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Introduction to Robotics
Analysis, Control, Applications
Solution Manual
Saeed B. Niku
© Copyrighted 2010.
This solution manual may not be copied, posted, made available to students, placed on
BlackBoard or any other electronic media system and the Internet without prior expressed
consent of the copyright owner.
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Page 2 of 6
© Copyrighted 2010.
This solution manual may not be copied, posted, made available to students, placed on BlackBoard or any other
electronic media system or the Internet without prior expressed consent of the copyright owner.
2
CHAPTER ONE
Problem 1.1
Draw the approximate workspace for the following robot. Assume the dimensions of the
base and other parts of the structure of the robot are as shown.
Estimated student time to complete: 15-25 minutes
Prerequisite knowledge required: Text Section(s) 1.14
Solution:
The workspace shown is approximate.
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© Copyrighted 2010.
This solution manual may not be copied, posted, made available to students, placed on BlackBoard or any other
electronic media system or the Internet without prior expressed consent of the copyright owner.
3
Problem 1.2
Draw the approximate workspace for the following robot. Assume the dimensions of the
base and other parts of the structure of the robot are as shown.
Estimated student time to complete: 20-30 minutes
Prerequisite knowledge required: Text Section(s) 1.14
Solution:
The workspace shown is approximate.
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© Copyrighted 2010.
This solution manual may not be copied, posted, made available to students, placed on BlackBoard or any other
electronic media system or the Internet without prior expressed consent of the copyright owner.
50
Problem 3.3
Suppose the following frame was subjected to a differential translation of [1 0 0.5] d =
units and a differential rotation of [0 0.1 0] δ = .
a. What is the differential operator relative to the reference frame?
b. What is the differential operator relative to the frame A?
0 0 1 10
100 5
010 0
000 1
A
⎡ ⎤
⎢ ⎥
= ⎢ ⎥
⎢ ⎥
⎢ ⎥ ⎣ ⎦
Estimated student time to complete: 10 minutes
Prerequisite knowledge required: Text Section(s) 3.6-3.8
Solution:
a.
0 0 0.1 1
0 00 0
0.1 0 0 0.5
0 00 0
⎡ ⎤
⎢ ⎥
Δ = −
⎣ ⎦
b.
[ ] [ ][ ] 1
0 1 0 5 0 0 0.1 1 0 0 1 10
001 0 0 0 0 0 100 5
1 0 0 10 0.1 0 0 0.5 0 1 0 0
000 1 0 0 0 0 000 1
00 0 0
0 0 0.1 0.5
0 0.1 0 1
00 0 0
A A A −
⎡ ⎤⎡ ⎤⎡ ⎤ −
⎢ ⎥⎢ ⎥⎢ ⎥
⎡ ⎤ Δ= Δ = ⎣ ⎦ − −
⎣ ⎦⎣ ⎦⎣ ⎦
⎡ ⎤
⎢ ⎥ − − =
⎣ ⎦
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© Copyrighted 2010.
This solution manual may not be copied, posted, made available to students, placed on BlackBoard or any other
electronic media system or the Internet without prior expressed consent of the copyright owner.
100
Problem 6.5
Simplify the block diagram of Figure P.6.5.
+- A G1
H3
H1
+ G2 -
H2
+-
B
Figure P.6.5
Estimated student time to complete: 30 minutes
Prerequisite knowledge required: Text Section(s) 6.8.
Solution:
The following sequence is used to simplify the block diagram:
+- A G1
H3
H1
G2
H2 /G1
+-
B
+-
+- A
H3
G2
H2 /G1
+-
B 1
1 1 1
G
+ G H
+- A
H3
H2 /G1
+-
B 1 2
1 1 1
G G
+ G H
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