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 8_Modeling for Example2

Dynamic analysis of quick-return mechanism 小4 >X5 X3 V2 X2 1=4m,12=1.5m,14=1.9m Initial condition q(0)=[0.91901.77681.0934020.43561.35062.63201.09380.91443.7766-0.2368-0.00883.99970 Kinematic Constraints No. Kind o R 0 s so R, C 1 ax 1 -4/2 0 ay 12 0 0」 Number of constraint equations:2

Dynamic analysis of quick-return mechanism l1  4m , l2  1.5m , l4  1.9m Initial condition (0) 0.9190 1.7768 1.0934 0 2 0.4356 1.3506 2.6320 1.0938 0.9144 3.7766 0.2368 0.0088 3.9997 0 T q    Kinematic Constraints No. Kind i P i s Q i s Ri  i j P j s Q j s Rj  j C 1 ax 1 1 / 2 0 l      0 2 ay 1 1 / 2 0 l      0 Number of constraint equations: 2

os 2 Φ0=y- sin No. Kind i SiP 59 R j R 3 ax v [8 0 4 ay 2 0 o Number of constraint equations:2 Φ2)=X2, Φw2=y32 No. Kind o R 0, s s R, 0 C 5 2 3 Lo] o Number of constraint equations:2 (2,3) -[ c0s4,- sin; No. Kind sip sio 父 0, j s 。 &) 8 6 1 8 8 Number of constraint equations:2 - -4

(1) 1 1 1 cos 2 ax l   x   , (1) 1 1 1 sin 2 ay l   y   No. Kind i P i s Q i s Ri  i j P j s Q j s Rj  j C 3 ax 2 0 0       0 4 ay 2 0 0       0 Number of constraint equations: 2 ( 2 ) 2 ax   x , (2) 2 ay   y No. Kind i P i s Q i s Ri  i j P j s Q j s Rj  j C 5 r 2 20 l      3 0 0       Number of constraint equations: 2 ( 2,3) 3 2 2 2 2 3 2 2 2 cos sin sin cos 0 r x x l y y                                  No. Kind i P i s Q i s Ri  i j P j s Q j s Rj  j C 6 t 1 0 0       1 0       3 0 0       1 0       Number of constraint equations: 2     (1,3) 1 3 1 1 3 1 3 1 sin cos t  x x  y y              

No. Kind s"o R 59 R C 7 4 0 0 Number of constraint equations:2 Φ1,4) cosφ4 sinφ4 2-[ sin No. Kind i s 59 R 0, s9 R, 8 C -112 J Ce Number of constraint equations:2 (45) [-[- cos sin 厂2] -sin No. Kind siP 。 0 j 59 R 8 C 9 ay 5 [8 4 10 a 5 0 Number of constraint equations:2 Φ5)=y5-4, Φ5)=4

No. Kind i P i s Q i s Ri  i j P j s Q j s Rj  j C 7 r 1 1 / 2 0 l      4 4 / 2 0 l      Number of constraint equations: 2 (1,4 ) 4 4 4 4 1 1 1 1 4 4 4 1 1 1 cos sin / 2 cos sin / 2 sin cos 0 sin cos 0 r x l x l y y                                                    No. Kind i P i s Q i s Ri  i j P j s Q j s Rj  j C 8 r 4 4 / 2 0 l      5 0 0       Number of constraint equations: 2 ( 4,5) 5 4 4 4 4 5 4 4 4 cos sin / 2 sin cos 0 r x x l y y                                  No. Kind i P i s Q i s Ri  i j P j s Q j s Rj  j C 9 ay 5 0 0       4 10 a 5 0 Number of constraint equations: 2 (5) 5 4 ay   y  , (5) 5 a   

The Jacobian matrix 1 0 1sin4/200 0 0 0000 0 000 0 -4cos4/200 0 0 0000 000 0 0 0 10 0 0 0000 0 000 0 0 0 01 0 0 0000 0 000 0 0 0 -1 0 1 singz 1 0000 0 000 0 0 0 0-1-12c0s42 0 1000 0 000 = sind-cos a 00 0 -sing cos 000 0 000 0 0 -1 00 0 00100 0 000 人 0 1sin4/200 0 00010-,si吨，/2000 0 -1 -4cos4/200 0 0 00011,cos4/2000 0 0 0 00 0 0 00-10-4si吨/2100 0 0 0 00 0 0 000-114c04/2010 0 0 0 00 0 0 0000 0 010 0 0 0 00 0 0 0000 0 001 a=-sin (y3-y)-cos (x;-x) 01 -4c0s44212 0 -1,sin44212 0 0 0 0 -1cos442 0 -42sin442 0 2sin(+2cos(+cos(y)2-sin(x V= 0 Y= 0 -1c0s442/2+1,c0s项0212 0 -1sin442/2+lsin442/2 1cos4项2/2 I sin212 0 0

The Jacobian matrix 1 1 1 1 2 2 2 2 1 1 1 1 1 1 4 1 0 sin / 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 cos / 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 sin 1 0 0 0 0 0 0 0 0 0 0 0 0 1 cos 0 1 0 0 0 0 0 0 0 sin cos 0 0 0 sin cos 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 sin / 2 0 0 0 0 0 0 1 0 sin l l l l a l l                    q 4 1 1 4 4 4 4 4 4 / 2 0 0 0 0 1 cos / 2 0 0 0 0 0 0 0 1 cos / 2 0 0 0 0 0 0 0 0 0 0 0 0 1 0 sin / 2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 cos / 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 l l l l                 sin ( ) cos ( ) 1 3 1 1 3 1 a    y  y   x  x 0 0 0 0 0 0 0 0 0 0 0 0 0 0        v , 2 1 1 1 2 1 1 1 2 2 2 2 2 2 2 2 2 2 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 2 2 1 1 1 4 4 4 2 2 1 1 1 4 4 4 2 4 4 4 4 cos / 2 sin / 2 0 0 cos sin 2sin ( ) 2cos ( ) cos ( ) sin ( ) 0 cos / 2 cos / 2 sin / 2 sin / 2 cos / 2 s l l l l y y x x y y x x l l l l l l                                                             2 4 4 in / 2 0 0         

Body number 1 2 ￥ 5 Mass(Kg) 100 1000 5 30 50 Moment of Inertia 100 2000 0.05 10 1.5 (Kg.m2) m 0> m 0L0 J 0 0 M- 24= 0 J 0 0 0 ms ms 200,-4<x<1.2andx<0 F= 0,other cases L=165521N.m2

Body number 1 2 3 4 5 Mass (Kg) 100 1000 5 30 50 Moment of Inertia (Kg.m2) 100 2000 0.05 10 1.5    5 5 5 4 4 4 3 3 3 2 2 2 1 1 1 J m m J m m J m m J m m J m m M ,    0000000000000FL A Q       0, other cases 200, 4 1.2 and 0 5 5 x x F  2 L  165521 N.m