第 31 卷 Vol. 31 总第 122 期!"#$%&' Z[\ ]^ _` a, :b c $ ' X $, C $ b c! >, O 47 2$b c 1 X, 9?, S, 4b c =>01, ; O 47 ' 0 $ 01 #, 04b c

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1 !"#$%&' Z[\ ]^ _` a, :b c $ ' X $, C $ b c! >, O 47 $b c 1 X, 9?, S, 4b c =>01, ; O 47 ' 0 $ 01 #, 04b c $=>1 1 X C KL 9, 9( 4 1 X $; ' :b c ; ;1 # ;1 X!"#$:TP4 %&' :A % $: (017) % &' " $ () & RONG Bixian 牞 MO Kun 牞 PENG Bo 牞 ZHANG Fan 牗 Central Research Academy of Dongfang Electric Corporation 牞牞 Chengdu 牞 China 牘 Abstract 牶 The omnidirectional mobile platform of Mecanum wheel can realize movement of arbitrary direction 牞 it is the best choice to transport car motor unit in small storage space. In order to solve problems of Mecanum wheel precision roller curve 牞 the roller shaft size and the number of roller 牞 this paper presents an improved Mecanum wheel design. The mechanical analysis and verification are introduced 牞 and the mecanum wheel parametric design model is established by using protection method and special geometric transformation 牞 giving a set of optimized design process that can be realized by program. And parameter of the mecanum wheel motor units is optimized. This design is applied in practical engineering project 牞 and the application result shows that the design is reasonable and reliable. Key words 牶 Mecanum wheel 牷 omnidirectional movement 牷 design process 牷 design method c1 /01(Automated Guided Vehicle, AGV)& V _ a 4 ",3a 8RVU ; 8 C b4 #5CD VU6 W 3 AGV C K, W ac7 %8 360 ) / ^_ W 9 :, < ; / Y W!3E 3 a W %W /,; / Y # <a ; = A [1] A. Gfrerrer < HX> "B1 = IC # < E 9& D [] ; E?@( ; = N <R)*, \ =, =?@ <K = 0 3 (): *+,-: (1989-),,016 6!"# $I "," %!,"#$ %&' ( )*+,- P " &'(1981-),,010 8 $ "#,"!, "#$ %&' ( )*+ 7 $ ", c,c@,- $ 8, _ () $ ", *+, $"# $ "

$, "F [3-4] ;GHH A = I N,# F X> _,J\] D < [5] ;KL < A = N )*, # <M# 3, "F, E 0 E = < NO #,Z/E$ $(Mecanum Wheel) U& 1973 VW"#$ Bengt llon,mecanum G X>N Y, = [8] ; = = \, 1 O= I & 1 m A 9\, Z$ $= [ \ n Y] (), = n ; m \ 45 D), P C = 9&ab, D>H, > c, % W &WP =) * ; W / 8 [5]!$

2 , "F [3-4] ;GHH A = I N,# F X> _,J\] D < [5] ;KL < A = N )*, # <M# 3, "F, E 0 E = < NO #,Z/E [6] ;O N >,?@( EC 0 ;, 0, 8 W /N. W [7] a E P ; / Y Q Z,] b A ;, D > RS, b T # R % ^R #,^R ; / Y <,a b4 "F 1 FGHI01 JK45 ; (Mecanum Wheel) U& 1973 VW"#$ Bengt llon,mecanum G X>N Y, = [8] ; = = \, 1 O= I & 1 m A 9\, Z = [ \ n Y] (), = n ; m \ 45 D), P C = 9&ab, D>H, > c, % W &WP =) * ; W / 8 [5]! FGHILMJK45 NO FGHI67 Mecanum G X>N =, as ; / W, = IC P 3,IC a;, 3 3= P, 3;! W! 1 FGHI01 W ^<; \, Z O 3 :[ ) [Y ) I[ P C_) Z ] _ [ ), `! 3 = CD IICP EF IC N, 4, Q Pa ; O a xy 7

$! 5 RST"U! = D _ C, F a = F b = 1 mg; =! 4 PQ!,= EF a a #, #, Q x M# AB = 3= EF [ CD ()9\ a Q #, O= A IC WP,< A WP = <, X> < _:, B, = < _:,&X>, = D D?$ $, E F * a _,E F _ 3 ED * C _ C, F a AE = F b EB,F a + F b = F c = mg, { F a = mg EB AB F b = mg AE AB AE AB, EB = AB, F a = mg { = 0 F b (1) () + C _ C.,A _ D,.$

3 ! 5 RST"U! = D _ C, F a = F b = 1 mg; =! 4 PQ!,= EF a a #, #, Q x M# AB = 3= EF [ CD ()9\ a Q #, O= A IC WP,< A WP = <, X> < _:, B, = < _:,&X>, = D D? P ; < NI, Q = I; < ] D > RS, b T # R % ^R #,V B1 Q Z 1 RST67 ; 4? m(kg) 0 F, = = = ; = ab η M 45, W /. W ; 0 R Q W /.,; = [ & = 4 ), 4* 4 W?, 5 F c F d a P D,F a F b a; = D, N EDD >., E F * a _,E F _ 3 ED * C _ C, F a AE = F b EB,F a + F b = F c = mg, { F a = mg EB AB F b = mg AE AB AE AB, EB = AB, F a = mg { = 0 F b (1) () + C _ C.,A _ D,.= & E _* EDa[τ],d a *, : τ max = 4 3 F a A = 4 3 d 4 mg π 1 d [τ] (3) ( ) 槡 mg 3[τ] (4) π = d, = d RSVWXY67 = d I; 4, 4,Q 4 D =,&= 4 C*S! * a, 6 = & 4F b 0 a a 0 a D /, ED, 0 a EDa[τ], ED& *, F c S z τ max = (D - d)i z (5) 8

$I A 7,V = & P A 8! 7 FGHI Z [\! as W / W I=, W /. S. O ; = P C,? 1, X>A,V,= A 9&?,? b β,y = A b θ,v = A _:a θ = π N + β @ O ; = P C, A?$ b β 0,=! 8 ]^RSZ!., Y = A b θ a, 4 I/NW @, :A?

L om L cd = L ef = L CD sinη (9) = r max = R - L om (10) r = R - L op (11) L cd / tan(θ / ) = L

4 τ max! 6 RS "U! S z = 3 3 D 3 ( ) - d [ ( ) ] (6) I z = π 64 (D4 - d ) 4 (7) F c 1 1 (a3 - D ) 3 = (a - d) π 64 (a4 - D ) = 4 8mg (a + ad + D ) 3π(a 4 - D ) [τ] (8) 4 = ED Q 0 a # = < N,= < M S 67 R ; I A 7,V = & P A 8! 7 FGHI Z [\! as W / W I=, W /. S. O ; = P C,? 1, X>A,V,= A 9&?,? b β,y = A b θ,v = A _:a θ = π N + O ; = P C, A? b β 0,=! 8 ]^RSZ!., Y = A b θ a, 4 :A? b β 0, θ , A b θ 360 N N, P, O = A b θ, = L AB Y ; WP A 9, ` = 0 a, X> A _ : A 0 b b9 ocm L om L cd = L ef = L CD sinη (9) = r max = R - L om (10) r = R - L op (11) L cd / tan(θ / ) = L CDsinη / tan(θ / ) (1) b b9 ocp L op = R - (L ef / ) L CD = 槡 = a + L om (13) - a sinη + sinηtan(θ / )+ tan(θ / ) 槡 a + [1 + tan (θ / )][R - a ] sinη tan(θ / ) ) (14) + sinηtan(θ /! 9 _`RSZ! 9

$P #, = 0 0 = < A X> _,= a (- L CD,a + L om) [0,(a + R + L om )] ( L CD,a + L om) _, #a: (- L CD x L CD,y > 0) (0),; / Y c \, ] % A = D D?$

5 ; V = K 9& CQS ".= E V, 10 V = B! 10 ]^RSab! E = & _ G ; WP QP ; GE V, = _ ; GH 0: L GH > L GE (15) L GH = sin π (R - a - r ) (16) N (a + L GE r ) = (17) cosη r = R - R 槡 - (L cd / ) (18) R : sin π N > 1 cosη x L CD [ ] (a + L 4 om ) 1 - (a + r + L om ) R R - L CDsinη 槡 ( ) a y (a + r + L om ) = 1 (19) A b θ = 0 = < P, EC,? A b θ, N, X> A _, E P ar = ED = E D? P #, = 0 0 = < A X> _,= a (- L CD,a + L om) [0,(a + R + L om )] ( L CD,a + L om) _, #a: (- L CD x L CD,y > 0) (0),; / Y c \, ] % A = D D? P, ; <R 9, D > RS, b T # R % ^R #, ^R ; / Y < # # 11 3 c ] Y ; 4? m = 600 kg 0 R = 15 5 mm = ab η = 45 a, ] A N ;! 11 FGHI67 = $ 45 #, ED [τ]= 130 MPa, = d = 1 mm,a S ",= M;, Z a 1 mm, a 8 mm 90 ED = 0 a 15 8 mm,as ",= 0 M a = mm; = <a 8 ;? A b θ 45,.= L = mm, A b,m θ = ,. 10

$600 kg, = = 0 < M\ U V+,! 1 _` S! ; = N& Solidworks N 8, 13! 13 RS! < ] ; F = = 0 < M\ U, : %&: [1]. Mecanum! )*[D]. H,014 []Gfrerrer A. Geometry and kinematics of the Mecanum wheel[j].$ Computer Aided Geometric Design,008,5(9):784-791 [3] E,. Mecanum *! / > [J]. $ 8 "#,011,40(5):43-46 [4],,,. ;! W )*[J]. ' ",013,7(4):7-11 [5]GHH,,,. N:) W N [J].?/0 $,013(6):51-55 [6]O. Mecanum! W " E )* [D].

Computer Aided Geometric Design,008,5(9):784-791 [3] E,. Mecanum *! / > [J]. $ 8 "#,011,40(5):43-46 [4],,,. ;! W )*[J]. ' ",013,7(4):7-11 [5]GHH,,,. N:) W N [J].?/0 $,013(6):51-55 [6]O. Mecanum! W " E )* [D].

6 E P,.= L = mm, = 0 r max = mm = #a: x y = 1( x ) (1) Y = Mathematic N # 8, 1 N 4 0 ] b ;,< A X> R = D D? P, ; <R 9, b T # R % ^R #,^R ; / Y < < 4? 600 kg, = = 0 < M\ U V+,! 1 _` S! ; = N& Solidworks N 8, 13! 13 RS! < ] ; F = = 0 < M\ U, : %&: [1]. Mecanum! )*[D]. H,014 []Gfrerrer A. Geometry and kinematics of the Mecanum wheel[j]. Computer Aided Geometric Design,008,5(9): [3] E,. Mecanum *! / > [J]. $ 8 "#,011,40(5):43-46 [4],,,. ;! W )*[J]. ' ",013,7(4):7-11 [5]GHH,,,. N:) W N [J].?/0 $,013(6):51-55 [6]O. Mecanum! W " E )* [D].,01 [7] L,,. Mecanum = 9 [J]. $ 8 "#,015():38-4 [8]Villiers M D,Bright G. Development of a Control Model for a Four Wheel Mecanum Vehicle [J]. Journal of Dynamic Systems Measurement & Control,01,134(1): 檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹檹 WX"Y 1. C C _! "#$%& ' 6,, I :ISSN , :CN / TM. C ( C)*,+, CAJ - CD 4-. /0, 1 C C C 3C 4 56 C 789 ) :; _ 9 4 C & C 3& C C 4 C 56 C ' 000 YA % 3. C B, 16,88 C,DEB D , , 5 F5, G M HIJ, K L :MN 78 F O! 11

2. 3. 1 2 TI 3 TI TABLE 4 RANDBIN 5 6 172 6 Research of Modern Basic Education 2012 6

6 2012 6 Research of Modern Basic Education Vol. 6 June 2012 201200 20 1. G 1976-171 2. 3. 1 2 TI 3 TI TABLE 4 RANDBIN 5 6 172 6 Research of Modern Basic Education 2012 6 1 GPS 4. 01 TI - nspire cx 1.