleus)
Figure 3.1 Energy levels in the atom.
Metals
IA
1 1
H
2 3
Li
IIA
4
Be
3 11
Na
12
Mg
4 19
K
Transition Zone
Nonmetals
VIIA VIIIA
1
2
112
Mechatronics
4.3.3.8 The AND-OR-INVERT gate
Some logic families provide a gate known as an AND-OR-INVERT (AOI) gate
(see Figure 4.8).
Here, we note that
QA BC D
4:18
4.3.3.9 The exclusive-OR gate
The exclusive-OR gate (EOR or XOR) is a very useful two
The static clocked (level-sensitive) R-S flip-flop is shown in Figure 4.37 and its
truth table is given in Table 4.19. The symbol X represents either the binary state 0
or 1.
The first five rows in the truth table give the static input and output states.
Semiconductor electronic devices
a.c.
Line
input
optional
switch, fuse
lamp
Step-down
transformer
Rectifier
Ripple reduction
capacitor (filter)
Regulator
(stabilizer)
55
Low voltage
d.c. output
Figure 3.13 The main stages of a power supply system.
3.5 Pow
Semiconductor electronic devices
V
Vdd
M1
V1
M2
V2
Vout
M3
M4
Figure 3.52 The CMOS NOR gate.
Table 3.7 Truth table for Example 3.6
EXAMPLE
3.6
V1
V2
0V
0V
5V
5V
0V
5V
0V
5V
M1
M2
M3
M4
Vout
Analyze the CMOS NOR gate shown in Figure 3.52 for its switching
Digital electronics
155
frequency f/2. This single flip-flop is a divide-by-2 counter. In a similar manner an
n flip-flop binary counter will yield an output frequency that is f divided by 2n.
4.9.3 The Schmitt trigger
A noisy input signal to a logic gate
Digital electronics
145
0
00
01
1
0
1
0
10
1
1
0
11
Figure 4.49 State transition diagram for a modulo-4 updown counter.
Table 4.31 States of a modulo-4 binary updown counter
Current
state q1
0
0
1
1
0
0
1
1
Current
state q2
Next
state Q1
Next
state Q2
0
1
162
Mechatronics
4.9.8 Standard integrated circuits
Many of the circuit configurations discussed in this chapter are available as
standard integrated circuit packages. For a comprehensive listing reference should
be made to catalogs from the many IC manuf
176
Mechatronics
R1
V1
+
R2
V2
RF
+
R3
V3
+
+
Vo
Figure 5.6 The summing amplifier.
Vout
N
X
Vi
i1
if
Rf Ri :
5:10
This circuit can be used to combine the outputs of many sensors such as a
microphone array.
5.8 The difference amplifier
The op amp can also
188
Mechatronics
Rf
if
Ri
ii
in
Vout
+
+
Vs
Figure 5.20 Circuit for Example 5.2.
Solution
This is a non-inverting amplifier, so from Equation 5.6:
(a) The voltage gain of this amplifier is
1
Rf
8
1 3:
4
Ri
5:46B
(b) The output voltage is
Rf
Vout 1
Vs 3
Microcomputers and microcontrollers
207
&
ROM
&
Digital I/O ports
&
A serial communication interface
&
Timers
&
Analog-to-digital (A/D) converters, and digital-to-analog (D/A) converters
The CPU executes the software stored in ROM and controls all the
mic
Electrical components and circuits
R1
V1
27
R3
+ V3
+
Vs
V2
+
R2
R4
V4
+
V2
Figure 2.9 Assigning currents and voltages for mesh 2.
The same line of reasoning applies to the second mesh. Figure 2.9 depicts the
voltage assignment around the second mesh, fo
78
Mechatronics
3.6.3.2 The depletion MOSFET
Figure 3.38 shows the basic structure and symbol for a depletion-type MOSFET.
The channel between the source and drain terminals is a straight-through piece of
semiconductor material.
In an n-channel depletion-