H a r b i n I n s t i t u t e o f T e c h n o l o g y课程设计说明书课程名称：机械原理设计题目：凸轮机构院系：实验学院班级：0936105设计者：许士海学号：6090810532指导教师：林林设计时间：2011年5月3日至7日哈尔滨工业大学H a r b i n I n s t i t u t e o f T e c h n o l o g y课程设计说明书（论文）课程名称：机械原理设计题目：连杆机构运动分析院系：实验学院班级：0936005班设计者：许士海学号：6090810532指导教师：林琳设计时间：4月25日-4月30日哈尔滨工业大学1.设计题目第32题：升程/mm 升程运动角/。

升程运动规律升程许用压力角/。

回程运动角/。

回程运动规律回城许用压力角/。

远休止角/。

近休止角/。

150 120 余弦加速度35 90 正弦加速度65 55 952.运动方程式及运动线图本实验假设凸轮逆时针旋转。

（1）确定凸轮机构推杆升程、回程运动方程，并绘制推杆位移、速度、加速度线图。

（设定角速度为ω= 2π/3.）升程：（ 0 <φ< 2π/3）由公式：s=h/2[1-cosπφΦ0];v =πhω/(2Φ0)sin(πφΦ0);a = π2h ω2/(2Φ0) cos(πφΦ0).由此得：s = 75*(1 - cos(1.5*φ));v=0.225/2 * ω * sin(1.5 *φ);a = 0.675/4 *φ^2 .* cos(1.5*φ);回程：（ 35*π/36 <φ< 53*π/36）由公式 s = h[1 – T/Φ'0 + 1/2πsin(2πT/Φ'0)];v = - hω/Φ'0[1 –cos(2πT/Φ'0)];a = -2πhω2/Φ'02 sin(2πT/Φ'0) ; T = φ–(Φ0- Φs)得到s= 0.150*(53/18 - 2*φ/π + 1/(2*π)*sin (4*φ- 35* π/9));v = -0.300/π * ω* (1 - cos(4*φ- 35*π/9));a = -1.200 *φ^2/π*sin(4*φ- 35* π/9);由上述公式通过编程得到位移、速度、加速度曲线如下：（编程见附录）1. 凸轮机构的s d ds -ϕ线图及基圆半径和偏距的确定凸轮机构的s d ds -ϕ线图如下图所示（代码详见附录）：确定凸轮基圆半径与偏距：见下页：= 142mm，偏距e = 20mm。

基圆半径为r2.滚子半径的确定及凸轮理论廓线和实际廓线的绘制得到的理论轮廓曲线为：求其最小曲率半径rmin = 90.0051= 10mm。

这里取半径为 rr程序代码见附录3.凸轮轮廓绘制得到的外包络轮廓，得到图线为：得到的内包络线图为：这里取内包络线图。

此即为凸轮的工作轮廓曲线。

附录1.求位移、速度、加速度的程序（matlab）w = 2*pi/3x = 0:(pi/100):(2*pi/3);s1 = 75*(1 - cos(1.5*x));v1=0.225/2 * w * sin(1.5 * x);a1 = 0.675/4 * x.^2 .* cos(1.5*x);y = (2*pi/3):(pi/100):(35*pi/36);s2 = 150;v2=0;a2 = 0;z = (35*pi/36 ):(pi/100):(53*pi/36);s3 = 0.150*(53/18 - 2*z/pi + 1/(2*pi).*sin (4*z - 35* pi/9)); v3 = -0.300/pi * w .* (1 - cos(4*z - 35* pi/9));a3 = -1.200 * z.^2/pi .*sin(4*z - 35* pi/9);c = (53*pi/36):(pi/100):( 2*pi);s4 = 0;v4 = 0;a4 = 0;plot(x,s1,'b',y,s2,'b',z,s3,'b',c,s4,'b')plot(x,v1,'g',y,v2,'g',z,v3,'g ',c,v4,'g')plot(x,a1,'r',y,a2,'r',z,a3,'r ',c,a4,'r')xlabel('转角/rad')ylabel('位移/(m/s)')title('位移与转角曲线')2.绘制凸轮机构dφ/ds – s线图x = 0:(pi/100):(2*pi/3);s1 = 75*(1 - cos(1.5*x));news1 = 75*1.5*sin(1.5*x);y = (2*pi/3):(pi/100):(35*pi/36);s2 = 150;news2 = 0;z = (35*pi/36 ):(pi/100):(53*pi/36);s3 = 150*(53/18 - 2*z/pi + 1/(2*pi).*sin (4*z - 35* pi/9)); news3 = 150*(-2/pi + 2/pi *cos(4*z - 35*pi/9));c = (53*pi/36):(pi/100):( 2*pi);s4 = 0;news4 = 0;plot(news1,s1,'b',news2,s2,'b',news3,s3,'b',news4,s4,'b')xlabel('ds/dp');ylabel('(位移s/mm)')title('ds/dp 与位移s曲线')grid3.确定滚子半径（1）.先求凸轮理论轮廓曲线，程序如下：w = 2*pi/3;s0 = 140;s = 150;e = 20;x = 0:(pi/100):(2*pi/3);x1 = (s + s0)*cos(x)-e*sin(x);y1 = (s0 + s)*sin(x) - e*cos(x);y = (2*pi/3):(pi/100):(35*pi/36);x2 = (s + s0)*cos(y)-e*sin(y);y2 = (s0 + s)*sin(y) - e*cos(y);z = (35*pi/36 ):(pi/100):(53*pi/36);x3 = (s + s0)*cos(z)-e*sin(z);y3 = (s0 + s)*sin(z) - e*cos(z);c = (53*pi/36):(pi/100):( 2*pi);x4 = (s + s0)*cos(c)-e*sin(c);y4 = (s0 + s)*sin(c) - e*cos(c);plot(x1,y1,'b',x2,y2,'b',x3,y3,'b',x4,y4,'b');xlabel('x/mm')ylabel('y/mm')title('理轮轮曲线')（2）.求其最小曲率半径rmin，程序如下：v=[];syms x1 x2 x3 x4 x5s0 = 140;e = 20;s1 = 75*(1 - cos(1.5*x1));t1 = (s1 + s0)*cos(x1)-e*sin(x1);y1 = (s0 + s1)*sin(x1) - e*cos(x1);tx1=diff(t1,x1);txx1=diff(t1,x1,2);yx1=diff(y1,x1);yxx1=diff(y1,x1,2);for xx1= 0:(pi/100):(2*pi/3);k1=subs(abs((tx1*yxx1-txx1*yx1)/(tx1^2+yx1^2)^1.5),{x1},{xx1}); v=[v,1/k1];ends2 = 150;t2 = (s2 + s0)*cos(x2)-e*sin(x2);y2 = (s0 + s2)*sin(x2) - e*cos(x2);tx2=diff(t2,x2);txx2=diff(t2,x2,2);yx2=diff(y2,x2);yxx2=diff(y2,x2,2);for xx2=(2*pi/3):(pi/100):(35*pi/36);k2=subs(abs((tx2*yxx2-txx2*yx2)/(tx2^2+yx2^2)^1.5),{x2},{xx2}); v=[v,1/k2];ends3 = 150*(53/18- 2*x3/pi + 1/(2*pi).*sin (4*x3 - 35* pi/9));t3 = (s3 + s0)*cos(x3)-e*sin(x3);y3 = (s0 + s3)*sin(x3) - e*cos(x3);tx3=diff(t3,x3);txx3=diff(t3,x3,2);yx3=diff(y3,x3);yxx3=diff(y3,x3,2);for xx3=(35*pi/36 ):(pi/100):(53*pi/36);k3=subs(abs((tx3*yxx3-txx3*yx3)/(tx3^2+yx3^2)^1.5),{x3},{xx3}); v=[v,1/k3];ends4 = 0;t4 = (s4 + s0)*cos(x4)-e*sin(x4);y4 = (s0 + s4)*sin(x4) - e*cos(x4);tx4=diff(t4,x4);txx4=diff(t4,x4,2);yx4=diff(y4,x4);yxx4=diff(y4,x4,2);for xx4=(53*pi/36):(pi/100):( 2*pi);k4=subs(abs((tx4*yxx4-txx4*yx4)/(tx4^2+yx4^2)^1.5),{x4},{xx4}); v=[v,1/k4];endmin(v)4.绘制凸轮轮廓曲线编程如下：w = 2*pi/3;s0 = 140;e = 20;r = 10;x = 0:(pi/100):(2*pi/3);s1 = 75*(1 - cos(1.5*x));x1 = (s1 + s0).*cos(x) - e*sin(x);y1 = (s0 + s1).*sin(x) - e*cos(x);n1 = -(75*1.5*sin(x) + s0).*sin(x) -e*cos(x);m1 = (s0 + 75*1.5*sin(x) ).*cos(x) + e*sin(x);xt1 = x1+(r*m1)./(sqrt(n1.^2+m1.^2));yt1 = y1 - (r*n1)./sqrt(m1.^2 +n1.^2);xw1 = x1 - (r*m1)./sqrt(m1.^2 +n1.^2);yw1 = y1 + (r*n1)./sqrt(m1.^2 +n1.^2);y = (2*pi/3):(pi/100):(35*pi/36);s2 = 150;x2 = (s2 + s0).*cos(y)-e*sin(y);y2 = (s0 + s2).*sin(y) - e*cos(y);n2 = -s0.*sin(y)-e*cos(y);m2 = s0 .*cos(y) + e*sin(y);xt2 = x2 + (r*m2)./sqrt(m2.^2+n2.^2);yt2 = y2 - (r*n2)./sqrt(m2.^2+n2.^2);xw2 = x2 - (r*m2)./sqrt(m2.^2+n2.^2);yw2 = y2 + (r*n2)./sqrt(m2.^2+n2.^2);z = (35*pi/36 ):(pi/100):(53*pi/36);s3 = 150*(53/18 - 2*z/pi + 1/(2*pi).*sin (4*z - 35* pi/9)); x3 = (s3 + s0).*cos(z)-e*sin(z);y3 = (s0 + s3).*sin(z) - e*cos(z);n3 = -(300/pi *cos(4*z - 35*pi/9) + s0).*sin(z)-e*cos(z); m3 = (s0 + 300/pi *cos(4*z - 35*pi/9)).*cos(z) + e*sin(z); xt3= x3 + (r*m3)./sqrt(m3.^2+n3.^2);yt3 = y3 - (r*n3)./sqrt(m3.^2+n3.^2);xw3 = x3 -(r* m3)./sqrt(n3.^2+m3.^2);yw3 = y3 + (r*n3)./sqrt(n3.^2+m3.^2);c = (53*pi/36):(pi/100):( 2*pi);s4 = 0;x4 = (s4 + s0).*cos(c)-e*sin(c);y4 = s0 .*sin(c) - e*cos(c);n4 = - s0.*sin(c)-e*cos(c);m4 = s0 .*cos(c) + e*sin(c);xt4= x4 + (r*m4)./sqrt(m4.^2+n4.^2);yt4 = y4 - (r*n4)./sqrt(m4.^2+n4.^2);xw4 = x4 - (r*m4)./sqrt(n4.^2+m4.^2);yw4 = y4 + (r*n4)./sqrt(n4.^2+m4.^2);plot(xt1,yt1,'b',xt2,yt2,'b',xt3,yt3,'b',xt4,yt4,'b');xlabel('x/mm')ylabel('y/mm')title('凸轮工作曲线')grid此程序外包络轮廓。