COMPUTER ORGANIZATION+DESIGN >I<
5th Edition
ISBN: 9781541868397
Author: Patterson
Publisher: ZYBOOKS (CC)
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Chapter 5, Problem 5.10.6E
Explanation of Solution
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Students have asked these similar questions
Problem 3: Consider the two-link planar elbow manipulator shown below with link information: a₁ = 3,
a₂ = 3.
a2
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ai
| di | 0i |
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02
21
02.
12
01
0 0 01
02
0
0
02
01
To
(a) Find the location of the end-effector P° if the joint angles are:
0₁ = 140°, 0₂ = 30°
(b) Find the values of joint variables 01, 02 if the robotic manipulator is commanded to reach the desired
location of Pº = [4.5, 3,0]. Notice there are possibly two sets of solutions.
(c) Also sketch the two poses of the robot for the computed joint variables.
Page 5 of 7
Problem 5: The following shows the schematic of a SCARA robot and its DH parameters. Complete the
following questions based on this information.
20
01
21
02.
22
done by
ai
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21
d3
1
a1
0
0
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2
a2
180°
0
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0
0
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The Jacobian matrix of this robot is given below:
-a1S1a2S12
-a2S12
J(q) =
a1c1 + a2c12
0
a2C12
0
10°
(a) For a₁ = 1, a2 = 2, is q = 180° a singularity configuration of this robot?
a1
3
[10°1
(b) For a₁ = 1, a2 = 2, is q = | 0° a singularity configuration of this robot?
3
(c) Consider the following sequence of rotations:
1) Rotate by 130° about the world z-axis
2) Rotate by 45° about the current x-axis
3) Rotate by -30° about the world/fixed y-axis
Compute the resulting overall rotation matrix R. Notice that you need to provide the numerical
solution to the matrix R.
(d) Find R giving the following rotation matrices.
1
0
0
1
√√3
го о
0
0
R₁₁ =
2
R₁ = 0
1
0
1
0
0
0
2
2
Chapter 5 Solutions
COMPUTER ORGANIZATION+DESIGN >I<
Ch. 5 - Prob. 5.1.1ECh. 5 - Prob. 5.1.2ECh. 5 - Prob. 5.1.3ECh. 5 - Prob. 5.1.4ECh. 5 - Prob. 5.1.5ECh. 5 - Prob. 5.1.6ECh. 5 - Prob. 5.2.1ECh. 5 - Prob. 5.2.2ECh. 5 - Prob. 5.2.3ECh. 5 - Prob. 5.2.4E
Ch. 5 - Prob. 5.2.5ECh. 5 - Prob. 5.2.6ECh. 5 - Prob. 5.3.1ECh. 5 - Prob. 5.3.2ECh. 5 - Prob. 5.3.3ECh. 5 - Prob. 5.3.4ECh. 5 - Prob. 5.3.5ECh. 5 - Prob. 5.3.6ECh. 5 - Prob. 5.4.1ECh. 5 - Prob. 5.4.2ECh. 5 - Prob. 5.4.3ECh. 5 - Prob. 5.4.5ECh. 5 - Prob. 5.4.6ECh. 5 - Prob. 5.5.1ECh. 5 - Prob. 5.5.2ECh. 5 - Prob. 5.5.3ECh. 5 - Prob. 5.5.4ECh. 5 - Prob. 5.5.5ECh. 5 - Prob. 5.5.6ECh. 5 - Prob. 5.6.1ECh. 5 - Prob. 5.6.2ECh. 5 - Prob. 5.6.3ECh. 5 - Prob. 5.6.4ECh. 5 - Prob. 5.6.5ECh. 5 - Prob. 5.6.6ECh. 5 - Prob. 5.7.1ECh. 5 - Prob. 5.7.2ECh. 5 - Prob. 5.7.3ECh. 5 - Prob. 5.7.4ECh. 5 - Prob. 5.7.5ECh. 5 - Prob. 5.7.6ECh. 5 - Prob. 5.8.1ECh. 5 - Prob. 5.8.2ECh. 5 - Prob. 5.8.3ECh. 5 - Prob. 5.8.4ECh. 5 - Prob. 5.9.1ECh. 5 - Prob. 5.9.2ECh. 5 - Prob. 5.9.3ECh. 5 - Prob. 5.10.1ECh. 5 - Prob. 5.10.2ECh. 5 - Prob. 5.10.3ECh. 5 - Prob. 5.10.4ECh. 5 - Prob. 5.10.5ECh. 5 - Prob. 5.10.6ECh. 5 - Prob. 5.11.1ECh. 5 - Prob. 5.11.2ECh. 5 - Prob. 5.11.3ECh. 5 - Prob. 5.11.4ECh. 5 - Prob. 5.11.5ECh. 5 - Prob. 5.11.6ECh. 5 - Prob. 5.12.1ECh. 5 - Prob. 5.12.2ECh. 5 - Prob. 5.12.3ECh. 5 - Prob. 5.12.4ECh. 5 - Prob. 5.12.5ECh. 5 - Prob. 5.12.6ECh. 5 - Prob. 5.13.1ECh. 5 - Prob. 5.13.2ECh. 5 - Prob. 5.13.3ECh. 5 - Prob. 5.13.4ECh. 5 - Prob. 5.13.5ECh. 5 - Prob. 5.13.6ECh. 5 - Prob. 5.14.1ECh. 5 - Prob. 5.14.2ECh. 5 - Prob. 5.14.3ECh. 5 - Prob. 5.14.4ECh. 5 - Prob. 5.14.5ECh. 5 - Prob. 5.14.6ECh. 5 - Prob. 5.15.1ECh. 5 - Prob. 5.15.2ECh. 5 - Prob. 5.15.3ECh. 5 - Prob. 5.15.4ECh. 5 - Prob. 5.16.1ECh. 5 - Prob. 5.16.2ECh. 5 - Prob. 5.17.1ECh. 5 - Prob. 5.17.2ECh. 5 - Prob. 5.17.3ECh. 5 - Prob. 5.17.4ECh. 5 - Prob. 5.17.5ECh. 5 - Prob. 5.17.6ECh. 5 - Prob. 5.18.1ECh. 5 - Prob. 5.18.2ECh. 5 - Prob. 5.18.3ECh. 5 - Prob. 5.18.4ECh. 5 - Prob. 5.18.5ECh. 5 - Prob. 5.18.6ECh. 5 - Prob. 5.19.1ECh. 5 - Prob. 5.19.2ECh. 5 - Prob. 5.19.3ECh. 5 - Prob. 5.19.4ECh. 5 - Prob. 5.19.6E
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