上海交通大学：《复杂系统动力学计算机辅助分析》课程教学资源_Chapter 5_Modeling for Example 4

Kinematics Analysis of a Gear-slider Mechanism y3 D℃ B3 0.8m ys B y木 0.4m 01 Bs X2 B2 Ba 0.4m ya 0.2m 0.1m 0.893m 0.6m The gear-slider mechanism is modeled as shown in the figure. Initial condition q(0)=[0000.3000.60.400.6-0.4014928 0.20 Kinematic Constraints No. Kind B s si0 & R 0 C 1 ax 1 0 o ay 1 0 0 Number of constraint equations:2 Φm=X1, Φ0=1

Kinematics Analysis of a Gear-slider Mechanism B5 B4 B3 B B2 1 x y 1 0.2m x1 x2 y2 x3 y3 x4 y4 E D B C A 0.1m 0.6m 0.4m 0.4m 0.8m 0.893m x5 y5 The gear-slider mechanism is modeled as shown in the figure. Initial condition   T q(0)  0 0 0 0.3 0 0 0.6 0.4 0 0.6  0.4 0 1.4928 0.2 0 Kinematic Constraints No. Kind Bi P i s Q i s Ri  i Bj P j s Q j s Rj  j C 1 ax 1       0 0 0 2 ay 1       0 0 0 Number of constraint equations:2 1 (1) x ax   , 1 (1) y ay  

No. Kind B e R B s'o R 3 g 1 0.2 0 2 0.1 3.1416 4 2 0.3 o o g 2 0.1 0.9273 3 0.4 4.0689 6 rd 「0 3 0.5 o o Number of constraint equations:4 For gear constraints,the equations are given by R(+0,)+R,9,+0,R,π R+R (x-x")sin-(v-y")cos0=0 :-) o-ke-xm后+5--后+写) e=-+号+0273-6，-gm++09273） Φa,2)=x1-x2)2+(0y-y2}-0.32 D2》=(x2-x3}+(02-y32-0.52

No. Kind Bi P i s Q i s Ri  i Bj P j s Q j s Rj  j C 3 g 1 0.2 0 2 0.1 3.1416 4 rd 1       0 0 2       0 0 0.3 5 g 2 0.1 0.9273 3 0.4 4.0689 6 rd 2       0 0 3       0 0 0.5 Number of constraint equations:4 For gear constraints, the equations are given by                        sin cos 0       P i P j P i P j i j i i i j j j j x x y y R R R R R             sin cos  0                          i j P i i i j j j j i P j i j P i i i j j j j i P j R R R R R y y R R R R R x x                               2  1 1  2 2 1 1 2 (1,2) 3 1 3 2 cos 3 1 3 2  x x sin   y y   g                          0.9273 5 4 5 1 0.9273 cos 5 4 5 1 sin 3 2 2 3 3 2 2 3 (2,3) x x   y y   g     2 2 1 2 2 1 2 (1,2)  x  x  y  y  0.3 rd      2 2 2 3 2 2 3 (2,3)  x  x  y  y  0.5 rd 

No. Kind B si0 R B, s R C 7 3 4 0 o 0.8 Number of constraint equations:2 3,4 x4] cosφ4 sin No. Kind B y° R B, R 8, 8 ax 4 0.6 9 ay 4 01 -0.4 Number of constraint equations:2 Φm(4)=x4-0.6, Φ)=y4+0.4 No. Kind B s'0 R 0 B s o R 8 10 rd T0.21 J [8 0.8 0.2 Number of constraint equations:1 Da4,5-(x3+0.2cos4,-0.2sin4,-x3)2+6y,+0.2sin4,+0.2cos4,-y)2-0.82

No. Kind Bi P i s Q i s Ri  i Bj P j s Q j s Rj  j C 7 r 3       0 0 4       0.8 0 Number of constraint equations:2                           3 3 4 4 4 4 4 (3,4) 4 0.8 0 sin cos cos sin y x y x r      No. Kind Bi P i s Q i s Ri  i Bj P j s Q j s Rj  j C 8 ax 4       0 0 0.6 9 ay 4       0 0 -0.4 Number of constraint equations:2 0.6 4 ( 4 )  x  ax  , 0.4 4 (4)  y  ay  No. Kind Bi P i s Q i s Ri  i Bj P j s Q j s Rj  j C 10 rd 3       0.2 0.2 5       0 0 0.8 Number of constraint equations:1     2 2 3 3 3 5 2 3 3 3 5 (4,5)  x  0.2cos  0.2sin  x  y  0.2sin  0.2cos  y  0.8 rd     

No. Kind B siQ R B, C 11 5 07 0.2 12 a帥 5 0 Number of constraint equations:2 Φ5)=y5-0.2, 币a5)=中5 D0F=15-2-4-2-2-1-2=2 Driving Constraints No. Kind B s o R B, 5 s'a R 0 C 13 aod 4 0 中ad(=中4 No. Kind B s 9 R 0 巴 s s' R 8) C) 14 aod 1 4 Φ0=中1-4π1

No. Kind Bi P i s Q i s Ri  i Bj P j s Q j s Rj  j C 11 ay 5       0 0 0.2 12 a 5 0 Number of constraint equations:2 0.2 5 (5)  y  ay  , 5 (5)     a DOF  15  2  4  2  2 1  2  2 Driving Constraints No. Kind Bi P i s Q i s Ri  i Bj P j s Q j s Rj  j C(t) 13 ad 4 0 4 (4)     a d No. Kind Bi P i s Q i s Ri  i Bj P j s Q j s Rj  j C(t) 14 ad 1 4t t a d     4 1 (1)  