PRECIZIA ROBOŢILOR INDUSTRIALI

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3. Pentru matricea de tipul (x – z – x) ( ψ ) δ ii−1 111 ( ψ ) ⎡ Δ × Δ pii −1 ⎤ T ( x−z− x) = ⎢ ⎥ ; (3.88) ⎢0 0 0 0 ⎥ ⎣ ⎦ ⎡ 0 Δβy· sγ x −Δαx· cγ x· sβy Δ βy· cγ x +Δαx· sβy· sγ x⎤ ⎢ ⎥ × =⎢ Δαx· cγ x· sβy −Δβy· sγ x 0 −Δγ x −Δαx· cβy ⎥ ; (3.89) ⎢ ⎥ ⎢⎣ −Δβy· cγ x − Δαx· sβy· sγ x Δ γ x + Δαx· cβy 0 ⎥⎦ ⎡ Δpx · cβ 1 y −Δ pz · cα · · · 1 x sβy +Δpy sα 1 x sβy ⎤ ii− ii− ii− ⎢ ⎥ Δ pii−1 = ⎢Δpy·( cα· · · ) ·( · · · ) · · ii 1 x cγ x − cβysαxsγ x +Δ pz cγ ii 1 x sαx+ cαxcβysγ x +Δpxsβ ii 1 y sγ x ⎥ − − − ⎢ ⎥ ⎢Δpx· cγ · ·( · · · ) ·( · · · ) ii 1 x sβy −Δpz sα ii 1 x sγ x −cαx cβy cγ x −Δ py cα ii 1 x sγ x + cβy cγ x sα ⎣ − − − x ⎥⎦ 4. Pentru matricea de tipul (y – z – x) ( ψ ) ⎡ Δ × Δ pii −1 ⎤ δTii−1 ( y −z− x) = ⎢ ⎥ ⎢0 0 0 0 ⎥ ⎣ ⎦ . ; (3.90) ; (3.91) ⎡ 0 Δβy· sγ x −Δαx· cγ x· sβy Δ βy· cγ x +Δαx· sβy· sγ x⎤ ⎢ ⎥ Δ ( ψ × ) =⎢ Δαx· cγ x· sβy −Δβy· sγ x 0 −Δγ x −Δαx· cβy ⎥ ; (3.92) ⎢ ⎥ ⎢⎣ −Δβy· cγ x − Δαx· sβy· sγ x Δ γ x + Δαx· cβy 0 ⎦⎥ ⎡ Δpx · cβ 1 y −Δ pz · cα · · · 1 x sβy +Δpy sα 1 x sβy ⎤ ii− ii− ii− ⎢ ⎥ Δ pii−1 = ⎢Δpy·( cα· · · ) ·( · · · ) · · ii 1 x cγ x − cβysαxsγ x +Δ pz cγ ii 1 x sαx+ cαxcβysγ x +Δpxsβ ii 1 y sγ ⎥ x ⎢ − − − ⎥ ⎢Δpx· cγ · ·( · · · ) ·( · · · ) ii 1 x sβy −Δpz sα ii 1 x sγ x −cαx cβy cγ x −Δ py cα ii 1 x sγ x + cβy cγ x sα ⎥ ⎣ − − − x ⎦ 5. Pentru matricea de tipul (x – z – y) ( ψ ) ⎡ Δ × Δ pii −1 ⎤ δTii−1 ( z− x− y) = ⎢ ⎥ ⎢0 0 0 0 ⎥ ⎣ ⎦ ; (3.93) ; (3.94) ⎡ 0 Δβy· sγ x −Δαx· cγ x· sβy Δ βy· cγ x +Δαx· sβy· sγ x⎤ ⎢ ⎥ Δ ( ψ × ) =⎢ Δαx· cγ x· sβy −Δβy· sγ x 0 −Δγ x −Δαx· cβy ⎥ ⎢ ⎥ ⎢⎣ −Δβy· cγ x − Δαx· sβy· sγ x Δ γ x + Δαx· cβy 0 ⎦⎥ ⎡ Δpx · cβ 1 y −Δ pz · cα · · · 1 x sβy +Δpy sα 1 x sβy ⎤ ii− ii− ii− ⎢ ⎥ Δ pii−1 = ⎢Δpy·( cα· · · ) ·( · · · ) · · ii 1 x cγ x − cβysαxsγ x +Δ pz cγ ii 1 x sαx+ cαxcβysγ x +Δpxsβ ii 1 y sγ ⎥ x ⎢ − − − ⎥ ⎢Δpx· cγ · ·( · · · ) ·( · · · ) ii 1 x sβy −Δpz sα ii 1 x sγ x −cαx cβy cγ x −Δ py cα ii 1 x sγ x + cβy cγ x sα ⎥ ⎣ − − − x ⎦ 6. Pentru matricea de tipul (y – x – y) ( ψ ) ⎡ Δ × Δ pii −1 ⎤ δTii−1 ( y − x− y) = ⎢ ⎥ ⎢0 0 0 0 ⎥ ⎣ ⎦ (3.95) (3.96) ; (3.97)
<strong>PRECIZIA</strong> ROBOȚILOR <strong>INDUSTRIALI</strong> . . ⎡ 0 Δαy· cγ y· sβx −Δβx· sγ y Δ γ y +Δαy· cβx ⎤ ⎢ ⎥ Δ ( ψ × ) =⎢Δβx· sγ y −Δαy· cγ y· sβx 0 −Δβx· cγ y −Δαy· sβx· sγ y⎥ ; (3.98) ⎢ ⎥ −Δγ − Δα · cβ Δ β · cγ + Δα · sβ · sγ 0 ⎢⎣ y y x x y y x y ⎥⎦ ⎡Δpx·( cα 1 y· cγ y −cβx· sαx· sγ y ) −Δ pz ·( cγ · · · ) · · 1 y sαx + cαy cβx sγ y +Δp ii ii y sβ ii 1 x sγ y⎤ − − − ⎢ ⎥ Δ pii−1 = ⎢ Δ py· cβ · · · · ii 1 x +Δ pzcα ii 1 y sβx+Δpxsα ii 1 x sβ ⎥ x ⎢ − − − ⎥ ⎢Δ px·( cα· · · ) ·( · · · ) · · ii 1 y sγ y + cβx cγ y sαx −Δpz sα ii 1 x sγ y −cαy cβx cγ y −Δpy cγ ii 1 y sβ ⎥ ⎣ − − − x⎦ 7. Pentru matricea de tipul (z – x – y) 112 ( ψ ) ⎡ Δ × Δ pii −1 ⎤ δTii−1 ( z− x− y) = ⎢ ⎥ ⎢0 0 0 0 ⎥ ⎣ ⎦ (3.99) ; (3.100) ⎡ 0 −Δβx· sγ y − Δαz· cβx· cγ y Δ γ y + Δαz· sβx ⎤ ⎢ ⎥ Δ ( ψ × ) =⎢Δ β x · sγ y +Δαz· cβx· cγ y 0 Δαz· cβx· sγ y −Δβx· cγ y⎥ ; (3.101) ⎢ ⎥ ⎢⎣ −Δγ y − Δαz· sβx Δβx· cγ y − Δαz· cβx· sγ y 0 ⎥⎦ ⎡Δpx·( cα 1 z· cγ y − sαz· sβx· sγ y ) +Δ py ·( cγ · · · ) · · 1 y sαz + cαz sβx sγ y −Δp ii ii z cβ ii 1 x sγ y ⎤ − − − ⎢ ⎥ Δ pii−1 = ⎢ Δ pz· sβ · · · · ii 1 x +Δpycα ii 1 z cβx−Δpxcβ ii 1 x sα ⎥ z ⎢ − − − ⎥ ⎢Δ px·( cα· · · ) ·( · · · ) · · ii 1 z sγ y + cγ y sαz sβx +Δpy sα ii 1 z sγ y − cαz cγ y sβx +Δpz cβ ii 1 x cγ ⎥ ⎣ − − − y ⎦ 8. Pentru matricea de tipul (y – x – z) ( ψ ) ⎡ Δ × Δ pii −1 ⎤ δTii−1 ( y − x− z) = ⎢ ⎥ ⎢0 0 0 0 ⎥ ⎣ ⎦ ; (3.102) ; (3.103) ⎡ 0 ⎢ Δ ( ψ × ) =⎢ Δγz −Δαy· sβx ⎢ ⎢⎣ Δβx· sγz −Δαy· cβx· cγz Δαy· sβx −Δγz 0 Δ βx· cγz +Δαy· cβx· sγz Δαy· cβx· cγz −Δβx· sγz ⎤ ⎥ −Δβx· cγz −Δαy· cβx· sγz⎥ ; ⎥ 0 ⎥⎦ (3.104) ⎡Δ px·( cα 1 y· cγz + sαx· sβx· sγz) −Δpz ·( cγ · · · ) · · 1 z sαx − cαy sβx sγz +Δp ii ii y cβ ii 1 x sγ z⎤ − − − ⎢ ⎥ Δ pii−1 = ⎢Δ pz·( sα· · · ) ·( · · · ) · · ii 1 x sγz+ cαycγzsβx−Δpxcα ii 1 y sγz− cγzsαxsβx+Δpycβ ii 1 x cγ ⎥ z ; ⎢ − − − ⎥ ⎢ Δpz · cα · · · · ii 1 y cβx −Δ py sβ ii 1 x +Δpx cβ ii 1 x sα ⎥ ⎣ − − − x ⎦ (3.105) 9. Pentru matricea de tipul (z – x – z) ( ψ ) ⎡ Δ × Δ pii −1 ⎤ δTii−1 ( z− x− z) = ⎢ ⎥ ⎢0 0 0 0 ⎥ ⎣ ⎦ ; (3.106) ⎡ 0 −Δγz − Δαz· cβx Δαz· cγz· sβx − Δβx· sγz ⎤ ⎢ ⎥ Δ ( ψ × ) =⎢ Δ γ z +Δαz· cβx 0 −Δβx· cγz −Δαz· sβx· sγ z⎥ ; (3.107) ⎢ ⎥ ⎢⎣Δβx· sγz −Δαz· cγz· sβx Δ βx· cγz +Δαz· sβx· sγ z 0 ⎥⎦
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FACULTATEA CONSTRUCŢII DE MAŞINI
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3. MODELAREA ERORILOR GEOMETRICE...
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j { { i; j} = 1 → n } p ij , vect
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{ unde i = 1 → n} qɺ i viteza li
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xy Q Δ J Matricea Jacobiană pentr
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NOȚIUNI GENERALE PRIVIND PRECIZIA
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ALGORITMI DE CALCUL ÎN CINEMATICA
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Page 57 and 58: ALGORITMI DE CALCUL ÎN CINEMATICA
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PRECIZIA ROBOȚILOR INDUSTRIALI Apl
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6. MODELAREA ERORILOR DINAMICE 6.1
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( ) ( C ) n n 0 ⎧ xy 0 0 xy xy
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171 PRECIZIA ROBOȚILOR INDUSTRIALI
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7. INFLUENȚA ERORILOR DINAMICE ASU
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Prin aplicarea modelului direct al
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q este un vector coloană m21 un ve
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8.APLICAȚII PRIVIND DETERMINAREA P
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APLICATII Matricea sistemelor de ti
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3 4 APLICATII ⎡ 0. 77 ⎢ −0. 6
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APLICATII Modulul erorilor vitezelo
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APLICATII Robot M MD 6 R 15 25,2777
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APLICATII Fig.8.4 Fig.8.5 Fig.8.6 1
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APLICATII 192 Algoritmul matricei J
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APLICATII 3 4 5 6 VD( t) OD( t) V(
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APLICATII Cupla Matricea erorilor d
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[M07] Moorring, B.W, Roth, Z.S, Dri
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PRECIZIA ROBOŢILOR INDUSTRIALI

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