凸輪計算-凸輪輪廓函數(shù)

擺動凸輪,基圓半徑最大，擺動角位移朝內(nèi),,,,,,,

,余弦修正函數(shù),,,,,,,

,余弦定理,cos(A)=(b^2+c^2-a^2)/(2*b*c),,,,,,

,中心距,AO,60.44005295,mm,60.44005295,,,

,基圓半徑,R0,36.5,mm,,,,

,擺桿長度,AB,39.5,mm,,,,

,初始角,a0,0.62182793,弧度,35.628116,度,0.621827930482,

,擺動角范圍,b,0.261799388,弧度,15,度,,

,推程角,w1,1.570796327,弧度,90,度,,

,回程角,w2,1.570796327,弧度,90,度,,

,,X=,60.4400529450463*sin(t)-39.5*sin(t+0.621827930482472-(15/180*pi)*(0.5-0.5*cos(2*t))),,,,,

,,Y=,60.4400529450463*cos(t)-39.5*cos(t+0.621827930482472-(15/180*pi)*(0.5-0.5*cos(2*t))),,,,,

,,t=,"(0,pi)",,,,,

,的推導(dǎo)過程：,,,,,,,

,擺角a,a=,"0.690726715052403-(15/180*pi)*(0.5-0.5*cos(2*t),t∈(0,pi)弧度制",,,,,

,擺桿AB上B點相對A坐標,,,,,,,

,,x=,"34*sin(0.690726715052403-(15/180*pi)*(0.5-0.5*cos(2*t))),t∈(0,pi)弧度制",,,,,

,,y=,"34*cos(0.690726715052403-(15/180*pi)*(0.5-0.5*cos(2*t))),t∈(0,pi)弧度制",,,,,

,B點相對O坐標,,,,,,,

,,x=,34*sin(0.690726715052403-(15/180*pi)*(0.5-0.5*cos(2*t))),,,,,

,,y=,57.42821606+34*cos(0.690726715052403-(15/180*pi)*(0.5-0.5*cos(2*t))),,,,,

,,,,,,,,,

,標準方法：,,,,,,,

,彎腰凸輪,,,,,,,

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,,基圓半徑r0,22,mm,,,,

,,行程h,17,mm,,,,

,,,,,,,,,

,,推程結(jié)束δ0,90,度,1.570796327,弧度,,

,,回程結(jié)束δ0,90,度,1.570796327,弧度,,

,,,,,,,,,

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,余弦運動,推程,s=,"h*(1-cos(pi*δ/δ0))/2,余弦運動規(guī)律",,,,

,,,,,,,,,

,,,x=,（s0+s)sin(δ)=（s0+h*(1-cos(pi*δ/δ0))/2)sin(δ),,,,

,,,y=,（s0+s)cos(δ)=（s0+h*(1-cos(pi*δ/δ0))/2)cos(δ),,,,

,,,,,,,,,

,,帶入數(shù)值,x=,(22+17*(1-cos(pi*t/(90/180*pi)))/2)*sin(t),,,,

,,,y=,(22+17*(1-cos(pi*t/(90/180*pi)))/2)*cos(t),,,,

,,,t=,"(0,0.5*pi)",,,,

,,,,,,,,,

,余弦運動,回程,s=,"h*(1+cos(pi*δ/δ0))/2,余弦運動規(guī)律",,,,

,,,,,,,,,

,,,x=,（s0+s)sin(δ)=（s0+h*(1+cos(pi*δ/δ0))/2)sin(δ),,,,

,,,y=,（s0+s)cos(δ)=（s0+h*(1+cos(pi*δ/δ0))/2)cos(δ),,,,

,,,,,,,,,

,,帶入數(shù)值,x=,(22+17*(1+cos(pi*(t-0.5*pi)/(90/180*pi)))/2)*sin(t),,,,

,,,y=,(22+17*(1+cos(pi*(t-0.5*pi)/(90/180*pi)))/2)*cos(t),,,,

,,,t=,(0.5*pi，pi),,,,

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,正弦運動,推程,,,,,,

,,,,,,,,,

,,,,,,,,,

,,,s=,17*(T/(90/180*PI)-SIN(2*PI*T/(90/180*PI))/(2*PI)),,,,

,,,x=,(20+17*(T/(90/180*PI)-SIN(2*PI*T/(90/180*PI))/(2*PI)))*sin(t),,,,

,,,y=,(20+17*(T/(90/180*PI)-SIN(2*PI*T/(90/180*PI))/(2*PI)))*cos(t),,,,

,,,t=,"(0,0.5*pi)",,,,

,,,,,,,,,

,,,,,,,,,

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,正弦運動,回程,,,,,,

,,,,,,,,帶入T后注意T的區(qū)間

,,,s=,"17*(1-T/(90/180*PI)+SIN(2*PI*T/(90/180*PI))/(2*PI))，t=(0,pi/2)",,,,

,,,x=,"(20+17*(1-(t-pi/2)/(90/180*PI)+SIN(2*PI*T/(90/180*PI))/(2*PI)))*sin(t),t=(pi/2,pi)",,,,

,,,y=,"(20+17*(1-(t-pi/2)/(90/180*PI)+SIN(2*PI*T/(90/180*PI))/(2*PI)))*cos(t),t=(pi/2,pi)",,,,

,,,t=,(0.5*pi，pi),,,,

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,,,驗證：,t,t,s,x,y

,,,,0,0,0,0,20

,,,,10,0.174532925,0.149740856,1.903444417,10.79496972

,,,,20,0.34906585,1.113248406,2.406469453,6.611720484

,,,,60,1.047197551,13.67648114,39.88546265,23.027882