附2：习题4-3解答（1）凸轮的理论廓线方程：000()sin cos ()cos sin x s s e y s s e s ϕϕϕϕ=++⎧⎨=+-⎩=式中 （2）从动件在不同阶段的位移方程：2sin()[0,120]230[120,150][150,300]'0[300,360]h h s h h πϕϕϕφπφϕϕϕφϕ⎧-∈︒︒⎪⎪∈︒︒⎪=⎨⎪-∈︒︒⎪⎪∈︒︒⎩推程阶段远休止阶段回程阶段近休止阶段（3）求解凸轮的实际廓线：a r a r 00x =x-r cos y =y-r sin sin cos ()cos sin sin ()sin cos cos dx dy dxds s s e d d dy ds s s e d d θθθθϕϕϕϕϕϕϕϕϕϕ⎧⎨⎩⎧⎪=⎪⎪⎪⎪⎪⎨⎪-⎪=⎪⎪⎪⎪⎩⎧=++-⎪⎪⎨⎪=++-⎪⎩式中而同样，由于位移s 与从动件所处的运动阶段有关，所以有：2cos()[0,120]0[120,150]s [150,300]'0[300,360]h hd hd πϕϕφφφϕϕϕφϕ⎧-∈︒︒⎪⎪∈︒︒⎪=⎨⎪∈︒︒⎪⎪∈︒︒⎩推程阶段远休止阶段回程阶段近休止阶段（4）代入已知条件，并用Matlab 语言编程求解，编程代码如下： disp ' ******** 偏置直动滚子从动件盘形凸轮设计 ********' disp '已知条件:'disp ' 凸轮作逆时针方向转动,从动件偏置在凸轮轴心的右边'disp ' 从动件在推程作摆线运动规律运动,在回程作等速运动规律运动' ro = 50;rr = 10;e = 12;h = 30;ft = 120;fs = 30;fh = 150;fprintf (1,' 基圆半径 ro = %3.4f mm \n',ro) fprintf (1,' 滚子半径 rr = %3.4f mm \n',rr) fprintf (1,' 推杆偏距 e = %3.4f mm \n',e) fprintf (1,' 推程行程 h = %3.4f mm \n',h) fprintf (1,' 推程运动角 ft = %3.4f 度 \n',ft) fprintf (1,' 远休止角 fs = %3.4f 度 \n',fs) fprintf (1,' 回程运动角 fh = %3.4f 度 \n',fh) hd = pi / 180;du = 180 / pi; so = sqrt( ro^2 - e^2 ); d1 = ft + fs;d2 = ft + fs + fh; disp ' 'disp '计算过程和输出结果:'disp ' 1-1 推程(摆线运动规律运动)' s = zeros(ft);ds = zeros(ft);d2s = zeros(ft); for f = 1 : fts(f) = h * f / ft - h * sin(2 * pi * f / ft) / (2 * pi);s = s(f);ds(f) = h / (ft * hd) - h / (ft * hd) * cos(2 * pi * f / ft);ds = ds(f); d2s(f) = 2 * pi * h / (ft * hd) ^ 2 * sin(2 * pi * f / ft);d2s = d2s(f); enddisp ' 1-2 回程(等速运动规律运动)' s = zeros(fh);ds = zeros(fh);d2s = zeros(fh); for f = d1 : d2s(f) = h - h * (f-150) / fh; s = s(f); ds(f) = - h / (fh * hd);ds = ds(f); d2s(f) = 0;d2s = d2s(f); enddisp ' 2- 计算凸轮理论廓线与实际廓线的直角坐标'n = 360;s = zeros(n);ds = zeros(n);r = zeros(n);rp = zeros(n);x = zeros(n);y = zeros(n);dx = zeros(n);dy = zeros(n);xx = zeros(n);yy = zeros(n);xa = zeros(n);ya = zeros(n);xxa = zeros(n);yya = zeros(n);for f = 1 : nif f <= fts(f) = h * f / ft - h * sin(2 * pi * f / ft) / (2 * pi);s = s(f);ds(f) = h /(ft * hd) - h / (ft * hd) * cos(2 * pi * f / ft); ds = ds(f);elseif f > ft & f <= d1s = h;ds = 0;elseif f > d1 & f <= d2s(f) = h - h * (f-150) / fh; s = s(f);ds(f) = - h / (fh * hd);ds = ds(f);elseif f > d2 & f <= ns = 0;ds = 0;endxx(f) = (so + s) * sin(f * hd) + e * cos(f * hd); x = xx(f);yy(f) = (so + s) * cos(f * hd) - e * sin(f * hd); y = yy(f);dx(f) = (ds - e) * sin(f * hd) + (so + s) * cos(f * hd); dx = dx(f);dy(f) = (ds - e) * cos(f * hd) - (so + s) * sin(f * hd); dy = dy(f);xxa(f) = x + rr * dy / sqrt(dx ^ 2 + dy ^ 2);xa = xxa(f);yya(f) = y - rr * dx / sqrt(dx ^ 2 + dy ^ 2);ya = yya(f);r(f) = sqrt (x ^2 + y ^2 );rp(f) = sqrt (xa ^2 + ya ^2 );enddisp ' 2-1 推程(摆线运动规律运动)'disp ' 凸轮转角理论x 理论y 实际x 实际y' for f = 10 : 10 :ftnu = [f xx(f) yy(f) xxa(f) yya(f)];disp(nu)enddisp ' 2-2 回程(等速运动规律运动)'disp ' 凸轮转角理论x 理论y 实际x 实际y' for f = d1 : 10 : d2nu = [f xx(f) yy(f) xxa(f) yya(f)];disp(nu)enddisp ' 2-3 凸轮轮廓向径'disp ' 凸轮转角理论r 实际r'for f = 10 : 10 : nnu = [f r(f) rp(f)];disp(nu)enddisp '绘制凸轮的理论轮廓和实际轮廓:'plot(xx,yy,'r-.') % 理论轮廓(红色,点划线)axis ([-(ro+h-10) (ro+h+10) -(ro+h+10) (ro+rr+10)]) % 横轴和纵轴的下限和上限axis equal % 横轴和纵轴的尺度比例相同text(ro+h+3,0,'X') % 标注横轴text(0,ro+rr+3,'Y') % 标注纵轴text(-5,5,'O') % 标注直角坐标系原点title('偏置直动滚子从动件盘形凸轮设计') % 标注图形标题hold on; % 保持图形plot([-(ro+h) (ro+h)],[0 0],'k') % 横轴(黑色)plot([0 0],[-(ro+h) (ro+rr)],'k') % 纵轴(黑色)plot([e e],[0 (ro+rr)],'k--') % 初始偏置位置(黑色,虚线) ct = linspace(0,2*pi); % 画圆的极角变化范围plot(ro*cos(ct),ro*sin(ct),'g') % 基圆(绿色)plot(e*cos(ct),e*sin(ct),'c--') % 偏距圆(蓝绿色,虚线)plot(e + rr*cos(ct),so + rr*sin(ct),'y') % 滚子圆(黄色)plot(xxa,yya,'b') % 实际轮廓(蓝色)（5）求解凸轮理论廓线和实际廓线坐标值如下：******** 偏置直动滚子从动件盘形凸轮设计********已知条件:凸轮作逆时针方向转动,从动件偏置在凸轮轴心的右边从动件在推程作摆线运动规律运动,在回程作等速运动规律运动基圆半径ro = 50.0000 mm滚子半径rr = 10.0000 mm推杆偏距 e = 12.0000 mm推程行程h = 30.0000 mm推程运动角ft = 120.0000 度远休止角fs = 30.0000 度回程运动角fh = 150.0000 度计算过程和输出结果:1-1 推程(摆线运动规律运动)1-2 回程(等速运动规律运动)计算凸轮理论廓线与实际廓线的直角坐标2-1 推程(摆线运动规律运动)凸轮转角理论x 理论y 实际x 实际y10.0000 20.2659 45.8284 16.5674 36.537520.0000 28.1734 42.3200 23.8536 33.301230.0000 36.0243 38.3959 31.4216 29.518140.0000 44.1625 33.9622 39.1460 25.311550.0000 52.6430 28.5078 46.7788 20.407760.0000 61.0261 21.3770 53.9159 14.345370.0000 68.4036 12.1267 59.9368 6.8057 80.0000 73.6533 0.8019 64.1128 -2.1946 90.0000 75.8133 -12.0000 65.8180 -12.3064 100.0000 74.4098 -25.3056 64.6887 -22.9602 110.0000 69.5921 -38.0996 60.7079 -33.5092 120.0000 62.0165 -49.6616 54.2107 -43.41102-2 回程(等速运动规律运动)凸轮转角理论x 理论y 实际x 实际y 150.0000 28.8770 -74.0165 25.2424 -64.7004 160.0000 14.9014 -76.0270 14.3851 -66.0404 170.0000 1.1258 -75.4900 2.4259 -65.5749 180.0000 -12.0000 -72.5386 -8.9229 -63.0238 190.0000 -24.0666 -67.3832 -19.3110 -58.5864 200.0000 -34.7179 -60.3010 -28.4390 -52.5180 210.0000 -43.6616 -51.6242 -36.0665 -45.1192 220.0000 -50.6772 -41.7260 -42.0190 -36.7223 230.0000 -55.6208 -31.0065 -46.1908 -27.6786 240.0000 -58.4280 -19.8770 -48.5462 -18.3440 250.0000 -59.1126 -8.7451 -49.1177 -9.0659 260.0000 -57.7635 1.9999 -48.0018 -0.1704 270.0000 -54.5386 12.0000 -45.3524 8.0487 280.0000 -49.6567 20.9409 -41.3723 15.3401 290.0000 -43.3865 28.5615 -36.3031 21.5028 300.0000 -36.0357 34.6616 -30.4141 26.39132-3 凸轮轮廓向径凸轮转角理论r 实际r10.0000 50.1094 40.118220.0000 50.8402 40.962930.0000 52.6498 43.111940.0000 55.7114 46.616350.0000 59.8663 51.036660.0000 64.6619 55.791770.0000 69.4702 60.322080.0000 73.6577 64.150490.0000 76.7571 66.9586100.0000 78.5951 68.6426110.0000 79.3387 69.3420120.0000 79.4501 69.4501130.0000 79.4501 69.4501140.0000 79.4501 69.4501150.0000 79.4501 69.4501160.0000 77.4736 67.5889170.0000 75.4984 65.6197180.0000 73.5245 63.6524190.0000 71.5521 61.6869200.0000 69.5812 59.7237210.0000 67.6121 57.7628220.0000 65.6448 55.8044230.0000 63.6795 53.8489240.0000 61.7165 51.8964250.0000 59.7559 49.9474260.0000 57.7981 48.0021270.0000 55.8432 46.0611280.0000 53.8916 44.1247290.0000 51.9438 42.1935300.0000 50.0000 40.2681310.0000 50.0000 40.0000320 50 40330.0000 50.0000 40.0000340 50 40350.0000 50.0000 40.0000360.0000 50.0000 40.0000（6）由Matlab绘制的实际图轮廓线和理论图轮廓线如下：图例：绿色——基圆；红色点划线——理论廓线；蓝色——实际廓线；黄色——滚子圆；蓝绿色，虚线——偏距圆；黑色，虚线——初始偏置位置；。