基于MatLab的縫紉機(jī)運(yùn)動(dòng)分析

1、 中國(guó)地質(zhì)大學(xué)（武漢）基于MatLab的縫紉機(jī)針頭運(yùn)動(dòng)分析圖示為一縫紉機(jī)針頭及其挑線器機(jī)構(gòu)，設(shè)已知機(jī)構(gòu)的尺寸lAB=32mm，lBC=100mm，lBE=28mm，lFG=90mm，原動(dòng)件1以等角速度1=5rad/s逆時(shí)針?lè)较蚧剞D(zhuǎn)試用圖解法求機(jī)構(gòu)在圖示位置時(shí)縫紉機(jī)針頭和挑線器擺桿FG上點(diǎn)G的速度及加速度。畫(huà)機(jī)構(gòu)簡(jiǎn)圖建立數(shù)學(xué)模型L1 + L2 = S3L6 + S5 = L1 + L4（1）建立機(jī)構(gòu)的閉環(huán)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為：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）閉矢量方程分量形式對(duì)時(shí)間求一階導(dǎo)數(shù)的矩陣形式（速度方程）為：= w1-L2 sin2 0000L2 cos200100L4 cos4S5 cos50sin50L4 sin4-S5 sin50cos51-1000w2w4w5v3v5L1 sin1-L1 cos1L1 cos1-L1 sin10（3）閉矢量方程分量形式對(duì)時(shí)間求二階導(dǎo)數(shù)的矩陣形式（加速度方程）為：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首先創(chuàng)建fengposition函數(shù)，函數(shù)fsolve調(diào)用它來(lái)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; %繪圖plot(t,Res(:,4)gridxlim(0 1.25)title(針頭位移曲線圖)xlabel(時(shí)間（s）)ylabel(針頭位移) plot(t,v3)gridxlim(0 1.25)title(針頭速度曲線圖)xlabel(時(shí)間（s）)ylabel(針頭速度) plot(t,a3)gridxlim(0 1.25)title(針頭加速度曲線圖