哈工大机械原理大作业连杆46

I机械原理大作业设计说明书课程名称：机械原理设计题目：连杆运动分析（46）院系：班级：设计者：学号：哈尔滨工业大学1平面连杆机构运动分析一、题目及原始数据如图所示颚式矿石破碎机机构，已知各构件尺寸为：lAB=100mm，lBC=lBE=460mm，lCD=250mm，lEF=265mm，lFG=670mm，xD=300mm，yD=500mm，xG=430mm，yG=210mm，δ=30°.试求构件2上E的轨迹，构件5的角位移、角速度、角加速度。二、建立数学模型（1）以A为原点建立直角坐标系（2）该机构由一个三级杆组构成（3）数学关系yb=absinωt；xb=abcosωt。bd=squrt（（xd-xb）^2+（yd-yb）^2)C点：（xc-xd）^2+(yc-yd)^2=cd;(xc-xb)^2+(yc-yb)^2=cb.E点：(xe-xc)^2+(ye-yc)^2=ce;(xe-xb)^2+(ye-yb)^2=eb.2F点：(xf-xe)^2+(yf-ye)^2=ef;(xf-xg)^2+(yf-yg)^2=fg.构件5的角位移：d=21FFΨ=arccos(（2*fg^2-d^2)/2*fg^2)构件5的角速度：ω=dΨ/dt构件5的角加速度:α=dω/dt三、计算流程图连杆机构分析建立坐标系杆组分析MATLAB编程角位移角速度角加速度E点轨迹三级杆组3四、用matlab编程（程序）1、构件5的角位移xa=0;ya=0;xd=300;yd=-500;xg=-430;yg=210;fe=265;ab=100;gf=670;be=460;bc=460;cd=250;a7=pi/6;ec=2*bc*sin(a7/2);a1=0:0.001:2*pi;t=a1./10;xb=ab.*cos(a1);yb=ab.*sin(a1);a2=atan((yd-yb)./(xd-xb))+pi;bd=sqrt(((yb-yd).*(yb-yd))+((xb-xd).*(xb-xd)));a3=acos((bd.*bd+cd.*cd-bc.*bc)./(2*bd.*cd));xc=xd-cd.*sin(a2+a3-pi/2);yc=yd+cd.*cos(a2+a3-pi/2);fori=1:length(a1)ifatan((yc(i)-yb(i))./(xc(i)-xb(i)))0a4(i)=atan((yc(i)-yb(i))./(xc(i)-xb(i)));elsea4(i)=atan((yc(i)-yb(i))./(xc(i)-xb(i)))+pi;endendfori=1:length(a1)ifa4(i)+5*pi/12piye(i)=yc(i)+ec.*cos(a4(i)-1/12*pi);结束4xe(i)=xc(i)-ec.*sin(a4(i)-1/12*pi);elseye(i)=yc(i)-ec.*sin(a4(i)-7*pi/12);xe(i)=xc(i)-ec.*cos(a4(i)-7*pi/12);endendfori=1:length(a1)ifatan((ye(i)-yg)./(xe(i)-xg))0a5(i)=atan((ye(i)-yg)./(xe(i)-xg));elsea5(i)=atan((ye(i)-yg)./(xe(i)-xg))+pi;endendge=sqrt((ye-yg).*(ye-yg)+(xe-xg).*(xe-xg));a6=acos((ge.*ge+fe.*fe-gf.*gf)./(2*ge.*fe));xf=xe-fe.*cos(a5+a6-pi);yf=ye-fe.*sin(a5+a6-pi);a10=acos((ge.*ge+gf*gf-fe*fe)./(2*gf.*ge));plot(t,a5-a10);title('构件5的角位移');xlabel('t/s');ylabel('角度rad');gridon;2、构件5的角速度xa=0;ya=0;xd=300;yd=-500;xg=-430;yg=210;fe=265;ab=100;gf=670;be=460;bc=460;cd=250;a7=pi/6;ec=2*bc*sin(a7/2);a1=0:0.001:2*pi;5t=a1./10;xb=ab.*cos(a1);yb=ab.*sin(a1);a2=atan((yd-yb)./(xd-xb))+pi;bd=sqrt(((yb-yd).*(yb-yd))+((xb-xd).*(xb-xd)));a3=acos((bd.*bd+cd.*cd-bc.*bc)./(2*bd.*cd));xc=xd-cd.*sin(a2+a3-pi/2);yc=yd+cd.*cos(a2+a3-pi/2);fori=1:length(a1)ifatan((yc(i)-yb(i))./(xc(i)-xb(i)))0a4(i)=atan((yc(i)-yb(i))./(xc(i)-xb(i)));elsea4(i)=atan((yc(i)-yb(i))./(xc(i)-xb(i)))+pi;endendfori=1:length(a1)ifa4(i)+5*pi/12piye(i)=yc(i)+ec.*cos(a4(i)-1/12*pi);xe(i)=xc(i)-ec.*sin(a4(i)-1/12*pi);elseye(i)=yc(i)-ec.*sin(a4(i)-7*pi/12);xe(i)=xc(i)-ec.*cos(a4(i)-7*pi/12);endendfori=1:length(a1)ifatan((ye(i)-yg)./(xe(i)-xg))0a5(i)=atan((ye(i)-yg)./(xe(i)-xg));elsea5(i)=atan((ye(i)-yg)./(xe(i)-xg))+pi;endendge=sqrt((ye-yg).*(ye-yg)+(xe-xg).*(xe-xg));a6=acos((ge.*ge+fe.*fe-gf.*gf)./(2*ge.*fe));xf=xe-fe.*cos(a5+a6-pi);yf=ye-fe.*sin(a5+a6-pi);a10=acos((ge.*ge+gf*gf-fe*fe)./(2*gf.*ge));6plot(t(1:6283),diff(a5-a10)./diff(t));title('构件5的角速度');xlabel('t/s');ylabel('角速度rad/s');gridon;4.3构件5的角加速度xa=0;ya=0;xd=300;yd=-500;xg=-430;yg=210;fe=265;ab=100;gf=670;be=460;bc=460;cd=250;a7=pi/6;ec=2*bc*sin(a7/2);a1=0:0.001:2*pi;t=a1./10;xb=ab.*cos(a1);yb=ab.*sin(a1);a2=atan((yd-yb)./(xd-xb))+pi;bd=sqrt(((yb-yd).*(yb-yd))+((xb-xd).*(xb-xd)));a3=acos((bd.*bd+cd.*cd-bc.*bc)./(2*bd.*cd));xc=xd-cd.*sin(a2+a3-pi/2);yc=yd+cd.*cos(a2+a3-pi/2);fori=1:length(a1)7ifatan((yc(i)-yb(i))./(xc(i)-xb(i)))0a4(i)=atan((yc(i)-yb(i))./(xc(i)-xb(i)));elsea4(i)=atan((yc(i)-yb(i))./(xc(i)-xb(i)))+pi;endendfori=1:length(a1)ifa4(i)+5*pi/12piye(i)=yc(i)+ec.*cos(a4(i)-1/12*pi);xe(i)=xc(i)-ec.*sin(a4(i)-1/12*pi);elseye(i)=yc(i)-ec.*sin(a4(i)-7*pi/12);xe(i)=xc(i)-ec.*cos(a4(i)-7*pi/12);endendfori=1:length(a1)ifatan((ye(i)-yg)./(xe(i)-xg))0a5(i)=atan((ye(i)-yg)./(xe(i)-xg));elsea5(i)=atan((ye(i)-yg)./(xe(i)-xg))+pi;endendge=sqrt((ye-yg).*(ye-yg)+(xe-xg).*(xe-xg));a6=acos((ge.*ge+fe.*fe-gf.*gf)./(2*ge.*fe));xf=xe-fe.*cos(a5+a6-pi);yf=ye-fe.*sin(a5+a6-pi);a10=acos((ge.*ge+gf*gf-fe*fe)./(2*gf.*ge));8yv=diff(a5-a10)./diff(t);plot(t(1:length(diff(yv)./diff(t(1:6283)))),diff(yv)./diff(t(1:6283)));title('构件5的角加速度');xlabel('t/s');ylabel('角加速度rad/s*s');gridon;4.4试件2上E点的轨迹xa=0;ya=0;xd=300;yd=-500;xg=-430;yg=210;fe=265;ab=100;gf=670;be=460;bc=460;cd=250;a7=pi/6;ec=2*bc*sin(a7/2);a1=0:0.001:2*pi;t=a1./10;xb=ab.*cos(a1);yb=ab.*sin(a1);a2=atan((yd-yb)./(xd-xb))+pi;bd=sqrt(((yb-yd).*(yb-yd))+((xb-xd).*(xb-xd)));a3=acos((bd.*bd+cd.*cd-bc.*bc)./(2*bd.*cd));xc=xd-cd.*sin(a2+a3-pi/2);yc=yd+cd.*cos(a2+a3-pi/2);ce=sqrt((xe-xc).*(xe-xc)+(ye-yc).*(ye-yc));eb=sqrt((xe-xb).*(xe-xb)+(ye-yb).*(ye-yb));plot(xe,ye,'k');xlabel('x位移/mm');ylabel('y位移/mm');title('E点的运动轨迹');grid;5．程序运行结果910116．结果分析通过对该机构划分基本杆组，使用Matlab数学软件，实现了对各个构件的运动分析。计算结果分析如下：随着构件1转动，杆5在一定角度内来回摆动，实现循环工作；当杆5由角度最大转动到角度最小的过程中，加速度逐渐增大至最大，可以实现破碎矿石的过程，破碎后，随着杆1的继续转动，杆5向返回的方向摆动至角度最大，循环往复工作。