Chapter2SolutionsforIntroductiontoRobotics
1.a)Use(2.3)toobtain
b)Use(2.74)toget
α =90 degrees
β =90 degrees
γ = 90 degrees
2.a)Use(2.64)toobtain
b)Answeristhesameasin(a)accordingto(2.71)
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3.Use(2.19)toobtainthetransformationmatrices.TherotationisX-Y-Zfixedangles,souse (2.64)forthat3×3submatrix,withangles
γ =0 degrees
β = sin 1 tripod_height distance_along_optical_axis =
αC =0 degrees
αD =120 degrees
αE =240 degrees
Thepositionvectorstothecamera-frameoriginsare
wherehorizontal_distance= (distance_along_optical_axis)2 (tripod_height)2 . Combiningtherotationandtranslationyieldsthetransformationmatricesvia(2.19)as
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4.Thecamera-frameoriginislocatedat B PCORG =[7 25]T.Use(2.19)togetthe transformation, B C T .TherotationisZ-Y-XEulerangles,souse(2.71)with
α =0 degrees
β = 110 degrees γ = 20 degrees
Theobject’spositionin{A}is
6. (2.1)
7. (2.2)
Thisworkis
8. (2.12) Velocityisa“freevector”andonlywillbeaffectedbyrotation,andnotbytranslation:
(2.31)
(2.37) Using(2.45)wegetthat