PRECIZIA ROBOŢILOR INDUSTRIALI

ALGORITMI DE CALCUL ÎN CINEMATICA ȘI DINAMICA ROBOȚILOR .
Tipul matricei Expresia de definiţie
R
R
( γ z − βx −α
z )
( α − β − γ )
z x z
Restricţii
( , ) ( , ) ( , )
52
Tabelul 2.10
s c s c c s c c c s s s
⎡− αz ⋅ βx ⋅ γz + αz ⋅ γz − αz ⋅ βx ⋅ γz − αz ⋅ γz αz ⋅ βx
⎤
⎢ ⎥
z ⋅ x ⋅ z = ⎢ z ⋅ x ⋅ z + z ⋅ z z ⋅ x ⋅ z − z ⋅ z − z ⋅ x ⎥
⎢ ⎥
⎣ sβx ⋅sγ z sβx ⋅cγ
z cβx
⎦
R z α R x β R z γ cα cβ sγ sα cγ cα cβ cγ sα sγ cα sβ
⎛ α
γ iz ∈( − 11 ; )
tan iz β
A 2 , iz ⎞
⎜ − ⎟
⎝ sβx sβx
⎠
iz
Expresiile unghiurilor de orientare
α z
x β γ z
Arc cos( γ iz )
⎛ γ γ iy
Atan 2 ix ⎞
⎜ , ⎟
⎝ sβx sβx
⎠
γ = ± 1
Atan 2( β , α )
± π
0
ix ix
Tipul matricei Expresia de definiţie
R
R
( γ z − βy −α
z )
( αz − βy − γ z )
Restricţii
( , ) ( , ) ( , )
Tabelul 2.11
⎡cαz ⋅cβy ⋅cγ z −sα z ⋅sγ z −cα z ⋅cβy ⋅sγ z −sα z ⋅cγ z cαz ⋅sβy
⎤
⎢ ⎥
z ⋅ y ⋅ z = ⎢ z ⋅ y ⋅ z + z ⋅ z − z ⋅ y ⋅ z + z ⋅ z z ⋅ y ⎥
⎢ ⎥
⎢⎣ −sβy ⋅cγ z sβy ⋅sγ
z cβy
⎥⎦
R z α R y β R z γ sα cβ cγ cα sγ sα cβ sγ cα cγ sα sβ
⎛ β
γ iz ∈( − 1, 1)
tan iz α ⎞
A 2 , iz
⎜ ⎟
⎜ sβy sβ
⎟
⎝ y ⎠
Expresiile unghiurilor de orientare
α z
β y
γ z
Arc cos( γ iz )
γ iz = ± 1
Atan 2( − αiy , βiy
)
π
Tipul matricei Expresia de definiţie
R
R
( γ z − βy −α
x )
( αx − βy − γ z )
Restricţii
( , ) ( , ) ( , )
⎛ γ iy γ ⎞
Atan 2 , ix
⎜ − ⎟
⎜ sβy sβ
⎟
⎝ y ⎠
± 0
Tabelul 2.12
⎡ cβy ⋅cγ z −cβy ⋅sγ
z sβy
⎤
⎢ ⎥
x ⋅ y ⋅ z = ⎢ x ⋅ y ⋅ z + x ⋅ z − x ⋅ y ⋅ z + x ⋅ z − x ⋅ y ⎥
⎢ ⎥
⎢⎣ −cα x ⋅sβy ⋅ cγ z + sαx ⋅sγ z cαx ⋅sβy ⋅ sγ z + sαx ⋅cγ z ⋅ cαx ⋅cβy
⎥⎦
R x α R y β R z γ sα sβ cγ cα sγ sα sβ sγ cα cγ sα cβ
αiz ∈( − 1, 1)
⎛ β
tan iz γ ⎞
A 2 , iz
⎜ − ⎟
⎜ cβy cβ
⎟
⎝ y ⎠
α iz = ± 1
tan ( iy , iy )
Expresiile unghiurilor de orientare
α x
β y
γ z
Arc sin( α iz )
⎛ αiy α ⎞
Atan 2 , ix
⎜ − ⎟
⎜ cβy cβ
⎟
⎝ y ⎠
A 2 γ β ± π / 2
0