凸轮大作业选题：凸轮5-C一：题目及原始数据：利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，已知数据如下所示，凸轮沿逆时针方向做匀速运动。

具体要求如下：1.推程运动规律为等加速等减速运动，回程运动规律为五次多项式运动；2.近休凸轮转角为0°-30°；推程凸轮转角30°-210°；远休凸轮转角210°-280°；回程凸轮转角280°-360。

°3.初选基圆半径为22mm；4.偏距为+14mm5.滚子半径为18mm6.推杆行程为35mm7.许用压力角为α1=35°，α2=65°。

8.最小曲率半径为0.35r r9.计算点数取120.二：推杆运动规律及凸轮轮廓线方程1.推程加速阶段：s1=70.*a1.*a1/pi/pi;x1=(s0+s1).*sin(a1)+e*cos(a1);y1=(s0+s1).*cos(a1)-e*sin(a1);k1=140*a1/pi^2;i1=[(k1-e).*sin(a1)+(s0+s1).*cos(a1)].*[(k1-e).*(k1-e)+(s0+ s1).*(s0+s1)].^(-1/2);j1=[-(k1-e).*cos(a1)+(s0+s1).*sin(a1)].*[(k1-e).*(k1-e)+(s0 +s1).*(s0+s1)].^(-1/2);x10=x1-18*j1;y10=y1-18*i1;2.推程减速阶段：s11=35-70.*(pi-a11).*(pi-a11)/pi/pi;x11=(s0+s11).*sin(a11)+e*cos(a11);y11=(s0+s11).*cos(a11)-e*sin(a11);k11=140.*(pi-a1)/pi^2;i11=[(k11-e).*sin(a11)+(s0+s11).*cos(a11)].*[(k11-e).*(k11-e)+(s0+s11).*(s0+s11)].^(-1/2);j11=[-(k11-e).*cos(a11)+(s0+s11).*sin(a11)].*[(k11-e).*(k11 -e)+(s0+s11).*(s0+s11)].^(-1/2);x101=x11-18*j11;y101=y11-18*i11;3.远休阶段：x2=(s0+s2).*sin(a2)+e*cos(a2);y2=(s0+s2).*cos(a2)-e*sin(a2);k2=0;i2=[(k2-e).*sin(a2)+(s0+s2).*cos(a2)].*[(k2-e).*(k2-e)+(s0+ s2).*(s0+s2)].^(-1/2);j2=[-(k2-e).*cos(a2)+(s0+s2).*sin(a2)].*[(k2-e).*(k2-e)+(s0 +s2).*(s0+s2)].^(-1/2);x20=x2-18*j2;y20=y2-18*i2;4.回程阶段：a30=33*pi/18-a3;s3=(350.*a30.*a30.*a30/(4*pi/9)^3-525.*a30.*a30.*a30.*a30/( 4*pi/9)^4+210.*a30.*a30.*a30.*a30.*a30/(4*pi/9)^5);x3=(s0+s3).*sin(a3)+e*cos(a3);y3=(s0+s3).*cos(a3)-e*sin(a3);k3=-1050.*a30.*a30/(4*pi/9)^3+2100.*a30.*a30.*a30/(4*pi/9)^ 4-1050.*a30.*a30.*a30.*a30/(4*pi/9)^5;i3=[(k3-e).*sin(a3)+(s0+s3).*cos(a3)].*[(k3-e).*(k3-e)+(s0+ s3).*(s0+s3)].^(-1/2);j3=[-(k3-e).*cos(a3)+(s0+s3).*sin(a3)].*[(k3-e).*(k3-e)+(s0 +s3).*(s0+s3)].^(-1/2);x30=x3-18*j3;y30=y3-18*i3;5.近休阶段：s4=0;x4=(s0+s4).*sin(a4)+e*cos(a4);y4=(s0+s4).*cos(a4)-e*sin(a4);k4=0;i4=[(k4-e).*sin(a4)+(s0+s4).*cos(a4)].*[(k4-e).*(k4-e)+(s0+ s4).*(s0+s4)].^(-1/2);j4=[-(k4-e).*cos(a4)+(s0+s4).*sin(a4)].*[(k4-e).*(k4-e)+(s0 +s4).*(s0+s4)].^(-1/2);x40=x4-18*j4;y40=y4-18*i4;三：matlab计算程序e=14;r0=22s0=sqrt(r0^2-e^2);c111=1;c3=1;for(i=1:0.1:200) %由压力角条件循环求合适基圆半径if (c111<35/180)&&(c3<65/180) %判断条件else a1=0:pi/60:pi/2; % 推程加速阶段 s1=70.*a1.*a1/pi/pi;x1=(s0+s1).*sin(a1)+e*cos(a1);y1=(s0+s1).*cos(a1)-e*sin(a1);k1=140*a1/pi^2; % 对s1求导i1=[(k1-e).*sin(a1)+(s0+s1).*cos(a1)].*[(k1-e).*(k1-e)+(s0+ s1).*(s0+s1)].^(-1/2);j1=[-(k1-e).*cos(a1)+(s0+s1).*sin(a1)].*[(k1-e).*(k1-e)+(s0 +s1).*(s0+s1)].^(-1/2);x10=x1-18*j1;y10=y1-18*i1;a11=pi/2:pi/60:pi; % 推程减速阶段s11=35-70.*(pi-a11).*(pi-a11)/pi/pi;x11=(s0+s11).*sin(a11)+e*cos(a11);y11=(s0+s11).*cos(a11)-e*sin(a11);k11=140.*(pi-a1)/pi^2;i11=[(k11-e).*sin(a11)+(s0+s11).*cos(a11)].*[(k11-e).*(k11-e)+(s0+s11).*(s0+s11)].^(-1/2);j11=[-(k11-e).*cos(a11)+(s0+s11).*sin(a11)].*[(k11-e).*(k11 -e)+(s0+s11).*(s0+s11)].^(-1/2);x101=x11-18*j11;y101=y11-18*i11;a2=pi:pi/60:25*pi/18; %凸轮远休阶段s2=35;%推杆行程x2=(s0+s2).*sin(a2)+e*cos(a2);y2=(s0+s2).*cos(a2)-e*sin(a2);k2=0;i2=[(k2-e).*sin(a2)+(s0+s2).*cos(a2)].*[(k2-e).*(k2-e)+(s0+ s2).*(s0+s2)].^(-1/2);j2=[-(k2-e).*cos(a2)+(s0+s2).*sin(a2)].*[(k2-e).*(k2-e)+(s0 +s2).*(s0+s2)].^(-1/2);x20=x2-18*j2;y20=y2-18*i2;a3=25*pi/18:pi/60:33*pi/18;%推杆回程阶段a30=33*pi/18-a3;s3=(350.*a30.*a30.*a30/(4*pi/9)^3-525.*a30.*a30.*a30.*a30/( 4*pi/9)^4+210.*a30.*a30.*a30.*a30.*a30/(4*pi/9)^5);x3=(s0+s3).*sin(a3)+e*cos(a3);y3=(s0+s3).*cos(a3)-e*sin(a3);k3=-1050.*a30.*a30/(4*pi/9)^3+2100.*a30.*a30.*a30/(4*pi/9)^ 4-1050.*a30.*a30.*a30.*a30/(4*pi/9)^5;i3=[(k3-e).*sin(a3)+(s0+s3).*cos(a3)].*[(k3-e).*(k3-e)+(s0+ s3).*(s0+s3)].^(-1/2);j3=[-(k3-e).*cos(a3)+(s0+s3).*sin(a3)].*[(k3-e).*(k3-e)+(s0 +s3).*(s0+s3)].^(-1/2);x30=x3-18*j3;y30=y3-18*i3;a4=33*pi/18:pi/60:2*pi;%推杆近休阶段s4=0;x4=(s0+s4).*sin(a4)+e*cos(a4);y4=(s0+s4).*cos(a4)-e*sin(a4);k4=0;i4=[(k4-e).*sin(a4)+(s0+s4).*cos(a4)].*[(k4-e).*(k4-e)+(s0+ s4).*(s0+s4)].^(-1/2);j4=[-(k4-e).*cos(a4)+(s0+s4).*sin(a4)].*[(k4-e).*(k4-e)+(s0 +s4).*(s0+s4)].^(-1/2);x40=x4-18*j4;y40=y4-18*i4;plot(x10,y10,'-g*',x101,y101,'-g+',x20,y20,'-r*',x30,y30,'-b*',x40,y40,'-k*',x1,y1,'-g*',x11,y11,'-g+',x2,y2,'-r*',x3,y3,'-b*',x4,y4,'-k*')%凸轮轮廓曲线绘制title(‘凸轮轮廓曲线绘制');xlabel('Variable X'); %X轴ylabel('Variable Y'); %Y轴text(-250,-200,'工作廓线') %文字标注text(100,-100,'理论廓线');grid on %加网格axis equal%坐标相等a1=0:pi/60:pi/2;%压力角计算force1=abs(atan((k1).*(s0+s1).^-1)); c1=max(force1);a11=pi/2:pi/60:pi;force11=abs(atan((k11).*(s0+s11).^-1));c11=max(force11);c111=max(c1,c11);a2=pi:pi/60:25*pi/18;force2=abs(atan((k2).*(s0+s2).^-1));c2=max(force2);a3=25*pi/18:pi/60:33*pi/18;force3=abs(atan((k3).*(s0+s3).^-1));c3=max(force3);a4=33*pi/18:pi/60:2*pi;force4=abs(atan((k4).*(s0+s4).^-1));c4=max(force4);r0=r0+1; %每循环一次基圆半径+1s0=sqrt(r0^2-e^2);endend%求最大压力角位置c111c3[m1,n1]=sort(force1);bend1=n1(end-1+1:end)jiaodu1=(bend1(end)-1)*3[m11,n11]=sort(force11);bend11=n11(end-1+1:end)jiaodu11=(bend11(end)-1)*3+90 [m3,n3]=sort(force3);bend3=n3(end-1+1:end)jiaodu=(bend3(end)-1)*3+250vv=i1./j1;vv1=diff(vv);vv2=diff(vv,2);vv22=[0,vv2];p=(1+vv1.^2).^(3/2)./vv22;g=min(p)vv1=i11./j11;vv11=diff(vv1);vv21=diff(vv1,2);vv221=[0,vv21];p1=(1+vv11.^2).^(3/2)./vv221;g1=min(p1)vv2=i2./j2;vv222=diff(vv2);vv223=diff(vv2,2);vv2211=[0,vv223];p2=(1+vv222.^2).^(3/2)./vv2211;g2=min(p2)vv=i3./j3;vv1=diff(vv);vv2=diff(vv,2);vv22=[0,vv2];p=(1+vv1.^2).^(3/2)./vv22;g3=min(p)vv=i4./j4;vv1=diff(vv);vv2=diff(vv,2);vv22=[0,vv2];p=(1+vv1.^2).^(3/2)./vv22;g4=min(p))ro=sqrt(s0^2+e^2) %求合适基圆半径x1y1x11y11x2y2x3y3x4y4x10y10x101y101x20y20x30y30x40y40force1force11force2force3force4c111c3jiaodu11jiaodu3四：计算结果及分析：（1）工作廓线坐标：1;推程加速阶段X坐标14 24.9479312972938 35.8335795427018 46.6331664128873 57.323071617132667.8798591305935 78.2803034241300 88.5014157831108 98.5204708048515108.315033160764 117.862984704875 127.142552005136 136.132334367976144.811332419744 153.158977301315 161.155160523920 168.780264525614176.015193958402 182.841407726263 189.240951783976 195.196492695966200.691351943287 205.709540955551 210.235796832989 214.255618712129 217.755304716715 220.721989423648 223.143681761924 225.009303250807226.308726472013 227.0328136593412推程加速阶段Y坐标209.532813659341 208.532370629552 206.998924199561 204.935879972465202.347567871334 199.239236813805 195.617049448531 191.488076931747186.860293712014 181.742572281261 176.144677840557 170.0772******** 163.551861181761 156.580882432274 149.177605251176 141.356170650697133.131574562033 124.519659744732 115.537106908501 106.20142493273596.5309400655771 86.5447839816669 76.2628805759777 65.705931370278654.8953994088027 43.8534915206956 32.6031388287473 21.16797538678679.57231483194954 -2.15887505719948 -14.00000000000003推程减速阶段X坐标227.032813659341 227.134619685286 226.568905051752 225.331644205755 223.421214513810 220.838411540547 217.586454974950 213.670985176905209.100050353069 203.884084407342 198.0358******** 191.570525763878184.505401336072 176.860074548737 168.656256843411 159.917723656843150.670231233150 140.941425726738 130.760744942876 120.159313091203109.169828954466 97.8264479001947 86.1646581868564 74.221152038085562.0336919788640 49.6409729459048 37.0824807009210 24.398347089867511.6292027035831 -1.18397249451846 -14.00000000000004推程减速阶段Y坐标-14.0000000000000 -25.9228338599749 -37.8904674143353 -49.8635381159681 -61.8024134893063 -73.6673405558026 -85.4185959941913 -97.0166364509177 -108.422248415730 -119.596697079292 -130.501873593764 -141.100440163605 -151.355972402351 -161.233098401750 -170.697633972432 -179.716713530067 -188.258916117849 -196.294386074865 -203.794947880574 -210.734214728044 -217.0876******** -222.832864069368 -227.949297596606 -232.418705078147 -236.225024238547 -239.354479443456 -241.795636066125 -243.539445995213 -244.579284102998 -244.910975527746 -244.5328136593415远休阶段X坐标-14.0000000000000 -26.7786721222032 -39.4839457654822 -52.0809966579133 -64.5352971586108 -76.8127108955902 -88.8795863311907 -100.702848998602 -112.250092156677 -123.489665614559 -134.390762482652 -144.923503612169 -155.059019491793 -164.769529377011 -174.028********* -182.810305697758 -191.0911******** -198.848174053764 -206.060195464824 -212.707420203182 -218.771628687875 -224.236199344965 -229.086154166116 -233.308199762282 6远休阶段Y坐标-244.532813659341 -243.464986549453 -241.729838834477 -239.332126433691 -236.278421310122 -232.577093457254 -228.238287957455 -223.273897175014 -217.697528159994 -211.524465352257 -204.771628687875 -197.457527222762 -189.602208400634 -181.227203104369 -172.355466641343 -163.011315824535 -153.220362321829 -143.009442456216 -132.406543649295 -121.440727709697 -110.142051176688 -98.5414829372844 -86.6708193426842 -74.5625970566802 7减速阶段X坐标-234.573962542258 -237.924423961410 -240.528414701632 -242.301034179885 -243.179109387654 -243.122053300159 -242.111828793401 -240.152099129043 -237.266657296952 -233.497236106624 -228.900808808014 -223.546496133102 -217.512199933386 -210.881086014932 -203.738039329490 -196.166213373622 -188.243792502170 -180.0410******** -171.618025436311 -163.022********* -154.287835944964 -145.434490148429 -136.467891333878 -127.380539946257 -118.153582814159 -108.759487623767 -99.16559150875688减速阶段Y坐标-70.4794512845940 -58.1011116825609 -45.5418784536957 -32.8365161989020 -20.0390090002643 -7.21694579130250 5.55380225566372 18.194003075560030.6254874984057 42.7749931638176 54.5773610652433 65.978032703814576.9348117792082 87.4188705720677 97.4149974868349 106.921098432862115.946980634777 124.512462892978 132.644871079527 140.375991577690147.738568287212 154.762440563530 161.470429890068 167.874092062809173.969459073374 179.732900602872 185.1172389914419近休X坐标-92.6420511766881 -82.6518154464002 -72.4350368350310 -62.0197188225945 -51.4344090718031 -40.7081211809080 -29.8702551594429 -18.9505168448415 -7.97883648080264 3.01471331942776 13.999999999999910近休Y坐标1 188.460739555420 193.050970998372 197.112063148625 200.632884834880203.603785729623 206.016622800007 207.864782627336 209.143199533988209.848369468082 209.978359607845 209.532813659341（2）理论廓线坐标;推程加速阶段X坐标12.8000000000000 22.8728273179084 32.8885297342726 42.825360681316652.6617133932777 62.3761432336542 71.9473900632018 81.354400741436490.5763518517692 99.5926727370081 108.383068927807 116.927546041764125.206434225271 133.200413203958 140.890538000620 148.258265371979155.285481007489 161.954527524708 168.248233286539 174.149942056033179.643543494319 184.713504496809 189.344901352090 193.523452696839197.235553228942 200.468308129584 203.209568133643 205.447965176251 207.172948531918 208.374821351328 209.044777489697推程加速阶段Y坐标191.572858202826 190.652383395923 189.241484022951 187.343250393275 184.961604006512 182.101293199539 178.767888983898 174.967781050798170.708173911217 165.997083129187 160.843331597179 155.256545793692149.247151954669 142.826372082411 136.006219708068 128.799495316842121.219781338553 113.281436600464 104.999590134052 96.390134222989187.4697165758390 78.2557315040260 68.7663099834431 59.020308476717649.0372963926355 38.8375420595755 28.4419970910307 17.87227902341457.15065210936054 -3.69999384635310 -14.6561667163081推程减速阶段X坐标209.193734991700 209.188778273809 208.573036193737 207.342473187261 205.495287697520 203.0319******** 199.955103403567 196.269775760348191.983156349172 187.104683111356 181.645993349332 175.620886984768169.0452******** 161.937156885096 154.316496362355 146.205213858842137.627077770212 128.607625755855 119.174072750844 109.35521228870799.1813115200797 88.6840003369476 77.8961550352902 66.851776970326355.5858666782191 44.1342939559169 32.5336644067296 20.82118297320159.03451499079487 -2.78835469420737 -14.6092639913715推程减速阶段Y坐标-16.4015145824514 -27.3181030218633 -38.2760890490105 -49.2392576762938 -60.1711110106104 -71.0350090000076 -81.7943109934888 -92.4125175513741 -102.853********* -113.0812******** -123.060653160544 -132.757237971647 -142.137258475553 -151.167983975963 -159.817777845352 -168.0562******** -175.854233625249 -183.184184769079 -190.020********* -196.337291242469 -202.113395111709 -207.327521359409 -211.960806247121 -215.996393696655 -219.419502857395 -222.217487685822 -224.379888298036 -225.898473888143 -226.767277038293 -226.982619279687 -226.543127798025远休阶段X坐标-12.9711482618274 -24.8107233108544 -36.5822938918588 -48.2535949481094 -59.7926362546736 -71.1677901013991 -82.3478779822689 -93.3022560535201 -104.000899126289 -114.414482963567 -124.514464655894 -134.273160855494 -143.663823654403 -152.660713898624 -161.239171737366 -169.375684213972 -177.0479******** -184.234939088932 -190.916953302526 -197.0756******** -202.694230799421 -207.757213383730 -212.250747887182 -216.162517844044远休阶段Y坐标-226.562241489795 -225.572888364055 -223.965255630689 -221.743749699274 -218.914459563151 -215.485140109924 -211.465190865844 -206.865630232365 -201.699065285474 -195.979657220565 -189.723082537593 -182.946490072876 -175.668453995324 -167.908922895934 -159.689165110094 -151.0317******** -141.960288314811 -132.499762924347 -122.676064893652 -112.516120296192 -102.0477******** -91.2997275085610 -80.3014319762869 -69.0830358006497回程阶段X坐标-217.335260464284 -220.421346316413 -222.795183195622 -224.398577389943 -225.188547506355 -225.137585355545 -224.233655449440 -222.479896624979 -219.893983296304 -216.507098988589 -212.362488116223 -207.513585489574 -202.021********* -195.953825087341 -189.379262026933 -182.367612804067 -174.985894648424 -167.296364561343 -159.354690783951 -151.208619312605 -142.897173644983 -134.450395994491 -125.889635960919 -117.228428433346 -108.474068637267 -99.6300563428237 -90.6995930141100回程阶段Y坐标-65.2999580017652 -53.9008411016096 -42.4544037000726 -30.9651421357433 -19.4561855319938 -7.96455046569805 3.46312822959339 14.774462367317425.9148401896814 36.8306478920168 47.4721553190688 57.795992842225267.7671217377121 77.3601986319145 86.5602513186570 95.3626114072227103.772082503801 111.801357318003 119.468732676936 126.795209558515133.801107529679 140.502367786106 146.906758880859 153.010*********158.793589895652 164.219890434419 169.232439040273近休阶段X坐标-84.7013039329720 -75.5673741224230 -66.2263193920283 -56.7037429235150 -47.0257454370771 -37.2188536511159 -27.3099475743478 -17.3261868295693 -7.29493621101956 2.75630932061967 12.8000000000000近休阶段Y坐标172.306961879241 176.503744912797 180.216743450172 183.435780420462 186.152032667084 188.358055131435 190.0478******** 191.216639573932191.861366370818 191.980214498602 191.572858202826凸轮压力角0 0.00354431855997765 0.00708657544025155 0.0106247131274339 0.01415668242241860.0176804465517903 0.0211939852247537 0.0246952986180828 0.02818241127214470.0316533758817331 0.0351062769662460 0.0385392344046481 0.04195040682166590.0453379948127508 0.0487002439965149 0.0520354478845675 0.05534195055995420.0586181491567104 0.0618624961343669 0.0650735013425822 0.06824973387240840.0713898236920071 0.0744924630659183 0.0775564077582259 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0.165667032050483 0.145943761057100 0.1233999352907570.0990517714422343 0.0741698891884142 0.0502587840423935 0.02902100443043590.0123165659206908 0.00213229641216247推程最大压力角：0.193821958696751*180出现位置：90回程最大压力角：0.204580805091460*180出现位置292最小曲率半径：g2=4.2145<0.35*18故满足要求最后确定基圆半径：ro = 211五：凸轮机构图六：体会和建议在本次设计中，对凸轮结构的各项参数对最终凸轮形状的影响有了更深刻的认识。