Design of Rear Suspension Mechanisms of Mountain Bikes
/ I
Visual BASIC 6.0 II
Abstract The purpose of this work is to provide a design procedure of rear suspension mechanisms of mountain bikes by using the concept of engineering design method. First, the conditions and particularities of mountain biking are investigated and the performance specification of rear suspension mechanisms is set by focusing the investigations on the requirements of rear suspension mechanisms. Second, the requirements and constraints of generating different types of rear suspension mechanisms are developed and the systematic process of creative mechanism design is followed. Third, the different types of rear suspension mechanisms resulted from creative mechanism design are analyzed to realize the property of each type of rear suspension mechanisms and the procedure of kinematic design is developed by using the algorithm of heuristic combinatorial optimization method. Finally a computer aided design program written in Visual BASIC 6.0 programming language is developed to be the powerful tool of performance analysis and kinematic design of rear suspension mechanisms. III
I II III IV VI IX 6 -.. 6 -.. 6-3.. 0 3 3-.. 3 3-.. 4 3-3.. 30 3-4.. 3 3-5.. 3 33 4-.. 33 4-.. 35 4-3.. 37 IV
45 5-.. 45 5-.. 5 5-3.. 57 5-4.. 64 5-5.. 69 83 6-.. 83 6-.. 84 6-3.. 94 08.. 0 V
...3.4.5.6.7.8.9.. 7.. 7.. 9...... 3.. 3.. 4.. 4.0.. 5. 6. TREK STP400.. 7.3.. 8.4.. 9.5...6.. 3. 4. 4. 4.3 4.4 4.5 4.5 4.6.. 6.. 34.. 35.. 36.. 38 40 4 4 VI
4.7 4.8 5. 5. 5.3 5.4 5.5 5.6 5.7 5.8 5.9.. 43.. 44.. 46.. 48.. 49.. 5.. 53.. 54.. 56.. 57.. 58 5.0.. 60 5... 6 5... 65 5.3.. 66 5.4.. 67 5.5.. 70 5.6.. 70 5.7.. 7 5.8.. 7 5.9.. 73 5.0.. 74 5... 75 5... 75 5.3 Giant Warp -DS 76 5.4 Giant Warp-DS. 77 VII
5.5.. 78 5.6.. 78 5.7 Giant ATX-... 79 5.8 Giant ATX- 80 5.9.. 8 5.30.. 8 5.3.. 8 6. 6. 6.3 6.4 6.5 6.6 6.7 6.8 6.9.. 85.. 85.. 9.. 9.. 93.. 95.. 96.. 97.. 97 6.0.. 98 6... 99 6. 50.. 99 6.3.. 00 6.4 /. 0 6.5 /. 0 6.6.. 04 6.7.. 04 6.8 / 07 VIII
3. 3. 6... 7 9.. 9 IX
996 J. G. Seifert [] Suspension system Rigid frame bike Suspension fork bike Front and rear suspension bike996 [] 99697
E. L. Wang S. A. Needle M. L. Hull[3-5] Off-road bicycle 999 [6] CAD/CAE/CAM 988 E. Pennestri A. Strozzieri[7] Force ratio curve 986 [8] Leverage ratio 989 [9] 994 [0] Busby[]
[] Wilcox [3]Y Harris[4] Lawwill[5] D Aluisio [6] Harris Shiau[7] [8] [9] [0] GT STS-Lobo DH000Schwinn Homegrawn straight 8 ATX-00 3
4
Visual BASIC 6.0 5
Mountain biking Mountain bike MTB Mountain bike rear suspension mechanisms - Mountain biking Racing bicycle.a 68 Bicycle moto cross BMX.b 04 6
. a b. 6 6. 7
3 6 4 3 Bottem bracket 5 8
3 4.3.3 9
Crankset Chain Rear sprocket Freewheel Shifters Front derailleur Rear Rim brakes Brake blocks Hub brakes Brake pads Brake drum Disk Handle bar Handle stem Headset bearings Front fork Main frame Front suspension Front suspension Saddle Seatpost Wheels Drop-outs Hub Bearing Axis Spokes Rim Tire Inner tire.4 0
8 3 4 7 5 8 3 6 5 0 6 7 9 4 9 0 3 4 3 5 4 6 5 7 6 8 7 9 8 0 9 0.4
.5 3 4.5.6
.7.6 a b.7.8 3
3.9a.9b a b.8 a b.9 4
4.9 a b agiant Warp-DS bgiant ATX-.0 5
-.. 6
TREK SOFT TAIL PRO STP Pivotless rear suspension system.5. Litespeed.3a Moots.3b ½ 5.438. a b. TREK STP400 7
alitespeed Tsali bmoots YBB.3 Linkage suspension mechanism.0a.4a 3 4.4b.0 b 8
3 4 agiant Warp DS- 6 3 4 5 bgiant ATX-.4 9
-3-3 4 5 0
887 John Boyd Dunlop.5.5
.6 3.6
3- [4] Pahl Beitz[5] Planning and clarifying the task Ideas 3
Proposal Conceptual design Working structure 3 Embodiment design Construction structure 4 Detail design 3 4 3-4
Objectives tree method 3-3. 5
3. 6
Performance specification method 3 4 7
.5 770 70 700 330 00 30 3 4 50 5 Eye-to-eye length 0000 Travel /5/3 400 000 lbs/in. 7 357 kgw/cm 6 6585 0 3. D / W Demand Wish 8
D/W D D D 3 30700 75 95 D 4 W W W 7 W 50 5 0000 6 /5/3 400 lbs/in.000 lbs/in. 7 kgw/cm ~357 kgw/cm 8 0 kgw 3. ISOASJISDIN CNS Christiaans Bremner 9
Radke Amplification Attenuation 3.5 4.5 Hz Grandjean 3. (Hz) 34 4 5 4~0 8~ 0~0 3. 3-3 -3 6 7 8 9 0 30
3 3-4 3. 3
Force ratio curve F. Freudenstein T. W. Lee Heuristic combinatorial optimization 3-5 3
4-3 4 5 4. Swim arm 33
asuzuki Full-Floater bhonda Pro-Link 4. 4.a 4. b 6 5 6 4.c 3 4 34
a 6 5 4 3 4 3 b c 4. 4- Topological structure 35
983 [6] Design constraints 93 989 [7] Link Revolute pair 4.3 4.3 36
3 4 4-3 4-37
3 4.4 (b) (c) (a) (d) (e) 4.4 38
4.4 3 4 P 3 4.5 4.5 4.6 39
40 3 P 3 4 P 3 4 3 4 3 4 5 6 3 4 5 6 3 4 3 4 5 6 3 4 3 4 6 5 3 4 3 4 5 6
4 3 3 4 3 4 5 6 3 4 5 6 3 4 3 4 5 6 3 4 6 5 3 4 3 4 6 5 3 4 3 4 5 6 3 4 3 4 5 6 4.5
4 3 4 3 4 6 5 6 5 3 4 6 5 3 4 3 4 6 5 3 4 5 6 6 5 4 3 6 5 3 4 6 5 4 3 6 5 4 3 6 5 4 3 6 5 4 3 4.6
6-6-5 6-66- 4.7a 6-4.7b 6-6 4.7c 4.7d 6-5 E B 4 6 6-6 5 B 4 6 6-6 6- B E 4.8 F E 3 4 5 A D B 6 C F' B' 3 4 5 A' D' 6 C' G G' a6- b6-6 6 5 4 3 6 4 5 3 c 6- d 6-6 4.7 43
6-6- 6-6 6-7 6-3 6-4 6-5 6-8 6-9 6-0 6-6- 4.8 4.8 6-6-6 6-6-7 6-6-5 6-6-5 4.7 6-6 6- BE 44
Assur group Force ratio Visual BASIC 6.0 5- Assur groups 5. A C B A C XA YAXCYC AB BC r r AB BC B XBYB AB BC r AB r CB 45
Y A rab B á â è3 rcb ra rb è4 rc C X 5. B r r + r = r + r B = 5. A AB C CB X Y X Y B B = X + r cos θ = X + r cos θ 5.a A A AB AB 3 3 C C = Y + r sin θ = Y + r sin θ 5.b CB CB 4 4 r X A C AC α = tan Y X C A ( ) C Y X A 5.3 r AC r AB 46
β = cos r + r r AB AC CB ( ) AB r r AC 5.4 rab θ3 θ = α + Mβ 3 5.5 r + k M AC r AB M k M -B XBYB X Y B B = X + r cos θ 5.6a A A AB AB 3 3 = Y + r sinθ 5.6b rcb θ4 θ 4 = tan Y X B C ( ) B Y X C 5.7 3 4 D 47
Y A è3 3 4 r AB B C r CB á r CD è D X 5. 5. A C XAYA XCYC r r CB CD B D B = X + C rcb cos ( θ + α) X 5.8a B = Y + C rcb sin ( θ + α) Y 5.8b X Y D D = X + r cos θ 5.9a C C CD CD = Y + r sin θ 5.9b 3 4 r 3 r AB AB 48
θ 3 = tan Y X B A ( ) B Y X A 5.0 r AB [ ( X X ) + ( Y Y ) ] = 5. B A B A 5 Giant ATX- 5.3 3 4 5 6 D E 6 Y B 3 ä A â è6 ã 5 4 è4 C è5 F D á è G X 5.3 49
ABCDEF ADF XAYA XDYD XFYF rdc r DG 5 rbc 6 rab r AE C G C = X + r cos D DC ( θ + α) X 5.a C = Y + r sin D DC ( θ + α) Y 5.b X Y G G X D + r DG cos θ = 5.3a D DG = Y + r sin θ 5.3b 5 6 r r A C AB CB XAYA XCYC δ = tan Y X C A ( ) C + r r Y X AB AC BC γ = cos ( ) r AB A r r AC 5.4 5.5 5.4 5.5 θ = δ + M γ 6 5.6 M = B XBYB Ar AB 6 X B X A + r AB cos θ = 5.7a 6 50
Y B = Y + r sinθ 5.7b A AB 6 E XEYE E = X + r cos A AE 6 ( θ + β) X 5.8a E = Y + r sin A AE 6 ( θ + β) Y 5.8b E F 3 4 θ 3 = θ 4 = tan Y X F E ( ) F Y X E 5.9 r [ ( X X ) + ( Y Y ) ] EF = 5.0 F E F E 5. 5.0 B C E è4è5 è6 è r EF 5-5.4 Q Nt P Nt Force ratio 5. 5
W P P Q 5.4 ( ) ( ) P f ( ) = 5. Q 5
5.5 5.5 Force ratio curve Principle of virtual work 5.6 Free-body diagram Q P P δs U δ = P δs = Pδs 5. U 53
P s äè B á è D y C Q 5.6 Q δy U δ = Q δy = Qδy 5.3 U δ U + δu = P δ s + Qδy = 0 5.4 0 5.4 P Q δy δs = 5.5 5.5 y s y 54
δy = δ [ r sin( θ α) ] CD = r CD cos ( θ α) δθ 5.6 s δs = δr = δ δθ = r = δ ( ( XB XA ) + ( YB YA ) ) ( X + r cosθ X ) + ( Y + r sin θ Y ) AB ( C CB A C CB A ) AB [( X + r cos θ X ) r sin θ + ( Y + r sin θ Y ) r cosθ ] C CB A CB C CB A 5.7 CB 5.6 5.7 5.5 P Q rab rcd cos ( θ α) ( X + r cosθ X ) r sinθ + ( Y + r sinθ Y ) r cosθ C CB A CB C CB A CB = 5.8 5.8 5.7 Q Free-body diagram P 5. 5.5 δy = δ [ r sin( θ α) ] DC = r DC cos ( θ α) δθ 5.9 55
B E â 6 P A äè6 D è6 á 5 C äè è G Q 5.7 δs = δ r = δ δθ = r = δ ( ( XF XE) + ( YF YE ) ) ( X X r cos( θ +β) ) + ( Y Y r sin( θ +β ) EF ( ) F A AE 6 F A AE 6 EF 6 [( X X r cos( θ +β) ) r sinθ + ( Y Y r sin( θ +β) ) r cosθ ] F A AE 6 AE 6 F A AE 6 5.30 AE 6 5.9 5.30 5.5 P Q ref rcd cos( θ + α) δθ6 = 5.3 ( XF XA rae cos( θ6 + β ) rae sin θ6 + ( YF YA rae sin( θ6 + β) ) rae cosθ 6 δθ δθ δθ 6 = δθ δt δθ δt 6 θ& = θ& 6 = [ ( Y )( ) ( )( ) ] B YC X B X A Y B YA X B XC r sinθ ( X X ) + r cosθ ( Y Y ) CD B C CD B C 5.3 56
5.3 5.3 5-3 5.8 A C Q Q Free body diagram 5.8 Y A è3 3 r AB r CB C á r CD è D X Q 5.8 57
è3 P B C x C r BC á r CD è D Q C y a A x A è3 r AB A y 3 4 B P b 5.9 5.9a Q P C C x C y ( θ + α) Pcosθ r sin( θ + α) 0 Q r cos θ + Psin θ3 rbc cos 3 BC CD = 58 5.33 Q P
= cosθ 3 r BC Q r cosθ CD P 5.34 sin ( θ + α) sinθ r cos( θ + α) 3 BC B B x y Pcosθ = 5.35a 3 = Psin θ 5.35b 3 C x Pcosθ = 5.36a ( Psinθ Q) C y 3 + 3 = 5.36b A A x y = Pcos θ 5.37a 3 3 = Psin θ 5.37b 5.8 5.8 P Q = f ( ) 5.38 θ 5.8 r AB r = AB = r (X AB C ( θ + r ) = CB cos (X ( θ + α) X ) (Y + r sin( θ + α) Y ) B X A ) (Y A B Y C A ) CB A 5.39 59
L 0 k 5.38 P Q ( L r ( θ )) k 0 AB = = f ( θ ) 5.40 Q Q 5.39 5.0 AD F Q Free body diagram 5. Y B E 6 3 A â è6 5 C è5 4 F è4 D á è G Q X 5.0 60
F BC C è5 D x á è G Q D y -E y a B è 5 + -E x 3 E P E A x è4 â 6 A è6 F BC F x 4 F A y F y b6 c 5. 5.a Q 5 F BC D D x D y Q r F BC CD cos cos θ 5 θ + FBC sin θ5 rcd cos r sin( θ + α) = 0 CD ( θ + α) 5.4 6
Q 5 F BC F BC = cosθ 5 r CD sin Q r cosθ ( θ + α) sin θ r cos( θ + α) CD 5 CD 5.4 C C x y F BC cosθ = 5.43a F BC sin θ 5 5 = 5.43b D x = F cos θ 5.44a BC ( F sin θ Q) D y BC 5 + 5 = 5.44b 5.b 6 5 F BC P A A x A y F BC B B x y BC ( θ5 + π) = FBC cosθ5 ( θ5 + π) = FBC sin θ5 = F cos 5.45a = F sin 5.45b BC F BC cos θ + Psin θ 5 4 r r AB AE sin θ cos 6 F sin θ r cos θ ( θ + β) Pcos θ r sin( θ + β) = 0 6 BC 5 AB 4 AE 6 6 5.46 6
5 F BC 5.38 P F sin θ BC = sin θ r 4 AE r cos cosθ F cos θ r sin θ 5 AB 6 BC 5 AB 6 P 5.47 ( θ + β) cosθ r sin( θ + β) 6 4 AE 6 E E x y Pcosθ = 5.48a = Psin θ 4 4 5.48b A A x y = F cosθ Pcosθ 5.49a = F BC BC sin θ 5 5 Psin θ 4 4 5.49b 5.c E EF E -E x -E y F F x y = E = Pcosθ 5.50a x y 4 = E = Psin θ 5.50b 4 5.3 5.8 63
P Q = g( ) 5.5 θ 5.0 r EF r = EF = r ( ( ) ( ) ) EF ( θ ) = X F X E + YF YE ( X X r cos( θ + β) ) + ( Y Y r sin( θ + β) ) ( ) F A AE 6 F A AE 6 5.5 L 0 k 5.5 P Q ( L r ( θ )) k 0 EF = = g( θ ) 5.53 Q Q 5.53 5-4 3 4 64
5. D 5.3 G y 3 5. 5. 5.3 65
5.3 4T 3T T48T 38T 8TT 0 5 5.4a b ½ ½ ½ 5.4c ½ 63.5 66
N/ N a (N/)5 N0 b ½ N/ N c 5.4 5.40 5.5 Q 6085 kgw 67
00 kgw 355.5 kgw 70 kgw 7080 /hr 50 kgw P max 5.40 5.5 EF EF = L 0 r EF 5.54 Travel EF k 68
5-5 Visual BASIC 6.0 3 4 5.5 3 5.6 5.7a 5.7b 69
5.5 5.6 70
a b 5.7 7
5.8 5.9 5.0 5.8 7
5.9 5.0 73
5. 3 5. 74
5. 3 5. 75
Giant Warp-DS Giant ATX- a b 5.3 Giant Warp -DS 76
Giant Warp-DS 5.3 Giant Warp-DS C00 B8030A-3070 D465-45 5.4 ABBC CD BD 75467 43 mm 5.5 0 9 3.7 mm 5.6 9. mm 4.06 5.9 4.06 5.9 C D 5.4 Giant Warp-DS 77
5.5 5.6 78
6 3 4 5 b 5.7 Giant ATX- 79
Giant ATX- 5.7 Giant ATX- ABCDE F -40 75 075 3500 00-5000 -800 G 390-0 5.8 5.9 0 5.30 5.3 5.30 470.8 mm 48.6 mm 0.8 mm.80. Giant Warp-DS 5.8 Giant ATX- 80
5.9 5.30 8
5.3 8
3- Heuristic combinatorial optimization 6-5-4 3 4 5-4 63.5 3 83
4 3-6- 6-6. ABC D ABC D 6. 5.8 5.3 6-84
Y B A D X C 6. Y B A F C G D 6. 85
F. Freudenstein T. W. Lee[8] Heuristic combinatorial optimization Dr. Shen Lin Mathematical programming technique Continuous method Discrete Combinatorial optimization 965 Dr. Shen Lin Heuristic method S s S C S f (s) C T T T 3 T f (T ) < f (T) T T 4 86
S Pseudorandom feasible solutiont x x x ë T y y y ë T T 3 g i G i f i g i i x x x i- y y y i- gain g i f i f i- G i i G ig g g i f i f 0 G i > 0 4 N C 5 87
6 Look-ahead procedure 35 7 g g g 8 9 35 0 i - q i q q i q 88
L N S T T BBk k T i i3 L T 3 i a i BB 5 b TEMIN c i i i 89
4 i a 3c i i b 3b L 5 5 L L T T 6 TT 6 5.8 5.3 90
6.3 0 5 B-Spline B-Spline 6.3 9
6.4 6.5 6.4 9
6.5 x y For-Next x y 800 30 700 0 80 473760 93
Root mean square error R.M.S.E n Σ i = ( f ( θ ) f ( θ )) designed n n wanted n 6. f designed f wanted n n 6. 6-3 Downhill Union Cycliste Internationale UCI 3.5 3.5 94
3 3 6.6 6. 5 4 3 5 0 5 0 5 30 6.6 0 5 0 5 0 5 4.5 4.5 4.3 4.0 3.5.0 6. 95
6. 0.0 6.7 6.86.9 6.0 6.7 96
6.8 6.9 97
6.0 6. 6. 98
6. 6. 50 99
40 69 6. 50 8 6. 45.3 6.3 6.3 00
50 kgw 40 kn/m 800 lb/in. 80 45 800 lb/in. 6. - 4. 4. 6.4 6.5 0.09 6.3 0
6.4 / 6.5 / 0
6.6 6.7a e 0. 0.7 0.8 0.7 0.5 90 6.6 6.8a b 0. 6.8a ABE AEF 90 03
6.6 6.7a 04
6.7b 6.7c 05
6.7d 6.7e 06
6.8a 6.8b 07
3 4 5 Visual BASIC 6.0 08
3 4 09
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. J. Olsen, Mountain Biking, Stackpole Books, 989.. R. Van der Plas, Bicycle Technology, Bicycle Books San Francisco, 99. 3. L. Zinn, Mountain Bike Performance Handbook, MBI Publishing Company, 998. 4. 5 8-34 995 5. G. Pahl and W. Beitz, Engineering Design, Second Edition, translated by Wallance, K., Blessing, L., and Bauert, F., edited by Wallance, K., Springer-Verlag London Limited, 996. 6. -3 983 7. 8 55-63 989 8. T. W. Lee and F. Freudenstein, Heuristic Combinatorial Optimization in the Kinematic Design of Mechanisms, ASME Journal of Engineering for Industry, Nov. 976, pp. 77-80.