PRECIZIA ROBOŢILOR INDUSTRIALI

MODELAREA ERORILOR CINEMATICE .I.
Aplicând erorile de tip ∈=∈ { ; ∈ } asupra acestor transformări, ele se transformă în matrice diferenţiale:
[ A]
[ ]
Q D G
{ [ T] k 1 m}
⎧ Δ ; = → ;
Qk
⎪
⎪ j−1 ( x )
j−1 x
j−1 Δ T = x
Q ⎨⎧ ⎫
⎪ ⎡δT ⎤ ; ⎡δT ⎤ ; ⎡ΔT ⎤ ⎪
⎪⎨ i ⎣ ⎦ yQk i ⎣ ⎦ yQk i ⎣ ⎦ yQk ⎬;
⎪⎪
⎩i = 1→ n; j = 1→ i;
⎪
⎩
⎭
{ A k 1 m}
⎧
⎪
Δ Qk ; = → ;
Δ =
Q ⎨ xy xy
⎪⎩ { ΔAijQk ; Δ AijlQk ; i = 1 → n; j = 1 → i; l = 1 → j}
;
{ J k 1 m}
⎧ Δ Qk ; = → ;
⎪
Δ J Q = ⎨⎧ ( ) xy 1
( ) xy
−
n 0 n 0 ( n) 0 xy ⎫
⎪⎨Δ J( θ ) ; Δ j( θ ) ; { Δ JQk}
⎬ .
Qk Qk
⎩⎩
⎭
146
(4.88)
(4.89)
(4.90)
În cadrul acestui paragraf se va prezenta modelul matematic de calcul, ca şi algoritmul matricelor
diferenţiale corespunzătoare erorilor cinematice.
Nr.crt Expresie de definire
1.
i−1 0 { [ ] j
n
∑ R k 0 } { ( [ ] k
j× qj⋅Δ j j ∑ R⋅ kk) × } qk⋅Δk
0 T ( )
( ) j= 0
k
0
Δ J k i
iv θ = e ⋅ Δ vi+ e =
⋅ Δ pn+
i−1 0 { [ R] j
∑ kj× } q
j
j⋅Δj i−1 j= 0 ⎧ 0 { [ ] j 0 } { [ ] j ⎫
+ e ⋅⎨∑⎡ j R kj qj j R kj } q ⎤
⎣
⋅ × ⋅Δ + Δ ⋅ × j ⎦
⋅Δj⎬⋅ vi+
⎩j= 0
⎭
n
0 { ( [ R] k
∑ ⋅ kk) × } q
k k⋅Δk n n
⎧ k i
0 ( )
{ [ ] k 0 } { [ ] k ⎫ 0
+ e =
⋅⎨∑ k R ⋅ kk× ⋅Δ qk + ∑ Δk R ⋅ kk× } ⋅qk ⎬⋅Δk⋅
pn
+
⎩k= i k= i
⎭
⎛ i−1 0 { ( [ ] j k−1 ∑ R⋅ k ) }
{ ( 0 [ ] m
j × qj⋅Δ ) ⎞
j
j n ∑ m R⋅ km × } qm⋅δ
⎜ m
j= 0 0
+Δ
{ ( [ ] i )
m i 1
i e i R ki } e =−
⎟
⋅⎜ ⋅ ⋅ × ⋅∑ ⎟⋅Δ
bk+
⎝ k= i
⎠
i−1 ⎡ 0 { ( [ R] j
∑ ⋅ kj) × } q
j
j⋅Δ ⎤
j i−1 ⎢ j= 0
⎛ 0 { { ( [ ] j 0 ) } { ( [ ] j
⎞⎥
i ⎢
e ⎜∑j R kj qj j R kj) } qj} j⎟⎥ Jim bk
⎣ ⎝ j= 0
⎠⎦
i−1 ⎛ 0 { ( [ R] ⋅
j k−1 ∑ k 0 ) } q [ R] m
j j × j⋅Δj ( m ⋅ k ) ⎞
n ∑ { m × } qm⋅δ
⎜ m
j= 0
0 { ( [ ] i
+Δi⋅e ⋅ Δi R ⋅ ki) × } ⋅ em=−
i 1
⎟
⎜ ∑
⎟⋅
bk
+
⎝ k= i
⎠
i−1 ⎧ 0 k 1
{ ( [ R] j −
k ) } q { ( 0 [ R] m
⎪ ∑ ⋅
j j × j⋅Δj n m km) ⎫
∑ ⋅ × } qm⋅δm
⎪
j= 0 0 { ( [ ] i
+Δ )
m i 1
i⋅⎨e ⋅ i R ⋅ ki × } ⋅ e =− ∑
⋅Jm⋅δ⎬ m ⋅bk
⎪ k= i
⎪
+Δ ⋅ ⋅ Δ ⋅ × ⋅ + ⋅ × ⋅Δ ⋅Δ ⋅ ⋅ +
⎩ ⎭
Nr.
ecuație
(4.91)