机器人学导论克雷格第二章作业答案.docx
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机器人学导论克雷格第二章作业答案.docx
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机器人学导论克雷格第二章作业答案
机器人学导论(克雷格)第二章作业答案
2.1
solution:
Accordingtotheequationofpuretransitiontransformation,thenewpointaftertransitionisasfollows:
2.3
solution:
Accordingtotheconstraintequations:
Thus,thematrixshouldbelikethis:
2.4
Solution:
=
2.7
Solution:
Accordingtotheequationofpurerotationtransformation,thenewcoordinatesareasfollows:
2.9
Solution:
Acordingtotheequationsforthecombinedtransformations,thenewcoordinatesareasfollows:
Transformationsrelativetothereferenceframe
Transformationsrelativetothecurrentframe
B
2.10
A
P=Trans(5,3,6)Rot(x,90)Rot(a,90)P
100510000-1002
=010300-1010003
0016010000105
0001000100011
2
=-2
8
1
2.12
0.5270.369-0.766-0.601
T1=-0.5740.8190-2.947
0.6280.4390.643-5.38
0001
0.920-0.39-3.82
T2=010-6
0.3900.92-3.79
0001
2.14
a)Forsphericalcoordinateswehave(forposihon)
1)r·cosγ·sinβ=3.1375
2)r·sinγ·sinβ=2.195
3)r·cosβ=3.214
I)Assumingsinβisposihve,fromaandb→γ=35°
units
frombandc→β=50°
fromc→r=5
units
II)Ifsinβwerenegative.Then
γ=35°β=50°r=5
Sinceorientationisnotspecified,nomoreinformationisavailabletochecktheresults.
b)ForcaseI,substifatecorrespondingvaluesofsinβ,cosβ,sinγ,cosγandrinspericalcoordinatestoget:
0.5265-0.57350.62753.1375
Tsph(r,β,γ)=Tsph(35,50,5)=0.36870.8190.4392.195
-0.76600.64283.214
0001
2.16
Solution:
Accordingtotheequationsgiveninthetextbook,wecangettheEuleranglesasfollows:
①
Whichleadto:
②
③
2.18
Solution:
①Sincethehandwillbeplacedontheobject,wecanobtainthis:
Thus:
②No,itcan’t.
Ifso,theelementatthepositionofthethirdrowandthesecondcolumnshouldbe0.However,itisn’t.
③x=5,y=1,z=0
Accordingtotheequationsoftheeulerangles:
2.21
(a)
(b)
#
θ
d
a
α
0-1
0
0
1-2
0
180
2-H
0
0
(c)
==
==
(d)
2.22
(a)
(b)
#
θ
d
a
α
0-1
+90
0
0
90
1-2
0
0
-90
=
3-H
0
0
0
(c)
==
===
(d)
2.23
(a)
(b)
#
θ
d
a
α
1
0
0
90
2
0
4
0
1
-90
4
0
90
5
0
0
-90
6
5
0
0
(c)
======
(d)
=
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