基于MatLab的缝纫机运动分析

1、 中国地质大学（武汉）基于MatLab的缝纫机针头运动分析图示为一缝纫机针头及其挑线器机构，设已知机构的尺寸lAB=32mm，lBC=100mm，lBE=28mm，lFG=90mm，原动件1以等角速度1=5rad/s逆时针方向回转试用图解法求机构在图示位置时缝纫机针头和挑线器摆杆FG上点G的速度及加速度。画机构简图建立数学模型L1 + L2 = S3L6 + S5 = L1 + L4（1）建立机构的闭环矢量方程向x,y方向投影并整理得角位移方程的分量形式为：L1 cos1 + L2 cos2 = 0L1 sin1 + L2 sin2 = S3S5 sin5 + 64 = L4 sin4 + L

2、1 sin1S5 cos5 + 24 = L1 cos1 + L4 cos42 4 = 112 /180（2）闭矢量方程分量形式对时间求一阶导数的矩阵形式（速度方程）为：= w1-L2 sin2 0000L2 cos200100L4 cos4S5 cos50sin50L4 sin4-S5 sin50cos51-1000w2w4w5v3v5L1 sin1-L1 cos1L1 cos1-L1 sin10（3）闭矢量方程分量形式对时间求二阶导数的矩阵形式（加速度方程）为：245a3a5-L2 sin2 0000L2 cos200100L4 cos4S5 cos50sin50L4 sin4-S5 si

3、n50cos51-1000=+ w1w1 L1 cos1w1 L1 sin1-w1 L1 sin1-w1 L1 cos10w2w4w5v3v5-w2 L2 cos2 000 0-w2 L2 sin2 000 00w4 L4 sin4S5 cos5 - w5 S5 sin50w5 cos50w4 L4 cos4-S5 sin5 - w5 S5 cos50- w5 sin50 000 0用MatLab求解求解2 、4、5、S3、S5首先创建fengposition函数，函数fsolve调用它来解方程function t = fengposition(R,th1,L1,L2,L4)t = L1*co

4、s(th1) + L2*cos(R(1);L1*sin(th1) + L2*sin(R(1) - R(4);. 64 + R(5)*sin(R(3) - L1*sin(th1) - L4*sin(R(2);. 24 + R(5)*cos(R(3) - L1*cos(th1) - L4*cos(R(2);. R(1) - R(2) - 112*pi/180;主程序如下：% 解方程L1 = 32;L2 = 100;L4 = 28; th1 = 0:1/36:2*pi; options = optimset(display,off); for i = 1:length(th1) Res(i,:) =

5、 fsolve(fengposition,1 1 1 1 5,options,th1(i),L1,L2,L4);end %求解速度方程w1 = 5;for j = 1:length(th1) A = -L2*sin(Res(j,1) 0 0 0 0;L2*cos(Res(j,1) 0 0 1 0;. 0 -L4*cos(Res(j,2) Res(j,5)*cos(Res(j,3) 0 sin(Res(j,3);. 0 L4*sin(Res(j,2) -Res(5)*sin(Res(j,3) 0 cos(Res(j,3);1 -1 0 0 0; B = w1*L1*sin(th1(j);-w1*

6、L1*cos(th1(j);w1*L1*cos(th1(j);-w1*L1*sin(th1(j);0; w = AB; w2(j) = w(1); w4(j) = w(2); w5(j) = w(3); v3(j) = w(4); v5(j) = w(5); end %求解加速度方程for j = 1:length(th1) C = -L2*sin(Res(j,1) 0 0 0 0;L2*cos(Res(j,1) 0 0 1 0;. 0 -L4*cos(Res(j,2) Res(j,5)*cos(Res(j,3) 0 sin(Res(j,3);. 0 L4*sin(Res(j,2) -Res(

7、j,5)*sin(Res(j,3) 0 cos(Res(j,3);. 1 -1 0 0 0; D = -w2(j)2*L2*cos(Res(j,1) + w12*L1*cos(th1(j);. w2(j)2*L2*sin(Res(j,1) + w12*L1*sin(th1(j);. w4(j)2*L4*sin(Res(j,2) + w5(j)2*(Res(j,5)*cos(Res(j,3) -. Res(j,5)*sin(Res(j,3) + w5(j)*v5(j)*cos(Res(j,3) -. w12*L1*sin(th1(j);w4(j)2*L4*cos(Res(j,2) - . w5(

8、j)2*(Res(j,5)*cos(Res(j,3)+Res(j,5)*sin(Res(j,3) - . w5(j)*v5(j)*sin(Res(j,3) - w12*L1*cos(th1(j);0; a = CD; a = CD; a3(j) = a(4);endt = th1/5; %绘图plot(t,Res(:,4)gridxlim(0 1.25)title(针头位移曲线图)xlabel(时间（s）)ylabel(针头位移) plot(t,v3)gridxlim(0 1.25)title(针头速度曲线图)xlabel(时间（s）)ylabel(针头速度) plot(t,a3)gridxlim(0 1.25)title(针头加