大作业（二）凸轮机构设计（题号：4-A）（一）题目及原始数据···············（二）推杆运动规律及凸轮廓线方程·········（三）程序框图·········（四）计算程序·················（五）程序计算结果及分析·············（六）凸轮机构图·················（七）心得体会··················（八）参考书···················一题目及原始数据试用计算机辅助设计完成偏置直动滚子推杆盘形凸轮机构的设计（1）推程运动规律为五次多项式运动规律，回程运动规律为余弦加速度运动规律；（2）打印出原始数据；（3）打印出理论轮廓和实际轮廓的坐标值；（4）打印出推程和回程的最大压力角，以及出现最大压力角时凸轮的相应转角；（5）打印出凸轮实际轮廓曲线的最小曲率半径，以及相应的凸轮转角；（6）打印最后所确定的凸轮的基圆半径。

表一偏置直动滚子推杆盘形凸轮机构的已知参数题号初选的基圆半径R0/mm 偏距E/mm滚子半径Rr/mm推杆行程h/mm许用压力角许用最小曲率半径[ρamin][α1] [α2]4-A 15 5 10 28 30°70˚0.3Rr计算点数：N=90q1=60; 近休止角δ1q2=180; 推程运动角δ2q3=90; 远休止角δ3q4=90; 回程运动角δ4二推杆运动规律及凸轮廓线方程推杆运动规律：（1）近休阶段：0o≤δ<60 os=0；ds/dδ=0;2/δd2d=0;s（2）推程阶段：60o≤δ<180 o五次多项式运动规律：Q1=Q-60;s=10*h*Q1*Q1*Q1/(q2*q2*q2)-15*h*Q1*Q1*Q1*Q1/(q2*q2*q2*q2)+6*h*Q1*Q1*Q 1*Q1*Q1/(q2*q2*q2*q2*q2);ds/dδ=30*h*Q1*Q1*QQ/(q2*q2*q2)-60*h*Q1*Q1*Q1*QQ/(q2*q2*q2*q2)+30*h*Q1*Q1*Q 1*Q1*QQ/(q2*q2*q2*q2*q2);2/δd2d=60*h*Q1*QQ*QQ/(q2*q2*q2)-180*h*Q1*Q1*QQ*QQ/((q2*q2*q2*q2))+1 s20*h*Q1*Q1*Q1*QQ*QQ/((q2*q2*q2*q2*q2));（3）远休阶段：180o≤δ<270 os=h=24;ds/dδ=0;2/δd2d=0;s(4)回程阶段：270≤δ<360Q2=Q-270;s=h*(1+cos(2*Q2/QQ))/2;ds/dδ=-h*sin(2*Q2/QQ);2/δd2d=-2*h*cos(2*Q2/QQ);s凸轮廓线方程：（1）理论廓线方程：s0=sqrt(r02-e2)x=(s0+s)sinδ+ecosδy=(s0+s)cosδ-esinδ(2)实际廓线方程先求x，y的一、二阶导数dx=(ds/dδ-e)*sin(δ)+(s0+s)*cos(δ);dy=(ds/dδ-e)*cos(δ)-(s0+s)*sin(δ);dxx=dss*sin(δ)+(ds/dδ-e)*cos(δ)+ds/dδ*cos(δ)-(s0+s)*sin(δ); dyy=dss*cos(δ)-(ds/dδ-e)*sin(δ)-ds/dδ*sin(δ)-(s0+s)*cos(δ); x1=x-rr*coso;y1=y-rr*sino;再求sinθ，cosθsinθ＝x’/sqrt((x’)2+(y’)2)cosθ＝-y’/sqrt((x’)2+(y’)2)最后求实际廓线方程x1=x-rr*cosθ;y1=y-rr*sinθ;三程序框图四 计算程序1. #include<stdio.h>#include<math.h> |α|>[α1]开始 读入：r 0，Δr 0，r t ，h 或（φ），e 或（l AB 、l OA ） δ，δ，δ，δ，[α]，[α]， [ρ]，N 计算：s 0 I =1 计算：s ，x ，y ，ds/dδ，dx/dδ，dy/dδ，x′，计算：α r 0=r 0= 是回程？ |α|>[α2]？ 选出α1max 及相应的凸轮转选出α2max 及相应的凸轮转计算：ρ ρ<0? |ρ|-r t ≥[ρamin ]计算ρa 选出|ρamin |及相应的凸轮转角I =I +1 I ≤N ？打印：x ，y ，x′，y′，ρamin ，δamin ，α1max ，δ1max ，α2max ，δ2max ， r 0，δ， svoid main(){doubler0,or,rr,h,e,q1,q2,q3,q4,a,a11,a22,Q,pi,pa,paa,QQ,A1,A2,B1,B2,C1,C2; /*定义变量*/double xz[90],yz[90],sz[90],x1z[90],y1z[90],Q1,Q2;double s0,s,x,y,y1,x1,dx,dxx,dy,dyy,ds,dss,sino,coso,p;int N,i,j;r0=19;e=5;h=28;rr=10;q1=60;q2=120;q3=90;q4=90;a11=30;a22=70;or=1;pi=3.141592653;pa=3; /*给已知量赋值*/N=90;A1=0;B1=0;C1=1000;for(; ;){Q=0;C1=1000;QQ=180/pi;r0=r0+or;s0=sqrt(r0*r0-e*e);for(i=1,j=0;i<=N;i++,j++){if(Q<60){ /*近休阶段*/s=0;ds=0;dss=0;a=atan(e/sqrt(r0*r0-e*e)); /*求压力角*/if(a>a11/QQ){break;}else{if(a>A1)A1=a;A2=Q;}}else if(Q>=60&&Q<180){ /*五次多项式运动*/Q1=Q-60;s=10*h*Q1*Q1*Q1/(q2*q2*q2)-15*h*Q1*Q1*Q1*Q1/(q2*q2*q2*q2)+6*h*Q1*Q1*Q 1*Q1*Q1/(q2*q2*q2*q2*q2);ds=30*h*Q1*Q1*QQ/(q2*q2*q2)-60*h*Q1*Q1*Q1*QQ/(q2*q2*q2*q2)+30*h*Q1*Q1 *Q1*Q1*QQ/(q2*q2*q2*q2*q2);dss=60*h*Q1*QQ*QQ/(q2*q2*q2)-180*h*Q1*Q1*QQ*QQ/((q2*q2*q2*q2))+120*h* Q1*Q1*Q1*QQ*QQ/((q2*q2*q2*q2*q2));a=atan(fabs(ds-e)/(sqrt(r0*r0-e*e)+s));if(a>a11/QQ){break;}else{ /*远休阶段*/if(a>A1)A1=a;A2=Q;}}else if(Q>=180&&Q<270){s=28;ds=0;dss=0;a=atan(fabs(ds-e)/(sqrt(r0*r0-e*e)+s));if(a>a22/QQ){break;}else{if(a>B1)B1=a;B2=Q;}}else if(Q>=270&&Q<360){ /*余弦加速度运动*/Q2=Q-270;s=h*(1+cos(2*Q2/QQ))/2;ds=-h*sin(2*Q2/QQ);dss=-2*h*cos(2*Q2/QQ);a=atan(fabs(ds-e)/(sqrt(r0*r0-e*e)+s));if(a>a22/QQ){break;}else{if(a>B1)B1=a;B2=Q;}}dx=(ds-e)*sin(Q/QQ)+(s0+s)*cos(Q/QQ);dy=(ds-e)*cos(Q/QQ)-(s0+s)*sin(Q/QQ);dxx=dss*sin(Q/QQ)+(ds-e)*cos(Q/QQ)+ds*cos(Q/QQ)-(s0+s)*sin(Q/QQ); dyy=dss*cos(Q/QQ)-(ds-e)*sin(Q/QQ)-ds*sin(Q/QQ)-(s0+s)*cos(Q/QQ);sino=dx/(sqrt(dx*dx+dy*dy));coso=-dy/(sqrt(dx*dx+dy*dy));x=(s0+s)*sin(Q/QQ)+e*cos(Q/QQ);y=(s0+s)*cos(Q/QQ)-e*sin(Q/QQ);x1=x-rr*coso;y1=y-rr*sino;sz[j]=s;yz[j]=y;xz[j]=x;x1z[j]=x1;y1z[j]=y1;p=pow(dx*dx+dy*dy,1.5)/(dx*dyy-dy*dxx); /*求理论轮廓曲率半径*/if(p<0){paa=(fabs(p)-rr);if(paa<pa){break;}else{if(paa<C1)C1=paa;C2=Q;}}Q=Q+4;}if(i==91){break;}}for(j=0;j<90;j++){printf("第%d组数据 ",j+1); /*输出数据*/ printf("s=%f ",sz[j]);printf("x=%f,y=%f;",xz[j],yz[j]);printf("x1=%f,y1=%f\n",x1z[j],y1z[j]);}printf("r0=%f\n",r0);printf("推程最大压力角(弧度)=%f,相应凸轮转角=%f\n",A1,A2-4);printf("回程最大压力角(弧度)=%f,相应凸轮转角=%f\n",B1,B2-4);printf("最小曲率半径=%f,相应凸轮转角=%f\n",C1,C2-4);}2.matalab绘图x=[5.000000 6.625241 8.218205 9.771130 11.276451 12.726835 14.115215 15.434827 16.679242 17.842397 18.918626 19.902685 20.789781 21.575590 22.256286 22.828551 23.298459 23.706615 24.097554 24.507799 24.963745 25.480318 26.060379 26.694836 27.363383 28.035800 28.673715 29.232729 29.664801 29.920768 29.952907 29.717406 29.176650 28.301221 27.071507 25.478865 23.526246 21.228245 18.610551 15.708757 12.566564 9.233376 5.761349 2.201948 -1.397906 -5.000000 -8.578422 -12.115052 -15.592657 -18.994297 -22.303399 -25.503841 -28.580030 -31.516981 -34.300384-36.916679 -39.353120 -41.597836 -43.639892 -45.469338 -47.077263-48.455831 -49.598328 -50.499187 -51.154019 -51.559634 -51.714055-51.616530 -51.233453 -50.364513 -48.991675 -47.144744 -44.866118-42.209132 -39.235944 -36.015085 -32.618764 -29.120045 -25.590019-22.095099 -18.694544 -15.438322 -12.365412 -9.502600 -6.863834-4.450154 -2.250205 -0.241303 1.608997 3.340895 5.000000];y=[23.473389 23.067427 22.549082 21.920881 21.185883 20.347670 19.410325 18.378415 17.256967 16.051445 14.767721 13.412051 11.991039 10.511608 8.980965 7.406568 5.800408 4.185421 2.572459 0.957412 -0.675351-2.349452 -4.092999 -5.935252 -7.903549 -10.020601 -12.302228 -14.755601 -17.378031 -20.156343 -23.066822 -26.075733 -29.140389 -32.210697-35.231149 -38.143149 -40.887607 -43.407693 -45.651627 -47.575413-49.145373 -50.340385 -51.153688 -51.594160 -51.686950 -51.473389-50.999220 -50.276588 -49.309014 -48.101211 -46.659063 -44.989598-43.100947 -41.002313 -38.703920 -36.216966 -33.553566 -30.726696-27.750129 -24.638366 -21.406568 -18.070478 -14.646352 -11.150869-7.601061 -4.014222 -0.407825 3.200559 6.792159 10.321065 13.715687 16.907573 19.835197 22.446270 24.699658 26.566822 28.032724 29.096164 29.769520 30.077928 30.057908 29.755535 29.224195 28.522064 27.709391 26.845720 25.987174 25.183912 24.477872 23.900907 23.473389];x1=[2.916667 3.864724 4.793953 5.699826 6.577930 7.423987 8.233875 9.003649 9.729558 10.408065 11.035865 11.609900 12.127372 12.585761 12.982834 13.316655 13.637197 13.989954 14.385216 14.841722 15.369724 15.961917 16.595549 17.241474 17.871626 18.461055 18.986391 19.423879 19.748587 19.934923 19.958013 19.795395 19.428612 18.844393 18.035244 16.999369 15.739987 14.264216 12.581802 10.703984 8.642680 6.409975 4.017612 1.476005 -1.207747 -4.033175 -6.919656 -9.772424 -12.577583 -15.321465 -17.990702 -20.572290 -23.053652 -25.422699 -27.667890-29.778285 -31.743603 -33.554270 -35.201463 -36.677159 -37.974167-39.086169 -40.007747 -40.734411 -41.262621 -41.589804 -41.714366-41.635699 -41.376364 -40.850805 -40.008452 -38.855049 -37.403903-35.676949 -33.704972 -31.526827 -29.187728 -26.736824 -24.224319-21.698402 -19.202199 -16.770908 -14.429195 -12.188866 -10.046784-7.982989 -5.959305 -3.919615 -1.795463 0.475989 2.916667];y1=[13.692810 13.455999 13.153631 12.787181 12.358432 11.86947411.322689 10.720742 10.066564 9.363343 8.614504 7.823697 6.9947736.131771 5.238896 4.320498 3.219708 1.821843 0.191177 -1.605194-3.495769 -5.415401 -7.320538 -9.196225 -11.051016 -12.905780 -14.783306 -16.701480 -18.669812 -20.688233 -22.747295 -24.829259 -26.909752-28.959788 -30.947932 -32.842380 -34.612723 -36.231183 -37.673270-38.917916 -39.947376 -40.747241 -41.306893 -41.620545 -41.688758-41.520236 -41.137755 -40.554855 -39.774375 -38.800119 -37.636833-36.290183 -34.766732 -33.073900 -31.219936 -29.213872 -27.065480-24.785228 -22.384225 -19.874168 -17.267286 -14.576280 -11.814260-8.994681 -6.131282 -3.238012 -0.328966 2.581683 5.107582 7.2405829.322318 11.314634 13.178220 14.874574 16.368490 17.630629 18.63974919.384302 19.863216 20.085799 20.070803 19.844722 19.439472 18.88962018.229473 17.490557 16.700486 15.884986 15.075231 14.320076 13.692810];plot(x1,y1,x,y,'r')：五程序计算结果及分析基圆半径r0=24.000000推程最大压力角(弧度)=0.513512,相应凸轮转角=172.000000回程最大压力角(弧度)=0.766377,相应凸轮转角=352.000000最小曲率半径=14.000000,相应凸轮转角=340.000000序号δS X Y X1 Y11 0 0.000000 5.00000023.473389 2.91666713.6928102 40.000000 6.62524123.067427 3.86472413.4559993 80.0000008.21820522.549082 4.79395313.1536314 120.0000009.77113021.920881 5.69982612.7871815 160.00000011.27645121.185883 6.57793012.3584326 200.00000012.72683520.3476707.42398711.8694747 240.00000014.11521519.4103258.23387511.3226898 280.00000015.43482718.3784159.00364910.7207429 320.00000016.67924217.2569679.72955810.06656410 360.00000017.84239716.05144510.4080659.36334311 40 0.00000018.91862614.76772111.0358658.61450412 440.00000019.90268513.41205111.6099007.82369713 480.00000020.78978111.99103912.127372 6.99477314 520.00000021.57559010.51160812.585761 6.13177115 560.00000022.2562868.98096512.982834 5.23889616 600.00000022.8285517.40656813.316655 4.32049817 640.00985923.298459 5.80040813.637197 3.21970818 680.074888 23.706615 4.18542113.989954 1.82184319 720.239680 24.097554 2.57245914.3852160.19117720 760.53804224.5077990.95741214.841722-1.60519421 800.99382724.963745-0.67535115.369724-3.49576922 84 1.62176025.480318-2.34945215.961917-5.41540123 88 2.428271 26.060379-4.09299916.595549-7.32053824 92 3.412322 26.694836-5.93525217.241474-9.19622525 96 4.566240 27.363383-7.90354917.871626-11.05101626 100 5.87654328.035800-10.02060118.461055-12.90578027 1047.32477228.673715-12.30222818.986391-14.78330628 1088.88832029.232729-14.75560119.423879-16.70148029 11210.54126029.664801-17.37803119.748587-18.66981230 11612.25517829.920768-20.15634319.934923-20.68863331 12014.00000029.952907-23.06682219.958013-22.74729532 12415.744822 29.717406-26.07573319.795395-24.82925933 12817.45874029.176650-29.14038919.428612-26.90975234 13219.11168028.301221-32.21069718.844393-28.95978835 13620.67522827.071507-35.231149 18.035244-30.94793236 14022.12345725.478865-38.143149 16.999369-32.84238037 14423.43376023.526246-40.88760715.739987-34.61272338 148 24.58767821.228245-43.40769314.264216-36.23118339 152 25.57172918.610551-45.65162712.581802-37.67327040 156 26.378240 15.708757-47.57541310.703984-38.91791641 160 27.00617312.566564-49.1453738.642680-39.94737642 164 27.4619589.233376-50.340385 6.409975-40.74724143 168 27.760320 5.761349-51.153688 4.017612-41.30689344 172 27.925112 2.201948-51.594160 1.476005-41.62054545 176 27.990141-1.397906-51.686950-1.207747-41.68875846 180 28.000000-5.000000-51.473389-4.033175-41.52023647 184 28.000000-8.578422-50.999220-6.919656-41.13775548 188 28.000000-12.115052-50.276588-9.772424-40.55485549 192 28.000000-15.592657-49.309014-12.577583-39.77437550 196 28.000000-18.994297-48.101211-15.321465-38.80011951 200 28.000000-22.303399-46.659063-17.990702-37.63683352 204 28.000000-25.503841-44.989598-20.572290-36.29018353 208 28.000000-28.580030-43.100947 -23.053652-34.76673254 212 28.000000-31.516981-41.002313-25.422699-33.07390055 216 28.000000-34.300384-38.703920-27.667890-31.21993656 220 28.000000-36.916679-36.216966-29.778285-29.21387257 224 28.000000-39.353120-33.553566-31.743603-27.06548058 228 28.000000-41.597836-30.726696 -33.554270-24.78522859 232 28.000000-43.639892-27.750129-35.201463-22.38422560 236 28.000000-45.469338-24.638366-36.677159-19.87416861 240 28.000000-47.077263-21.406568-37.974167-17.26728662 244 28.000000-48.455831-18.070478-39.086169-14.57628063 248 28.000000-49.598328-14.646352-40.007747-11.81426064 252 28.000000-50.499187-11.150869-40.734411-8.99468165 256 28.000000-51.154019-7.601061-41.262621-6.13128266 260 28.000000-51.559634-4.014222-41.589804 -3.23801267 264 28.000000-51.714055-0.407825-41.714366-0.32896668 268 28.000000-51.616530 3.200559-41.635699 2.58168369 272 27.965897-51.233453 6.792159-41.376364 5.10758270 276 27.694066-50.36451310.321065-40.8508057.24058271 280 27.155697-48.991675 13.715687-40.0084529.32231872 284 26.361266-47.14474416.907573-38.85504911.31463473 288 25.326238-44.86611819.835197-37.40390313.17822074 292 24.070757-42.20913222.446270-35.67694914.87457475 296 22.619261 -39.23594424.699658-33.70497216.36849076 300 21.000000-36.01508526.566822-31.52682717.63062977 304 19.244492-32.61876428.032724-29.18772818.63974978 308 17.386907-29.12004529.096164-26.73682419.38430279 312 15.463398-25.59001929.769520-24.22431919.86321680 316 13.511407-22.09509930.077928-21.698402 20.08579981 320 11.568926-18.69454430.057908-19.20219920.07080382 324 9.673762-15.43832229.755535-16.770908 19.84472283 328 7.862804-12.36541229.224195-14.42919519.43947284 332 6.171299-9.50260028.522064-12.18886618.8896285 336 4.632172-6.86383427.709391-10.04678418.2294786 340 3.275378-4.45015426.845720-7.98298917.49055787 344 2.127327-2.25020525.987174-5.95930516.70048688 348 1.210364 -0.24130325.183912-3.91961515.88498689 352 0.542336 1.60899724.477872-1.79546315.07523190 356 0.136247 3.34089523.9009070.47598914.320076运行结果截图：六凸轮机构图（廓线）七心得体会通过对凸轮机构的编程设计：（1）熟悉了推杆的运动规律特别是余弦加速度运动规律和五次多项式运动规律；（2）掌握了已知推杆运动规律用解析法对凸轮轮廓曲线的进行设计的方法以及设计时应该注意的各个性能要求；（3）加深了C语言的熟悉与应用。