Energy Recovery Ventilation and Enthalpy Wheels:
1. Select two manufactures that make Energy recovery ventilation (ERV) and
obtain performance specifications. Provide schematic one line diagram that
shows the major components.
2. Select two manufactures t
PROBLEMS
12.1
12.2
12.3
12.4
A certain Pennsylvania coal contains 74.2% C, 5.1% H, 6.7% 0, (dry basis, mass
percent) plus ash and small percentages of N and S. This coal is fed into a gasifier
along with oxygen and steam, as shown in Fig. P121. The exit
Closed Loop or Feedback Control Ari Handling System
1. Provide the sequence of operation/Sequence of Control for the shown Closed
Loop Air Handling System. The air handling system provides heating, cooling
and ventilation to the conditioned zone(s).
Close
Closed Loop or Feedback Control Ari Handling System
1. Provide the sequence of operation/Sequence of Control for the shown Closed
Reheat System.
Reheat Systems
The reheat system is a modification of the single zone system
in which air is cooled to the lev
Outline of Solutions for Additional Problems for Practice
1. We are given a RPRR (revolute-prismatic-revolute-revolute) robot manipulator. The choice of the D-H
coordinate frames and the corresponding D-H table are shown below. Here, the point p1 is given
Robot Modeling and Control
Mark W. Spong, Seth Hutchinson, M. Vidyasagar
John Wiley & Sons, Inc. 2006
Errata
Chapter 1
Page 29: In the caption for Figure 1.25, change Problem 1-15 to Problem 1-13.
Chapter 2
Bottom of page 43: the vectors x1 , x2 , and x
Homework: v-rep Assignment 2
1. Consider the RR (revolute-revolute) manipulator from the v-rep Assignment 1 in http:/crrl.poly.edu/
EL5223/vrep_hw1.html.
(a) Write a Matlab function to compute the forward kinematics of the manipulator considering the cent
Euler-Lagrange formulation for dynamics of an n-link manipulator
In the Euler-Lagrange dynamics formulation, the dynamics of an n-link manipulator are written as:
L
d L
= i , i = 1, . . . , n
dt qi
qi
(1)
where the Lagrangian L is defined as L = K P with
Basic Concepts of Robot Sensors, Actuators, Localization,
Navigation, and Mapping
EL5223
EL5223
Basic Concepts of Robot Sensors, Actuators, Localization, Navigation, and1 Mappin
/ 12
Sensors and Actuators
Robotic systems can utilize various types of senso
Kinematics (Forward Kinematics, Inverse Kinematics, and Velocity Kinematics)
Forward Kinematics: Given a robotic manipulator, the forward kinematics problem is to find the position
and angular orientation of the end-effector given the joint variables (i.e
Outline of Robot Control Algorithms
The dynamics of a robot manipulator can be written in the form
D(q)
q + C(q, q)
q + g(q) =
(1)
where is the vector of actuation forces/torques (forces for prismatic joints, torques for revolute joints).
Independent Jo
Homework: v-rep Assignment 2 Solutions
1. A v-rep simulation scene with the RR manipulator is at:
http:/crrl.poly.edu/EL5223/RR_vrep_scene.ttt .
Code to interact with v-rep can be written in any of the programming languages supported by
v-rep; the v-rep r
Hamiltonian Formulation for Dynamics
The Hamiltonian formulation provides a method to write the dynamics of a robotic manipulator as a set of
first-order differential equations instead of a set of second-order differential equations as in the Euler-Lagran
Integration of R = RS()
Definition of quaternion q in terms of Euler angles x , y , z :
x
y
z
x
y
z
) cos( ) cos( ) + sin( ) sin( ) sin( )
2
2
2
2
2
2
y
z
x
y
z
x
= sin( ) cos( ) cos( ) cos( ) sin( ) sin( )
2
2
2
2
2
2
y
z
x
y
z
x
= cos( ) sin( ) cos( ) +
ID
Task Task Name
Mode
1
Duration Start
Finish
Half 2, 2015
A
Kanika Shet - MS in MOT
S
O
N
D
Half 1, 2016
J
F
M
A
2
3
Fall 2015
4
Classes
77 days Wed 9/2/15 Thu 12/17/15
5
Projects
51 days Thu 10/1/15 Thu 12/10/15
6
Final Exams and
Submissions
12 days Fr
ASSIGNMENT 3 Boeing 787 Dreamliner
Boeing is an American Airline company headquartered in Chicago that designs,
manufactures and sells airplanes. It is one of the leading and globally renowned Airline
companies. T
To recommend the best software package as per the needs of the organization
Purpose and Issues with the current PM Tool:
With new and better technologies available in the market, it has become necessary to move to those
advancements so that it yields an o
Solutions for Problems 4.13 and 4.15
4.13. A rotation matrix is given as R = Rz, Ry, Rz, . Since R z, = S(k)R
z, , Ry, = S(j)Ry, ,
T
T
and R z, = S(k)R
z, , where j = [0, 1, 0] and k = [0, 0, 1] , we have
R = R z, Ry, Rz, + Rz, R y, Rz, + Rz, Ry, R z,
= S
Solutions for Problems 3.9, 3.10, 3.11, and 3.12
3.9. Here, we are given a three-link Cartesian manipulator with a spherical wrist. We had considered
a three-link Cartesian manipulator in Problem 3.7 in Homework 4. Using the D-H coordinate
frames defined
Solutions for Problems 3.13, 3.18, and 3.19
3.13. For this manipulator, we can easily find the coordinates of the end-effector position o =
[ox , oy , oz ]T as:
ox = (d3 + 1) cos(1 ) ;
oy = (d3 + 1) sin(1 ) ;
oz = d2 + 1.
(1)
T
Hence, given the desired en
Homework 6a (Problem numbers from textbook)
3.13 Solve the inverse position kinematics for the cylindrical manipulator shown below (i.e., given
the desired position of the end effector, find the corresponding variables for the robot joints).
3.18 The Stan
Solutions for Problems 2.17 and 2.24
2.17.
Given the rotation axis k = [kx , ky , kz ]T with kx2 + ky2 + kz2 = 1, one way to find the
rotation matrix Rk, corresponding to a rotation around axis k by an angle is to
utilize the formula for a rotation perfor
11
3. Identity element I = 1 + j0 = 1ej0
For all c C,
cI = c = Ic.
4. Inverse element
For all c1 C, let inverse c2 C be defined as c2 =
c1 c2 = m1
1 j1
.
m1 e
1 j1 j1
e e
= c2 c1 = 1ej0 = I
m1
2-28 Quaternion Q = qo + iq1 + jq2 + kq3 = (q0 , q1 , q2 , q3
Homework 5 (Problem numbers from textbook)
3.9 Write the forward kinematics equations (attach the DH frames, write the DH table, then write
the homogeneous transformation matrices and multiply them together to find the end effector
coordinate frame in ter
Homework 6b (Problem numbers from textbook)
4.13 Given the Euler angle transformation R = Rz, Ry, Rz, , show that
d
dt R
= S()R where
+ cfw_s s + c j
+ cfw_ + c k
= cfw_c s s i
The components of i, j, k, respectively, are called the nutation, spin, and
Solutions for Problems 3.4, 3.5, and 3.7
3.4. The choice of the D-H coordinate frames is shown in the figure below.
The corresponding D-H table is:
Link 1
Link 2
ai
a1
0
i
90o
0
di
0
d2
i
1
0
Hence, the homogeneous transformation matrices A1 and A2 and
ma
Homework 4 (Problem numbers from textbook)
3.4 Write the forward kinematics equations (attach the DH frames, write the DH table, then
write the homogeneous transformation matrices and multiply them together to find the end
effector coordinate frame in ter