机器人学导论克雷格第二章作业答案Word下载.docx

机器人学导论克雷格第二章作业答案Word下载.docx

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Solution:

=

2.7

Accordingtotheequationofpurerotationtransformation,thenewcoordinatesareasfollows:

2.9

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

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

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

2.16

Accordingtotheequationsgiveninthetextbook,wecangettheEuleranglesasfollows:

①

Whichleadto:

②

③

2.18

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

1-2

180

2-H

（c）

==

==

（d）

2.22

+90

90

-90

3-H

==

===

2.23

1

2

4

5

6

======