機(jī)械原理課程設(shè)計(jì)zdp
機(jī)械原理課程設(shè)計(jì)zdp,機(jī)械,原理,課程設(shè)計(jì),zdp
課 程 設(shè) 計(jì) 書(shū)機(jī)械原理課程設(shè)計(jì)任務(wù)書(shū)題目:連桿機(jī)構(gòu)設(shè)計(jì)B4-b設(shè)計(jì)參數(shù)轉(zhuǎn)角關(guān)系的期望函數(shù)連架桿轉(zhuǎn)角范圍計(jì)算間隔設(shè)計(jì)計(jì)算手工編程確定:a,b,c,d四桿的長(zhǎng)度,以及在一個(gè)工作循環(huán)內(nèi)每一計(jì)算間隔的轉(zhuǎn)角偏差值608520.5y=x(1x2)設(shè)計(jì)要求:1.用解析法按計(jì)算間隔進(jìn)行設(shè)計(jì)計(jì)算;2.繪制3號(hào)圖紙1張,包括:(1)機(jī)構(gòu)運(yùn)動(dòng)簡(jiǎn)圖;(2)期望函數(shù)與機(jī)構(gòu)實(shí)現(xiàn)函數(shù)在計(jì)算點(diǎn)處的對(duì)比表;(3)根據(jù)對(duì)比表繪制期望函數(shù)與機(jī)構(gòu)實(shí)現(xiàn)函數(shù)的位移對(duì)比圖;3.設(shè)計(jì)說(shuō)明書(shū)一份;4.要求設(shè)計(jì)步驟清楚,計(jì)算準(zhǔn)確。說(shuō)明書(shū)規(guī)范。作圖要符合國(guó)家標(biāo)。按時(shí)獨(dú)立完成任務(wù)。目錄第1節(jié) 平面四桿機(jī)構(gòu)設(shè)計(jì)31.1連桿機(jī)構(gòu)設(shè)計(jì)的基本問(wèn)題31.2作圖法設(shè)計(jì)四桿機(jī)構(gòu)31.3 解析法設(shè)計(jì)四桿機(jī)構(gòu)3第2節(jié) 設(shè)計(jì)介紹52.1按預(yù)定的兩連架桿對(duì)應(yīng)位置設(shè)計(jì)原理52.2 按期望函數(shù)設(shè)計(jì)6第3節(jié) 連桿機(jī)構(gòu)設(shè)計(jì)83.1連桿機(jī)構(gòu)設(shè)計(jì)83.2變量和函數(shù)與轉(zhuǎn)角之間的比例尺83.3確定結(jié)點(diǎn)值83.4 確定初始角、93.5 桿長(zhǎng)比m,n,l的確定133.6 檢查偏差值133.7 桿長(zhǎng)的確定133.8 連架桿在各位置的再現(xiàn)函數(shù)和期望函數(shù)最小差值的確定15總結(jié)18參考文獻(xiàn)19附錄20第1節(jié) 平面四桿機(jī)構(gòu)設(shè)計(jì)1.1連桿機(jī)構(gòu)設(shè)計(jì)的基本問(wèn)題 連桿機(jī)構(gòu)設(shè)計(jì)的基本問(wèn)題是根據(jù)給定的要求選定機(jī)構(gòu)的型式,確定各構(gòu)件的尺寸,同時(shí)還要滿(mǎn)足結(jié)構(gòu)條件(如要求存在曲柄、桿長(zhǎng)比恰當(dāng)?shù)龋?、?dòng)力條件(如適當(dāng)?shù)膫鲃?dòng)角等)和運(yùn)動(dòng)連續(xù)條件等。 根據(jù)機(jī)械的用途和性能要求的不同,對(duì)連桿機(jī)構(gòu)設(shè)計(jì)的要求是多種多樣的,但這些設(shè)計(jì)要求可歸納為以下三類(lèi)問(wèn)題:(1)預(yù)定的連桿位置要求;(2)滿(mǎn)足預(yù)定的運(yùn)動(dòng)規(guī)律要求;(3)滿(mǎn)足預(yù)定的軌跡要求;連桿設(shè)計(jì)的方法有:解析法、作圖法和實(shí)驗(yàn)法。1.2作圖法設(shè)計(jì)四桿機(jī)構(gòu) 對(duì)于四桿機(jī)構(gòu)來(lái)說(shuō),當(dāng)其鉸鏈中心位置確定后,各桿的長(zhǎng)度也就確定了。用作圖法進(jìn)行設(shè)計(jì),就是利用各鉸鏈之間相對(duì)運(yùn)動(dòng)的幾何關(guān)系,通過(guò)作圖確定各鉸鏈的位置,從而定出各桿的長(zhǎng)度。根據(jù)設(shè)計(jì)要求的不同分為四種情況 : (1) 按連桿預(yù)定的位置設(shè)計(jì)四桿機(jī)構(gòu) (2) 按兩連架桿預(yù)定的對(duì)應(yīng)角位移設(shè)計(jì)四桿機(jī)構(gòu)(3) 按預(yù)定的軌跡設(shè)計(jì)四桿機(jī)構(gòu)(4) 按給定的急回要求設(shè)計(jì)四桿機(jī)構(gòu)1.3 解析法設(shè)計(jì)四桿機(jī)構(gòu) 在用解析法設(shè)計(jì)四桿機(jī)構(gòu)時(shí),首先需建立包含機(jī)構(gòu)各尺度參數(shù)和運(yùn)動(dòng)變量在內(nèi)的解析式,然后根據(jù)已知的運(yùn)動(dòng)變量求機(jī)構(gòu)的尺度參數(shù)?,F(xiàn)有三種不同的設(shè)計(jì)要求,分別是:(1) 按連桿預(yù)定的連桿位置設(shè)計(jì)四桿機(jī)構(gòu)(2) 按預(yù)定的運(yùn)動(dòng)軌跡設(shè)計(jì)四桿機(jī)構(gòu)(3) 按預(yù)定的運(yùn)動(dòng)規(guī)律設(shè)計(jì)四桿機(jī)構(gòu)1) 按預(yù)定的兩連架桿對(duì)應(yīng)位置設(shè)計(jì)2) 按期望函數(shù)設(shè)計(jì)本次連桿機(jī)構(gòu)設(shè)計(jì)采用解析法設(shè)計(jì)四桿機(jī)構(gòu)中的按期望函數(shù)設(shè)計(jì)。下面在第2節(jié)將對(duì)期望函數(shù)設(shè)計(jì)四桿機(jī)構(gòu)的原理進(jìn)行詳細(xì)的闡述。第2節(jié) 設(shè)計(jì)介紹2.1按預(yù)定的兩連架桿對(duì)應(yīng)位置設(shè)計(jì)原理如下圖所示:設(shè)要求從動(dòng)件3與主動(dòng)件1的轉(zhuǎn)角之間滿(mǎn)足一系列的對(duì)應(yīng)位置關(guān)系,即=i=1, 2, ,n其函數(shù)的運(yùn)動(dòng)變量為由設(shè)計(jì)要求知、為已知條件。有為未知。又因?yàn)闄C(jī)構(gòu)按比例放大或縮小,不會(huì)改變各機(jī)構(gòu)的相對(duì)角度關(guān)系,故設(shè)計(jì)變量應(yīng)該為各構(gòu)件的相對(duì)長(zhǎng)度,如取d/a=1 , b/a=l c/a=m , d/a=n 。故設(shè)計(jì)變量l、m、n以及、的計(jì)量起始角、共五個(gè)。如圖所示建立坐標(biāo)系Oxy,并把各桿矢量向坐標(biāo)軸投影,可得2-1 為消去未知角,將上式 兩端各自平方后相加,經(jīng)整理可得令=m, =-m/n, =,則上式可簡(jiǎn)化為: 2-2 式 2-2 中包含5個(gè)待定參數(shù)、及,故四桿機(jī)構(gòu)最多可以按兩連架桿的5個(gè)對(duì)應(yīng)位置精度求解。2.2 按期望函數(shù)設(shè)計(jì)如上圖所示,設(shè)要求設(shè)計(jì)四桿機(jī)構(gòu)兩連架桿轉(zhuǎn)角之間實(shí)現(xiàn)的函數(shù)關(guān)系 (成為期望函數(shù)),由于連架桿機(jī)構(gòu)的待定參數(shù)較少,故一般不能準(zhǔn)確實(shí)現(xiàn)該期望函數(shù)。設(shè)實(shí)際實(shí)現(xiàn)的函數(shù)為月(成為再現(xiàn)函數(shù)),再現(xiàn)函數(shù)與期望函數(shù)一般是不一致的。設(shè)計(jì)時(shí)應(yīng)該使機(jī)構(gòu)的再現(xiàn)函數(shù)盡可能逼近所要求的期望函數(shù)。具體作法是:在給定的自變量x的變化區(qū)間到內(nèi)的某點(diǎn)上,使再現(xiàn)函數(shù)與期望函數(shù)的值相等。從幾何意義上與兩函數(shù)曲線(xiàn)在某些點(diǎn)相交。這些點(diǎn)稱(chēng)為插值結(jié)點(diǎn)。顯然在結(jié)點(diǎn)處:故在插值結(jié)點(diǎn)上,再現(xiàn)函數(shù)的函數(shù)值為已知。這樣,就可以按上述方法來(lái)設(shè)計(jì)四桿機(jī)構(gòu)。這種設(shè)計(jì)方法成為插值逼近法。 在結(jié)點(diǎn)以外的其他位置,與是不相等的,其偏差為偏差的大小與結(jié)點(diǎn)的數(shù)目及其分布情況有關(guān),增加插值結(jié)點(diǎn)的數(shù)目,有利于逼近精度的提高。但結(jié)點(diǎn)的數(shù)目最多可為5個(gè)。至于結(jié)點(diǎn)位置分布,根據(jù)函數(shù)逼近理論有 2-3試中i=1,2, ,3,n為插值結(jié)點(diǎn)數(shù)。 本節(jié)介紹了采用期望函數(shù)設(shè)計(jì)四桿機(jī)構(gòu)的原理。那么在第3節(jié)將具體闡述連桿機(jī)構(gòu)的設(shè)計(jì)。第3節(jié) 連桿機(jī)構(gòu)設(shè)計(jì)3.1連桿機(jī)構(gòu)設(shè)計(jì)設(shè)計(jì)參數(shù)表轉(zhuǎn)角關(guān)系的期望函數(shù)連架桿轉(zhuǎn)角范圍計(jì)算間隔設(shè)計(jì)計(jì)算手工編程確定:a,b,c,d四桿的長(zhǎng)度,以及在一個(gè)工作循環(huán)內(nèi)每一計(jì)算間隔的轉(zhuǎn)角偏差值608520.5y=x(1x2) 注:本次采用編程計(jì)算,計(jì)算間隔0.53.2變量和函數(shù)與轉(zhuǎn)角之間的比例尺 根據(jù)已知條件y=x(1x2)為鉸鏈四桿機(jī)構(gòu)近似的實(shí)現(xiàn)期望函數(shù), 設(shè)計(jì)步驟如下:(1)根據(jù)已知條件,可求得,。(2)由主、從動(dòng)件的轉(zhuǎn)角范圍=60、=85確定自變量和函數(shù)與轉(zhuǎn)角之間的比例尺分別為:31 3.3確定結(jié)點(diǎn)值 設(shè)取結(jié)點(diǎn)總數(shù)m=3,由式2-3可得各結(jié)點(diǎn)處的有關(guān)各值如表(3-1)所示。表(3-1) 各結(jié)點(diǎn)處的有關(guān)各值11.0670.0654.027.9721.5000.40530.049.6831.9330.65955.9880.833.4 確定初始角、 通常我們用試算的方法來(lái)確定初始角、,而在本次連桿設(shè)計(jì)中將通過(guò)編程試算的方法來(lái)確定。具體思路如下: 任取、,把、取值與上面所得到的三個(gè)結(jié)點(diǎn)處的、的值代入P134式8-17 從而得到三個(gè)關(guān)于、的方程組,求解方程組后得出、,再令=m, =-m/n, =。然求得后m,n,l的值。由此我們可以在機(jī)構(gòu)確定的初始值條件下找到任意一位置的期望函數(shù)值與再現(xiàn)函數(shù)值的偏差值。當(dāng)時(shí),則視為選取的初始、角度滿(mǎn)足機(jī)構(gòu)的運(yùn)動(dòng)要求。具體程序如下:#include#include#define PI 3.1415926#define t PI/180void main() int i; float p0,p1,p2,a0,b0,m,n,l,a5; float A,B,C,r,s,f1,f2,k1,k2,j; float u1=1.0/60,u2=0. 93/685,x0=1.0,y0=0.0;float a3,b3,a16,b13; FILE *p; if(p=fopen(d:zdp.txt,w)=NULL) printf(cant open the file!); exit(0); a0=4.02; a1=30; a2=55.98; b0=7.97; b1=49.68; b2=80.83; printf(please input a0: n); scanf(%f,&a0); printf(please input b0: n); scanf(%f,&b0); for(i=0;i3;i+)a1i=cos(bi+b0)*t); a1i+3=cos(bi+b0-ai-a0)*t); b1i=cos(ai+a0)*t);p0=(b10-b11)*(a14-a15)-(b11-b12)*(a13-a14)/(a10-a11)*(a14-a15)-(a11-a12)*(a13-a14); p1=(b10-b11-(a10-a11)*p0)/(a13-a14); p2=b10-a10*p0-a13*p1; m=p0; n=-m/p1; l=sqrt(m*m+n*n+1-2*n*p2); printf(p0=%f,p1=%f,p2=%f,m=%f,n=%f,l=%fn,p0,p1,p2,m,n,l); fprintf(p,p0=%f,p1=%f,p2=%f,m=%f,n=%f,l=%fn,p0,p1,p2,m,n,l); printf(n); fprintf(p,n); for(i=0;i5;i+)printf(please input one angle of fives(0-60): ); scanf(%f,&a5); printf(when the angle is %fn,a5); fprintf(p,when the angle is %fn,a5); A=sin(a5+a0)*t); B=cos(a5+a0)*t)-n; C=(1+m*m+n*n-l*l)/(2*m)-n*cos(a5+a0)*t)/m; j=x0+u1*a5; printf(A=%f,B=%f,C=%f,j=%fn,A,B,C,j); s=sqrt(A*A+B*B-C*C); f1=2*(atan(A+s)/(B+C)/(t)-b0;f2=2*(atan(A-s)/(B+C)/(t)-b0; r=(log(j)-y0)/u2; k1=f1-r; k2=f2-r; printf(r=%f,s=%f,f1=%f,f2=%f,k1=%f,k2=%fn,r,s,f1,f2,k1,k2); fprintf(p,r=%f,s=%f,f1=%f,f2=%f,k1=%f,k2=%fn,r,s,f1,f2,k1,k2); printf(nn); fprintf(p,nn); 結(jié)合課本P135,試取=86,=24時(shí):程序運(yùn)行及其結(jié)果為:p0=0.601242,p1=-0.461061,p2=-0.266414,m=0.601242,n=1.304040,l=1.938257when the angle is 0.000000r=0.000000,s=1.409598,f1=-125.595070,f2=-0.296147,k1=-125.595070,k2=-0.296147when the angle is 4.020000r=7.954308,s=1.538967,f1=-130.920624,f2=7.970002,k1=-138.874939,k2=0.015694when the angle is 30.000000r=49.732372,s=1.924767,f1=-152.252411,f2=49.680004,k1=-201.984787,k2=-0.052368when the angle is 55.980000r=80.838707,s=1.864505,f1=-161.643921,f2=80.830002,k1=-242.482635,k2=-0.008705when the angle is 60.000000r=85.018051,s=1.836746,f1=-162.288574,f2=84.909149,k1=-247.306625,k2=-0.108902由程序運(yùn)行結(jié)果可知:當(dāng)取初始角=86、=24時(shí)(=k1(k2)所以所選初始角符合機(jī)構(gòu)的運(yùn)動(dòng)要求。3.5 桿長(zhǎng)比m,n,l的確定 由上面的程序結(jié)果可得m=0.601242, n=1.304040, l=1.938257。3.6 檢查偏差值 對(duì)于四桿機(jī)構(gòu),其再現(xiàn)的函數(shù)值可由P134式8-16求得 3-2 式中: A=sin() ; B=cos()-n ;C=- ncos()/m 按期望函數(shù)所求得的從動(dòng)件轉(zhuǎn)角為 3-3 則偏差為 若偏差過(guò)大不能滿(mǎn)足設(shè)計(jì)要求時(shí),則應(yīng)重選計(jì)量起始角、以及主、從動(dòng)件的轉(zhuǎn)角變化范圍、等,重新進(jìn)行設(shè)計(jì)。同樣由上面的程序運(yùn)行結(jié)果得出每一個(gè)取值都符合運(yùn)動(dòng)要求,即 :=k1(k2) (3.7 桿長(zhǎng)的確定 根據(jù)桿件之間的長(zhǎng)度比例關(guān)系m,n,l和這樣的關(guān)系式b/a=l c/a=m d/a=n確定各桿的長(zhǎng)度,當(dāng)選取主動(dòng)桿的長(zhǎng)度后,其余三桿長(zhǎng)的度隨之可以確定;在此我們假設(shè)主動(dòng)連架桿的長(zhǎng)度為 a=50 ,則確定其余三桿的長(zhǎng)度由下面的程序確定:#include #include #include void main()float a=50,b,c,d;float m=0.601242,n=1.304040,l=1.938257;FILE *p;if(p=fopen(d:zdp.txt,w)=NULL)printf(cant open the file!);exit(0);b=l*a;c=m*a;d=n*a;printf(a=%fnb=%fnc=%fnd=%fn,a,b,c,d);fprintf(p,a=%fnb=%fnc=%fnd=%fn,a,b,c,d);fclose(p); 運(yùn)行結(jié)果為: a=50.000000b=96.912849c=30.062099d=65.2019963.8 連架桿在各位置的再現(xiàn)函數(shù)和期望函數(shù)最小差值的確定如下面的程序:#include#include#include#define PI 3.1415926#define t PI/180void main()float a0=86,b0=24,m=0.601242,n=1.304040,l=1.938257; float A,B,C,s,j,k1,k2,k;float x0=1.0,y0=0.0,u1=1.0/60,u2=0.693/85 ;float x130,y1130,y2130,a1130,f1130,f2130,r130;int i;FILE *p;if(p=fopen(d:zdp.txt,w)=NULL)printf(cant open the file! );exit(0);printf( i a1i f1i ri k xi y1i y2inn);fprintf(p, i a1i f1i ri k xi y1i y2inn);for(i=0; a1i=60;i+)a10=0;A=sin(a1i+a0)*t);B=cos(a1i+a0)*t)-n;C=(1+m*m+n*n-l*l)/(2*m)-n*cos(a1i+a0)*t)/m;j=x0+u1*a1i; s=sqrt(A*A+B*B-C*C);f1i=2*(atan(A+s)/(B+C)/(t)-b0;f2i=2*(atan(A-s)/(B+C)/(t)-b0;ri=(log(j)-y0)/u2;k1=f1i-ri;k2=f2i-ri;xi=a1i*u1+x0;y2i=log(xi);if(abs(k1)abs(k2)k=k1;y1i=f1i*u2+y0;printf( %-4d %-5.1f %-10.4f %-8.4f %-8.4f %-7.4f %-8.4f %0.4fn,i,a1i,f1i,ri,k,xi,y1i,y2i);fprintf(p, %-4d %-5.1f %-10.4f %-8.4f %-8.4 %-7.4f %-8.4f %0.4fn,i,a1i,f1i,ri,k,xi,y1i,y2i);elsek=k2;y1i=f2i*u2+y0;printf( %-6d%-7.1f%-12.4f%-10.4f%-10.4f%-9.4f%-10.4f%2.4fn,i,a1i,f2i,ri,k,xi,y1i,y2i);fprintf(p,%-6d%-7.1f%-12.4f%-10.4f%-10.4f%-9.4f%-10.4f%2.4fn,i,a1i,f2i,ri,k,xi,y1i,y2i);a1i+1=a1i+0.5;fclose(p);程序運(yùn)行結(jié)果見(jiàn)附錄??偨Y(jié)通過(guò)本次課程設(shè)計(jì),讓我學(xué)會(huì)了用解析法中的按期望函數(shù)設(shè)計(jì)連桿機(jī)構(gòu),理解了這一設(shè)計(jì)原理,知道怎樣實(shí)現(xiàn)連桿機(jī)構(gòu)兩連架桿的轉(zhuǎn)角之間的期望函數(shù)與再現(xiàn)函數(shù)之間的關(guān)系。在本次設(shè)計(jì)中,有一個(gè)非常重要的環(huán)節(jié)確定初始角、的值。這一環(huán)節(jié)我采用了C程序的方法來(lái)求解。雖然沒(méi)有用筆算那樣繁瑣,但是在編寫(xiě)程序時(shí),由于公式多,公式中設(shè)計(jì)的三角函數(shù)比較麻煩,因而在設(shè)計(jì)中我遇到了很多大小不同的問(wèn)題,但是最終憑借對(duì)公式的理解和對(duì)C程序的進(jìn)一步掌握完成了這一解析問(wèn)題。只有確定了初始角、,才能正確檢查偏差值,得到一對(duì)最理想的初始角使得偏差值。通過(guò)C程序的求解,得出的結(jié)果說(shuō)明能較好的滿(mǎn)足連桿機(jī)構(gòu)的設(shè)計(jì)要求。本次課程設(shè)計(jì),從不知道如何下手到完成。我學(xué)到了很多的東西,掌握了課程設(shè)計(jì)書(shū)的書(shū)寫(xiě)格式,為以后的設(shè)計(jì)打下了良好的基礎(chǔ)。參考文獻(xiàn):【1】孫恒,陳作模,葛文杰 . 機(jī)械原理M . 7版 . 北京:高等教育出版社,2006?!?】孫恒,陳作模 . 機(jī)械原理M . 6版 . 北京:高等教育出版社,2001。附錄:i為序列號(hào) a1i= f1i= ri = k = xi為自變量 y1i為再現(xiàn)函數(shù)值 y2i為望函數(shù)值 i a1i f1i ri k xi y1i y2i 0 0.0 -0.2961 0.0000 -0.2961 1.0000 -0.0024 0.0000 1 0.5 0.7781 1.0179 -0.2398 1.0083 0.0063 0.0083 2 1.0 1.8380 2.0274 -0.1894 1.0167 0.0150 0.0165 3 1.5 2.8844 3.0287 -0.1443 1.0250 0.0235 0.0247 4 2.0 3.9177 4.0218 -0.1041 1.0333 0.0319 0.0328 5 2.5 4.9385 5.0070 -0.0685 1.0417 0.0403 0.0408 6 3.0 5.9474 5.9844 -0.0370 1.0500 0.0485 0.0488 7 3.5 6.9446 6.9540 -0.0093 1.0583 0.0566 0.0567 8 4.0 7.9308 7.9160 0.0148 1.0667 0.0647 0.0645 9 4.5 8.9063 8.8705 0.0358 1.0750 0.0726 0.0723 10 5.0 9.8715 9.8177 0.0538 1.0833 0.0805 0.0800 11 5.5 10.8267 10.7575 0.0692 1.0917 0.0883 0.0877 12 6.0 11.7723 11.6903 0.0821 1.1000 0.0960 0.0953 13 6.5 12.7087 12.6160 0.0927 1.1083 0.1036 0.1029 14 7.0 13.6360 13.5348 0.1013 1.1167 0.1112 0.1103 15 7.5 14.5547 14.4467 0.1080 1.1250 0.1187 0.1178 16 8.0 15.4649 15.3519 0.1130 1.1333 0.1261 0.1252 17 8.5 16.3670 16.2505 0.1166 1.1417 0.1334 0.1325 18 9.0 17.2612 17.1425 0.1187 1.1500 0.1407 0.1398 19 9.5 18.1476 18.0281 0.1195 1.1583 0.1480 0.1470 20 10.0 19.0266 18.9074 0.1193 1.1667 0.1551 0.1542 21 10.5 19.8984 19.7804 0.1180 1.1750 0.1622 0.1613 22 11.0 20.7631 20.6472 0.1159 1.1833 0.1693 0.1683 23 11.5 21.6208 21.5079 0.1129 1.1917 0.1763 0.1754 24 12.0 22.4720 22.3627 0.1093 1.2000 0.1832 0.1823 25 12.5 23.3165 23.2115 0.1050 1.2083 0.1901 0.1892 26 13.0 24.1548 24.0545 0.1003 1.2167 0.1969 0.1961 27 13.5 24.9868 24.8917 0.0950 1.2250 0.2037 0.2029 28 14.0 25.8128 25.7233 0.0895 1.2333 0.2104 0.2097 29 14.5 26.6328 26.5493 0.0836 1.2417 0.2171 0.2165 30 15.0 27.4471 27.3697 0.0774 1.2500 0.2238 0.2231 31 15.5 28.2558 28.1847 0.0711 1.2583 0.2304 0.2298 32 16.0 29.0589 28.9943 0.0646 1.2667 0.2369 0.2364 33 16.5 29.8566 29.7986 0.0580 1.2750 0.2434 0.2429 34 17.0 30.6491 30.5976 0.0514 1.2833 0.2499 0.2495 35 17.5 31.4363 31.3915 0.0448 1.2917 0.2563 0.2559 36 18.0 32.2186 32.1803 0.0382 1.3000 0.2627 0.2624 37 18.5 32.9958 32.9641 0.0317 1.3083 0.2690 0.2688 38 19.0 33.7682 33.7428 0.0253 1.3167 0.2753 0.2751 39 19.5 34.5357 34.5167 0.0190 1.3250 0.2816 0.2814 40 20.0 35.2986 35.2857 0.0129 1.3333 0.2878 0.2877 41 20.5 36.0569 36.0499 0.0070 1.3417 0.2940 0.2939 42 21.0 36.8107 36.8094 0.0013 1.3500 0.3001 0.3001 43 21.5 37.5600 37.5642 -0.0042 1.3583 0.3062 0.3063 44 22.0 38.3049 38.3144 -0.0094 1.3667 0.3123 0.3124 45 22.5 39.0455 39.0600 -0.0144 1.3750 0.3183 0.3185 46 23.0 39.7819 39.8011 -0.0192 1.3833 0.3243 0.3245 47 23.5 40.5142 40.5378 -0.0236 1.3917 0.3303 0.3305 48 24.0 41.2423 41.2700 -0.0277 1.4000 0.3362 0.3365 49 24.5 41.9664 41.9980 -0.0315 1.4083 0.3421 0.3424 50 25.0 42.6866 42.7216 -0.0351 1.4167 0.3480 0.3483 51 25.5 43.4028 43.4410 -0.0382 1.4250 0.3539 0.3542 52 26.0 44.1151 44.1562 -0.0411 1.4333 0.3597 0.3600 53 26.5 44.8236 44.8672 -0.0437 1.4417 0.3654 0.3658 54 27.0 45.5283 45.5742 -0.0459 1.4500 0.3712 0.3716 55 27.5 46.2293 46.2771 -0.0478 1.4583 0.3769 0.3773 56 28.0 46.9267 46.9760 -0.0493 1.4667 0.3826 0.3830 57 28.5 47.6203 47.6709 -0.0505 1.4750 0.3882 0.3887 58 29.0 48.3105 48.3619 -0.0515 1.4833 0.3939 0.3943 59 29.5 48.9970 49.0491 -0.0520 1.4917 0.3995 0.3999 60 30.0 49.6801 49.7324 -0.0523 1.5000 0.4050 0.4055 61 30.5 50.3596 50.4119 -0.0523 1.5083 0.4106 0.4110 62 31.0 51.0357 51.0877 -0.0520 1.5167 0.4161 0.4165 63 31.5 51.7084 51.7598 -0.0513 1.5250 0.4216 0.4220 64 32.0 52.3778 52.4282 -0.0504 1.5333 0.4270 0.4274 65 32.5 53.0438 53.0930 -0.0492 1.5417 0.4325 0.4329 66 33.0 53.7064 53.7542 -0.0478 1.5500 0.4379 0.4383 67 33.5 54.3658 54.4119 -0.0461 1.5583 0.4432 0.4436 68 34.0 55.0219 55.0660 -0.0441 1.5667 0.4486 0.4490 69 34.5 55.6748 55.7167 -0.0419 1.5750 0.4539 0.4543 70 35.0 56.3244 56.3640 -0.0396 1.5833 0.4592 0.4595 71 35.5 56.9709 57.0079 -0.0370 1.5917 0.4645 0.4648 72 36.0 57.6142 57.6484 -0.0342 1.6000 0.4697 0.4700 73 36.5 58.2543 58.2855 -0.0312 1.6083 0.4749 0.4752 74 37.0 58.8913 58.9194 -0.0281 1.6167 0.4801 0.4804 75 37.5 59.5252 59.5500 -0.0248 1.6250 0.4853 0.4855 76 38.0 60.1559 60.1774 -0.0215 1.6333 0.4904 0.4906 77 38.5 60.7836 60.8016 -0.0180 1.6417 0.4956 0.4957 78 39.0 61.4082 61.4227 -0.0144 1.6500 0.5007 0.5008 79 39.5 62.0298 62.0406 -0.0108 1.6583 0.5057 0.5058 80 40.0 62.6483 62.6554 -0.0071 1.6667 0.5108 0.5108 81 40.5 63.2637 63.2671 -0.0034 1.6750 0.5158 0.5158 82 41.0 63.8761 63.8758 0.0003 1.6833 0.5208 0.5208 83 41.5 64.4855 64.4815 0.0040 1.6917 0.5257 0.5257 84 42.0 65.0919 65.0843 0.0076 1.7000 0.5307 0.5306 85 42.5 65.6953 65.6841 0.0112 1.7083 0.5356 0.5355 86 43.0 66.2957 66.2809 0.0147 1.7167 0.5405 0.5404 87 43.5 66.8930 66.8749 0.0182 1.7250 0.5454 0.5452 88 44.0 67.4874 67.4660 0.0214 1.7333 0.5502 0.5500 89 44.5 68.0788 68.0543 0.0246 1.7417 0.5550 0.5548 90 45.0 68.6672 68.6397 0.0275 1.7500 0.5598 0.5596 91 45.5 69.2527 69.2224 0.0302 1.7583 0.5646 0.5644 92 46.0 69.8351 69.8024 0.0328 1.7667 0.5694 0.5691 93 46.5 70.4146 70.3796 0.0350 1.7750 0.5741 0.5738 94 47.0 70.9911 70.9541 0.0370 1.7833 0.5788 0.5785 95 47.5 71.5645 71.5259 0.0386 1.7917 0.5835 0.5831 96 48.0 72.1350 72.0950 0.0400 1.8000 0.5881 0.587897 48.5 72.7025 72.6616 0.0409 1.8083 0.5927 0.5924 98 49.0 73.2670 73.2255 0.0415 1.8167 0.5973 0.5970 99 49.5 73.8285 73.7869 0.0416 1.8250 0.6019 0.6016 100 50.0 74.3870 74.3457 0.0413 1.8333 0.6065 0.6061 101 50.5 74.9425 74.9019 0.0405 1.8417 0.6110 0.6107 102 51.0 75.4949 75.4557 0.0392 1.8500 0.6155 0.6152 103 51.5 76.0443 76.0069 0.0374 1.8583 0.6200 0.6197 104 52.0 76.5907 76.5557 0.0350 1.8667 0.6244 0.6242 105 52.5 77.1340 77.1021 0.0319 1.8750 0.6289 0.6286 106 53.0 77.6743 77.6460 0.0283 1.8833 0.6333 0.6330 107 53.5 78.2114 78.1875 0.0239 1.8917 0.6377 0.6375 108 54.0 78.7456 78.7267 0.0189 1.9000 0.6420 0.6419 109 54.5 79.2766 79.2635 0.0131 1.9083 0.6463 0.6462 110 55.0 79.8045 79.7979 0.0066 1.9167 0.6506 0.6506 111 55.5 80.3292 80.3300 -0.0008 1.9250 0.6549 0.6549 112 56.0 80.8509 80.8599 -0.0090 1.9333 0.6592 0.6592 113 56.5 81.3694 81.3874 -0.0180 1.9417 0.6634 0.6635 114 57.0 81.8847 81.9127 -0.0280 1.9500 0.6676 0.6678 115 57.5 82.3968 82.4357 -0.0389 1.9583 0.6718 0.6721 116 58.0 82.9058 82.9566 -0.0508 1.9667 0.6759 0.6763 117 58.5 83.4115 83.4752 -0.0637 1.9750 0.6800 0.6806 118 59.0 83.9140 83.9916 -0.0776 1.9833 0.6841 0.6848 119 59.5 84.4133 84.5059 -0.0927 1.9917 0.6882 0.6890 120 60.0 84.9092 85.0181 -0.1088 2.0000 0.6923 0.693124
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