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007 RESEARCH ON A ROBOT THROWING BO-SHURIKEN OF OLD JAPANESE MILITARY ARTS 06R

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4 4. [] MSC Software Interactive Physics ( IP) Wofram Research Mathematica 4. Fig.4- - -

4.. Fig.4- Σ Σ m I L W v B i B i Σ i i = s i n i r i B i Σ i e Object m I y B Σ B L x B W ω B, i v B, i y B Σ B x B B,i B ni B ri y R B si Σ R x R Finger Fig.4- - -

W0 Σ x L L B B [ r ] T B B ri r x, i, y, i r x, i L / T B [,0] if = W B ry,i s = [,0 ] i (4-) T B if r = W y,i T B [ 0, ] if = W B ry,i n = [ 0, ] i (4-) T B if r = W y,i r y i =0 y r y i = ±W I m I( m) km k = L - -

4.. i T [ ω ] T v = H v (4-) c, i i B, i, B, i T [ ] T v (4-4), = H v, ω c i i B, i B, i R B H [ E, [ R r ] ] i B i (4-5) E R R Σ Σ a [ a ] T x, a y [ a ] [ a y, a x ]T e n i v e T n v i T c, i c, i i R n R B B n i (4-6) T s 0 (4-7) i v B, i = s i R R B B R B (4-) [ R r ] s = 0 4-7 B i i s i T s 0 (4-8) i vc, i = (4-8) (4-7) T T s v s v 0 (4-9) i B, i = i B, i = - 4 -

[ v T ω T T ] = J ~ [ v ω ] T B, i, B, i i B, i, B, i T T J ~ i E ( e) N H i L i nini H i (4-0) (4-) N E 0 0 k (4-) T i N H i L H (4-) (4-0)IP - 5 -

4.. IP (4-0) (4-0) ω = ~ B T [ ] J ( )[ v ω ] T 0 (4-4) B, i, i rx, i B, i, B, i B i B r y i (4-4) J ~ i B r x i B i B r x i (4-4) B r x i (4-) J ~ i e =0.m e=0.5 B =/rad B r y i =-W/ v B i-=[50] T B i-=70.0rad/s B i 00-0rad/s (4-) B r x i Mathematica - 6 -

4..4 Case B i 0rad (4-4) B r x i 0.07565m Fig4- Fig.4- Fig.4- Case 80 70 60 50 40 0 0 0 0-0 0 0.05 0. 0.5 0. Fig.4- Case - 7 -

Case B i 0rad (4-4) B r x i 0.094484m Fig4-4 Fig4-5 Fig.4-4 Case 80 70 60 50 40 0 0 0 0 0 0.05 0. 0.5 0. Fig.4-5 Case - 8 -

Case B i -0rad (4-4) B r x i 0.078m Fig4-6 Fig4-7 80 Fig.4-6 Case 60 40 0 0-0 0 0.05 0. 0.5 0. -40 Fig.4-7 Case (4-0) (4-4) IP - 9 -

4. 4. (4-0) (4-) v B i- B -i v B i- v B i- v B i- Link 4..5-0 -

4.. Fig.4-8 Σ Σ m I L W V B i B i Σ i s i n i r i B i Σ i e x A =0rad A =πrad 0< A </ AB AB - -

W y R m I x B L x B y B AB x B VB,i y B B, i y B B ω B,i B V B, i B ω B, i B r i B n i V D B s i ma I A L A R A ω A x R Σ Σ m I L W V B iσ i ω B iσ i s i Σ i n i Σ i r i Σ i B iσ i m A I A L A A ω A V D Σ AB Fig.4-8 - -

4.. Fig.4-9 Fig.4-9 =π/rad r x i 0 Fig.4- [ v T ω T T ] = J [ v ω ] T ~ B, i, B, i i B, i, B, i Fig.4-0 v Bi-=0m/s y R y R y R ω B, i ω B,i R R R v B, i x R x R v B,i x R B r x, i Fig.4-0 0m/s T T ~ [ v ω ] = J [ 0 ω ] T B, i, B, i i, B, i (4-5) v B i ω B i ω B i- r x i - -

Fig.4-8 = V v (4-6) V Bx, i Bx, i Bx, i V Bx, i = LAω A vbx, i = VBx, i LAω A ω B i- ω A (4-5) V Bx, i L 0 ωb, i A ω A 0 ~ = J i 0 (4-7) ω A V B iω B i ω A B r x i V B iω B i 4.. 4.. (4-7) L A =.0m =.0m e=0.5 B =/rad B r y i =-W/ AB =-π/9 V B iω B i Case-50m/s0radCase-50m/s0radCase-50m/s-.5rad/s (4-7) B r x i ω A Mathematica - 4 -

4..4 Case B i 0rad V B i -50m/s (4-7) B r x i.474m ω A.84rad/s Fig.4- Fig.4-Fig.4- Fig.4- Case - 5 -

6 4 0 8 6 4 0-0 0.0 0.0 0.0 0.04 0.05 0.06 Fig.4- Case 0 0-0 0 0.0 0.0 0.0 0.04 0.05 0.06-0 -0-40 -50-60 Fig.4- Case - 6 -

Case B i 0rad V B i -50m/s (4-7) B r x i 0.4988m ω A 4.5rad/s Fig.4-4 Fig.4-5 Fig.4-6 Fig.4-4 Case - 7 -

6 4 0 8 6 4 0 0 0.0 0.0 0.0 0.04 0.05 0.06 Fig.4-5 Case 0 0-0 0 0.0 0.0 0.0 0.04 0.05 0.06-0 -0-40 -50-60 Fig.4-6 Case - 8 -

Case B i -.5rad V B i -50m/s (4-7) B r x i.458 m ω A 4.00 rad/s Fig.4-7 Fig.4-8Fig.4-9 Fig.4-7 Case - 9 -

6 4 0 8 6 4 0 - -4 0 0.0 0.0 0.0 0.04 0.05 0.06 Fig.4-8 Case 0 0-0 0 0.0 0.0 0.0 0.04 0.05 0.06-0 -0-40 -50-60 Fig.4-9 Case (4-7) B r x i ω A IP - 0 -

4..5 Fig.4-8 AB Fig.4-0 Link Fig.4-0 4.4 [] (4-7) B r x i ω A - -

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- 4-5. Fig.5- = 0 0 0 G G G H H H H H H M M M M M M M M M τ τ τ & & & & & & & & & && && && (5-) )) cos( cos cos ( ) cos ( I I I m m m M g g g g g g = ) cos( cos cos ( ) cos ( I I m m M g g g g g = )) cos( cos ( I m M g g g = M M = ) cos ( I I m m M g g g = ) cos ( I m M g g = M M = M M = I m M g = )) sin( sin sin ( = g g m m m H )) sin( sin ( = g g m m H H H = ) sin ( g m H = H H = H H = )) sin( ) sin( sin ( )) sin( sin ( sin = g g g g m g m g m G )) sin( ) sin( ( ) sin( = g g g m g m G sin( ) = g g m G

Y Link g m, I X g Link m,, I g Link g i gi i di & i & i m i I i τ i Fig.5- - 5 -

5.4 NEC PC-98Xb(CPU: Inte Pentium 00MHz) Fig.5- D/A DC Trajectory Data Computer NEC PC-98Xb D/A Converter MICROSCIENCE QDA-998BPC AMP SMCM-6AI DC Servo motor Manipuator Joint Ange SMCM-0AI Encoder Counter MICROSCIENCE Encoder UDC498CPC A/D Converter MICROSCIENCE Acceeration Sensor CROSSBOW CXL04LP ADM698BPC Fig.5- - 6 -

5.5 Tabe.5- Tabe.5- Link Link [m] 0.4 0.00 [m] 0.4 0.8 [kg].7.06 Tabe.5- ZiegerNichos [] Tabe.5- Kp 40.80 6. 0. Kd 0.99 0.574 0.007 Ki 40.0 59.5.8-7 -

- 8-5.6 ( ) t 5 5 0 4 4 5 5 ) ( a t a t a t a t a t a t = (5-) TA = (5-) A T = (5-4) A = ) ( (0) ) ( (0) ) ( (0) n n n && && & & (5-5) = 0 4 5 a a a a a a A (5-6) = 0 0 6 0 0 0 0 0 0 0 4 5 0 0 0 0 0 0 0 0 0 0 4 4 5 n n n n n n n n n n n n t t t t t t t t t t t t T (5-7)

Fig.5- Link =0rad =rad 5 t (5-8)(5-9) Fig.5-4 Fig.5-5 5 4 (t) = 0.58875t.9475t. 95t (5-8) & 4 (t) =.9475t.775t. t (5-9) 775.5.0.5.0.5.0 0.5 0.0 0 0.5.5 Fig.5-4.5.0.5.0.5.0 0.5 0.0 0 0.5.5 Fig.5-5 - 9 -

5.7 PD 5.6 PD d (5-0) τ = K & p ( d ) K d (5-0) (5-0) (5-) PD τ = K ( ) ( & & p d K d d ) (5-) PD Fig.5-6 PD Kp Kd R Fig.5-6PD - 40 -

5.8 5.6 PD Link Link Fig.5-7 Fig.5-8.5.0.5.0.5.0 0.5 0.0-0.5 0 0.5.5 Fig.5-7.5.0.5.0.5.0 0.5 0.0-0.5 0 0.5.5 Fig.5-8 - 4 -

- 4-5.9 Link Fig.5-9 Fig.5- PD Computer NEC PC-98Xb Computer NEC PC-98Xb D/A Converter MICROSCIENCE QDA-998BPC D/A Converter MICROSCIENCE QDA-998BPC AMP SMCM-6AI SMCM-0AI AMP SMCM-6AI SMCM-0AI DC Servo motor DC Servo motor Manipuator Manipuator Encoder Encoder Encoder Counter MICROSCIENCE UDC498CPC Encoder Counter MICROSCIENCE UDC498CPC AMP AMP Soenoid Soenoid End-Effector End-Effector Link Trajectory Data Trajectory Data Joint Ange Joint Ange Reease Reease Reease Ange Reease Ange Computer NEC PC-98Xb Computer NEC PC-98Xb D/A Converter MICROSCIENCE QDA-998BPC D/A Converter MICROSCIENCE QDA-998BPC AMP SMCM-6AI SMCM-0AI AMP SMCM-6AI SMCM-0AI DC Servo motor DC Servo motor Manipuator Manipuator Encoder Encoder Encoder Counter MICROSCIENCE UDC498CPC Encoder Counter MICROSCIENCE UDC498CPC AMP AMP Soenoid Soenoid End-Effector End-Effector Link Link Link Link Trajectory Data Trajectory Data Joint Ange Joint Ange Reease Reease Reease Ange Reease Ange Fig.5-9

5.0 Fig.5-0 Link Fig.5-0 5. DA DA QDA-998BPC 0ch 4ch 0ch Link Fig.5- ch Link ch. 0 8 6 9 8 8 Fig.5-DA - 4 -

5. DA DA p npn Fig.5- I B V B R B DA ma 5k Tabe.5- Tabe.5-4 Fig.5- V cc = (V) R c = 7( Ω ) I c = 0.7(A) I B = 0.5(mA) R B = (k Ω ) B C E h FE = 000 V B = 0.5(V) GND GND Fig.5- Fig.5- Tabe.5- I c h FE SD686 4mA 000 t on =0.µst f =0.6µst stg =.5µs Tabe.5-4 - 44 -

5. 5.0 Fig.5-4 Fig.5-5 mm 0N 0 Tabe.5-5 Fig.5-4 Fig.5-5 Tabe.5-5 - 45 -

5.4 Fig.5-6 Link ONOFF procedure startup (procedure prestartup) (procedure start)link 0V Fig.5-6 - 46 -

5.5 Link Fig. Link 5.6 Link Link - 47 -

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; = πê; r x = r x ; r y = 0; = 0.; HL; e= 0.5; HL; k= ê; ; v Bx,i = 5; HxL; v By,i = 0; HyL; ω B,i = 70; HL; J; E = i 0 0y j 0 0 z ; k0 0 { H= i j 0 r y Cos@D r x Sin@D y z; k0 r y Sin@D r x Cos@D { HT = Transpose@HD ; NN = i 0 0y j 0 0 z ; k0 0 k{ NNN = Inverse@NND ; L= H.NNN.HT; LL = Inverse@LD ; n= J Sin@D Cos@D N; nt = Transpose@nD ; J= E H el NNN.HT.LL.n.nT.H; - 5 -

; i v Bx,i y ω B,i = H 0 0 L.J. v By,i j z k ω B,i { Nu :: 7.5 i j. H0. 00. r xl k. 0. r x 00. r 0. H0. 0. r x L y z 70 i i j.5 r x. 0. r x 00. r x j. H0. 00. r xl x { k k. 0. r x 00. r 0. H0. 0. r x L y z y z>> x. 0. r x 00. r x {{ ; ω B,i = 0; HL; SoveA 7.5` i.` H0.` 00.` rxl j k.` 0.` r x 00.` r 0.` H0.` 0.` r xl y z 70 i i.` H0.` 00.` rxl j.5` r x.` 0.` r x 00.` r x j x { k k.` 0.` r x 00.` r 0.` H0.` 0.` r xl y z y z ω x.` 0.` r x 00.` r B,i,r xe x {{ 88r x 0.07565<, 8r x 0.485<< - 5 -

; = πê; r x = r x ; r y = 0; =.0; HL; e= 0.5; HL; k= ê; ; v Bx,i = 0; HxL; v By,i = 0; HyL; ω B,i =ω; HL; J; E = i 0 0y j 0 0 z ; k0 0 { H= i j 0 r y Cos@D r x Sin@D y z; k0 r y Sin@D r x Cos@D { HT = Transpose@HD ; NN = i 0 0y j 0 0 z ; k0 0 k{ NNN = Inverse@NND ; L= H.NNN.HT; LL = Inverse@LD ; n= J Sin@D Cos@D N; nt = Transpose@nD ; J= E H el NNN.HT.LL.n.nT.H; - 5 -

; i AA = j k v Bx,i y z ; { v By,i ω B,i v Bx,i i y BB = v By,i j z ; k ω B,i { BB = J.AA êê MatrixForm i 0. H0.0. rxl.5 ω r x J.0. rx. r x. H.0.rxL.0.rx.r x N. ωh0.0.rxl rx.0. rx. r x j ω J.5 r x J. H0..r xl k.0.rx.r x y 0. H0.0.rxL.0.rx.r x NN z { ; ; =.0; H L; v Bx,i = 50; HxL; VV = v Bx,i H ωl;hl; v By,i = 0; HyL; ω B,i = 0; HL; i 0.` H0.` r SoveA9.5` ω r x 0.`L x j k.` r x 0.` r x.`.` H0.` r x.`l y.` ω H0.` r z VV, x 0.`L r x.` r x 0.` r x.` {.` r x 0.` r x.` vby,i, ω i i.` H0.`.` rxl j.5` r x j k k.` r x 0.` r x.` 0.` H0.` r x 0.`L y z y z ω B,i=, 8r x, ω<e.` r x 0.` r x.` { { 8ω 4.5, r x 0.4988<, 8ω.00, r x 0.6446< - 54 -

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