连杆的运动的分析一．连杆运动分析题目图1-13 连杆机构简图二．机构的结构分析及基本杆组划分1.。

结构分析与自由度计算机构各构件都在同一平面内活动，活动构件数n=5, PL=7,分布在A、B、C、E、F。

没有高副，则机构的自由度为F=3n-2PL-PH=3*5-2*7-0=12．基本杆组划分图1-13中1为原动件，先移除，之后按拆杆组法进行拆分，即可得到由杆3和滑块2组成的RPR II级杆组，杆4和滑块5组成的RRP II级杆组。

机构分解图如下：图二图一图三三．各基本杆组的运动分析数学模型 图一为一级杆组，ϕcos lAB x B =，ϕsin lAB y B =图二为RPR II 杆组，C B CB j j B E jB E y y B x x A A B S lCE y x S lCE x x -=-==-+=-+=0000)/arctan(sin )(cos )(ϕϕϕ由此可求得E 点坐标，进而求得F 点坐标。

图三为RRP II 级杆组，B i iE F iE F y H H A lEF A lEF y y lEF x x --==+=+=111)/arcsin(sin cos ϕϕϕ对其求一阶导数为速度，求二阶导数为加速度。

lCE=620;lEF=300;H1=350;H=635;syms t;fai=(255*pi/30)*t;xB=lAB*cos(fai);yB=lAB*sin(fai);xC=0;yC=-350;A0=xB-xC;B0=yB-yC;S=sqrt(A0.^2+B0.^2);zj=atan(B0/A0);xE=xB+(lCE-S)*cos(zj);yE=yB+(lCE-S)*sin(zj);a=0:0.0001:20/255;Xe=subs(xE,t,a);Ye=subs(yE,t,a);A1=H-H1-yB;zi=asin(A1/lEF);xF=xE+lEF*cos(zi);vF=diff(xF,t);aF=diff(xF,t,2);m=0:0.001:120/255;xF=subs(xF,t,m);vF=subs(vF,t,m);aF=subs(aF,t,m);plot(m,xF)title('位移随时间变化图像') xlabel('t(s)'),ylabel(' x')lAB=108;lCE=620;lEF=300;H1=350;H=635;syms t;fai=(255*pi/30)*t;xB=lAB*cos(fai);yB=lAB*sin(fai);xC=0;yC=-350;B0=yB-yC;S=sqrt(A0.^2+B0.^2);zj=atan(B0/A0);xE=xB+(lCE-S)*cos(zj);yE=yB+(lCE-S)*sin(zj);a=0:0.0001:20/255;Xe=subs(xE,t,a);Ye=subs(yE,t,a);A1=H-H1-yB;zi=asin(A1/lEF);xF=xE+lEF*cos(zi);vF=diff(xF,t);aF=diff(xF,t,2);m=0:0.001:120/255;xF=subs(xF,t,m);vF=subs(vF,t,m);aF=subs(aF,t,m);plot(m,vF)title('速度随时间变化图像') xlabel('t(s)'),ylabel(' V')lAB=108;lCE=620;lEF=300;H1=350;H=635;syms t;fai=(255*pi/30)*t;xB=lAB*cos(fai);yB=lAB*sin(fai);xC=0;yC=-350;A0=xB-xC;B0=yB-yC;S=sqrt(A0.^2+B0.^2);zj=atan(B0/A0);xE=xB+(lCE-S)*cos(zj);yE=yB+(lCE-S)*sin(zj);a=0:0.0001:20/255;Xe=subs(xE,t,a);Ye=subs(yE,t,a);A1=H-H1-yB;zi=asin(A1/lEF);xF=xE+lEF*cos(zi);vF=diff(xF,t);aF=diff(xF,t,2);m=0:0.001:120/255;xF=subs(xF,t,m);vF=subs(vF,t,m);aF=subs(aF,t,m);plot(m,aF)title('加速度随时间变化图像) xlabel('t(s)'),ylabel('a')凸轮机构设计2.凸轮的推程运动方程，回程运动方程与远休止，近休止方程。

a. 推程运动方程)2/3cos(5.47)2/3sin(45))2/3cos(1(303/20211ϕωϕωϕπϕ==-=≤≤a v S b. 远休止运动方程0603/2====≤≤a v mmh S πϕπC. 回程运动方程/120)/23(602/31=-=-=≤≤a v S πωπϕπϕπd.近休止运动方程0022/3====≤≤a v h S πϕπ计算机编程结果推杆位移图像x1=0:0.001:2*pi/3;x2=2*pi/3:0.001:pi;x3=pi:0.001:3*pi/2;x4=3*pi/2:0.001:2*pi;s1=30*(1-cos(3*x1/2));s2=60;s3=60*(3-2*x3/pi);s4=0;hold onplot(x1,s1,'k');plot(x2,s2,'k');plot(x3,s3,'k');plot(x4,s4,'k');xlabel('\phi'),ylabel('s') title('s-\phi')推杆速度图像x1=0:0.001:2*pi/3;x2=2*pi/3:0.001:pi;x3=pi:0.001:3*pi/2;x4=3*pi/2:0.001:2*pi;v1=45*sin(3*x1/2);v2=0;v3=-1200/pi;v4=0;hold onplot(x1,v1,'k');plot(x2,v2,'k');plot(x3,v3,'k');plot(x4,v4,'k');xlabel('\phi'),ylabel('v')title('v-\phi')推杆加速度图像x1=0:0.001:2*pi/3;x2=2*pi/3:0.001:pi;x3=pi:0.001:3*pi/2;x4=3*pi/2:0.001:2*pi;a1=67.5*cos(3*x1/2);a2=0;a3=0;a4=0;hold onplot(x1,a1,'k');plot(x2,a2,'k');plot(x3,a3,'k');plot(x4,a4,'k');xlabel('\phi'),ylabel('a')title('a-\phi')凸轮机构的s d ds -ϕ线图，并依次确定凸轮的基圆半径和偏距 1.凸轮机构s d ds -ϕ图像 x1=0:0.001:2*pi/3;x2=2*pi/3:0.001:7*pi/6;x3=7*pi/6:0.001:5*pi/3;x4=5*pi/3:0.001:2*pi;s1=30*(1-cos(3*x1/2));s2=60;s3=60*(3-2*x3/pi); s4=0;v1=45*sin(3*x1/2);v2=0;v3=-120/pi;v4=0;plot(v1,s1,'k',v2,s2,'k',v3,s3,'k',v4,s4,'k') xlabel('ds/d\phi'),ylabel('s')xlim([-60,100]);ylim([-100,100])axis([-100,100,-100,100]) grid on2.确定凸轮的基圆半径和偏距 由图可知：可取mme mm S 20,800==所以基圆半径 mm r 5.822080220=+= 偏距mm e 20=。

3.滚子半径的确定及凸轮理论轮廓和实际轮廓绘制 h=60;w=1;e=20;rr=20;s0=80;q=120*pi/180;qs=(120+60)*pi/180;q1=(120+60+90)*pi/180; for i=1:1:120 qq(i)=i*pi/180.0;s1=h/2-h/2*cos(pi*qq(i)/q); v1=(pi*w*h/q/2)*sin(pi*qq(i)/q); x(i)=(s0+s1)*cos(qq(i))-e*sin(qq(i)); y(i)=(s0+s1)*sin(qq(i))+e*cos(qq(i));b(i)=(s0+s1)*cos(qq(i))-e*sin(qq(i))-v1*sin(qq(i)); a(i)=-(s0+s1)*sin(qq(i))-e*cos(qq(i))+v1*cos(qq(i)); xx(i)=x(i)-rr*b(i)/sqrt(a(i)*a(i)+b(i)*b(i)); yy(i)=y(i)+rr*a(i)/sqrt(a(i)*a(i)+b(i)*b(i)); endfor i=121:1:180qq(i)=i*pi/180;s2=h;v2=0;x(i)=(s0+s2)*cos(qq(i))-e*sin(qq(i));y(i)=(s0+s2)*sin(qq(i))+e*cos(qq(i));a(i)=-(s0+s2)*sin(qq(i))-e*cos(qq(i))+v2*cos(qq(i)); b(i)=(s0+s2)*cos(qq(i))-e*sin(qq(i))-v2*sin(qq(i)); xx(i)=x(i)-rr*b(i)/sqrt(a(i)*a(i)+b(i)*b(i));yy(i)=y(i)+rr*a(i)/sqrt(a(i)*a(i)+b(i)*b(i));endfor i=181:1:270qq(i)=i*pi/180;qq1(i)=qq(i)-(120*pi/180+60*pi/180);s3=h-h*qq1(i)/(90*pi/180);v3=-w*h/(90*pi/180);x(i)=(s0+s3)*cos(qq(i))-e*sin(qq(i));y(i)=(s0+s3)*sin(qq(i))+e*sin(qq(i));a(i)=-(s0+s3)*sin(qq(i))-e*cos(qq(i))+v3*cos(qq(i)); b(i)=(s0+s3)*cos(qq(i))-e*sin(qq(i))-v3*sin(qq(i)); xx(i)=x(i)-rr*b(i)/sqrt(a(i)*a(i)+b(i)*b(i));yy(i)=y(i)+rr*a(i)/sqrt(a(i)*a(i)+b(i)*b(i));endfor i=271:1:360qq(i)=i*pi/180;x(i)=(s0+0)*cos(qq(i))-e*sin(qq(i));y(i)=(s0+0)*sin(qq(i))+e*cos(qq(i));a(i)=-(s0+0)*sin(qq(i))-e*cos(qq(i));b(i)=(s0+0)*cos(qq(i))-e*sin(qq(i));xx(i)=x(i)-rr*b(i)/sqrt(a(i)*a(i)+b(i)*b(i));yy(i)=y(i)+rr*a(i)/sqrt(a(i)*a(i)+b(i)*b(i));endplot(x,y,'r',xx,yy,'g')text(50,20,'实际轮廓')text(65,40,'理论轮廓')齿轮传动设计序号电机转速 （min /r ）输出轴转速（min /r ） 带传动最大传动比滑移齿轮传动定轴齿传动最大传动比模数 圆柱齿轮 圆锥齿轮 一对齿轮最大传动比模数一对齿轮最大传动比模数5 745 12 17 23 5.2≤ 4≤24≤34≤32.传动比的分配计算根据传动系统的原始参数可知，传动系统的总传动比为391.32824.43083.62332211======n ni n ni n ni 带传动的最大传动比为m ax p i ，滑移齿轮传动的最大传动比为m ax v i ，定轴齿轮传动每对齿轮的最大传动比为m ax d i 。