平面連桿機構(gòu)的運動分析

1、大作業(yè)（一）平面連桿機構(gòu)的運動分析（題號：5E）西北農(nóng)林科技大學(xué)班 級：機制103學(xué) 號：2010012447姓 名： 同組其他人員：（2010012444）完成日期：2011年10月24日一、題目：計算平面連桿機構(gòu)的運動學(xué)分析1.圖a所示的為一平面六桿機構(gòu)。假設(shè)已知各構(gòu)件的尺寸如表1所示，原動件1以等角速度1=1rad/s沿著逆時針方向回轉(zhuǎn)，試求各從動件的角位移、角速度和角加速度以及E點的位移、速度和加速度的變化情況。ABCDEFG2345621xy11（a）表1 平面六桿機構(gòu)的尺寸參數(shù)（單位：mm） ，題 號l1l2l3l4l5l65E26.5105.667.587.547.237.890

2、題目要求：每兩人一組，每組中至少打印出一份源程序，每人計算出原動件從0360時（N=36）各運動變量的大小，并繪出各組對應(yīng)的運動線圖以及E點的軌跡曲線。二、平面連桿的運動分析方程(1)位置分析L1+L2=L4+L3 L1+L2+L2=AG+L5+L6 方程式（1） 將機構(gòu)的封閉矢量方程式（1）寫在兩坐標(biāo)上的投影形式：L1*cosq1+L2*cosq2=L4+L3*cosq3L1*sinq1+L2*sinq2=L3*sinq3L1*cosq1+L2*cosq2+L2*cos(q2-a)=xg+L5*cosq5+L6*cosq6L1*sinq1+L2*sinq2+L2*sin(q2-a)=yg+L

3、5*sinq5+L6*sinq6化簡整理后方程左邊僅含未知量項的形式，即得：L2*cosq2-L3*cosq3=L4-L1cosq1（1)L2*sinq2-L3*sinq3=-L1sinq1 （2） （式2）L2*cosq2+L2*cos(q2-a)-L5*cosq5-L6*cosq6=xg-L1*cosq1（3）L2*sinq2+L2*sin(q2-a)-L5*sinq5-L6*sinq6=yg-L1*sinq14）在求解（式2）中各變量時，用牛頓迭代法會比較直觀，但由于牛頓迭代法不便于限制L5、L6的位置，在有兩種位置均滿足上式時，無法限定它得出題中要求的解。故在計算時改用復(fù)述矢量法直接求

4、解q2、q3、q5、q6.求q2、q3：L2=L3+L4+L1-2*L3*L4*cosq3-2*L1*L3*cos(q3-q1)-2*L1*L4*cosq1經(jīng)整理后并可簡化為： A*sinq3+B*cosq3+C=0；式中： A=2*L1*L3*sinq1 B=2*L3*(L1*cosq1-L4) B=L2-L1-L3-L4+2*L1*L4*sinq1解之可得 ： tan(q3/2)=Asqrt(A+B-C)/(B-C) Eq5FG實際運動中0q3p，故適當(dāng)選擇：tanq2=(L3*sinq3-L1*sinq1)/(L4+L3*cosq3-L1sinq1) 求q5、q6： 先有 xe=L4+L

5、3*cosq3+L2*cos(q2-a) (式3 ) ye=L3*sinq3+L2*sin(q2-a) tan =(yg-ye)/(xg-xe) cos=(xe-xg)+（ye- yg)+L5-L6/2*L5*sqrt(xe-xg)+（te-yg)則 q5=- q5=q5 tanq6=(ye+L5*sinq5-yg)/(xe+L5*cosq5-xg)（2）角速度分析分別將（式2）（式3）對時間求一次導(dǎo)數(shù)，可得-L2*w2*sinq2+L3*w3*sinq3=L1*w1*sinq1L2*w2*cosq2-L3*w3*cosq3=-L1*w1*cosq1-w2(L2*sinq2+L2sin(q2-

6、a)+L5*w5*sinq5+L6*w6*sinq6=L1*w1*sinq1 w2*(L2*cosq2+L2*cos(q2-a)-L5*w5*cosq5-L6*w6*cosq6=-L1*w1*cosq1（式4）vex=-L3*w3*sinq3-L2*w2*sin(q2-a)vey=L3*w3*cosq3+L2*w2*cos(q2-a) （式5）解之可得w2,w3.w5,w6,vex,vey.將（式4）（式5）寫成矩陣形式：-L2*sinq2 L3*sinq3 0 0 w2 L1*sinq1L2*cosq2 -L3*cosq3 0 0 w3 = w1 -L1*cosq1-L2*sinq2-L2*

7、sin(q2-a) 0 L5*sinq5 L6*sinq6 w5 L1*sinq1 L2*cosq2+L2*cos(q2-a) 0 L5*cosq5 -L6*cosq6 w6 -L1*cosq1（式6）E點速度vex w3 -L3*sinq3 -L2*sin(q2-a) vey w2 L3*cosq3 L2cos(q2-a) (式7）采用高斯消去法可求解（式6）可解得角速度w2,w3,w5,w6;將求解結(jié)果帶入（式7）可求得vex,vey.（3）角加速度分析分別將（式2）（式3）對時間取二次導(dǎo)數(shù)，可得加速度關(guān)系 -L2*sinq2 L3*sinq3 0 0 a2 L2*cosq2 -L3*co

8、sq3 0 0 a3 -L2*sinq2-L2*sin(q2-a) 0 L5*sinq5 L6*sinq6 a5 L2*cosq2+L2*cos(q2-a) 0 -L5*cosq5 L6*cosq6 a6 -w2*L2*cosq2 w3*L3*cosq3 0 0 w2 L1*w1*cosq1= -w2*L2*sinq2 w3*L3*sinq3 0 0 w3 + w1 L1*w1*sinq1 w2*L2*cosq2+w2*L2*cos(q2-a) 0 w5*L5*cosq5 w6*L6*cosq6 w5 L1*w1*cosq1 w2*L2*sinq2+w2*L2*sin(q2-a) 0 w5*L

9、5*sinq5 w6*L6*sinq6 w6 L1*w1*sinq1（式8）E點的加速度 aex -L2*sin(q2-a) -L3*sinq3 a2 L2*cos(q2-a) L3*cosq3 w2 Aey L2*cos(q2-a) L3*cosq3 a3 L2*sin(q2-a) L3*sinq3 w3采用高斯消去法可求解（式8）可解得角加速度2，3，5，6；將求解結(jié)果代入（式9）可求得aEx,aEy.三、程序流程圖調(diào)用高斯消去法子程序求解方程（6）求得w2,w3,w4,w5及w6再求出vEx及vEy調(diào)用高斯消去法子程序求解加速度方程（8）求得2，3，5，6，再求出aEx,aEyJ=l,N

10、開始讀入:l1,l2,l2,l3,l4,l5,l6,xG,yG,wlI=(I-1)*10調(diào)用牛頓迭代法法子程序求解方程（2）求得2,3,4,5及6并計算xG及yG調(diào)用系數(shù)矩陣A子程序，并計算A調(diào)用原動件位置參數(shù)B子程序，并計算BB(J)=B(J)w1J=l,N調(diào)用系數(shù)矩陣A子程序，并計算其矩陣DA調(diào)用系數(shù)矩陣B子程序，并計算其矩陣DBW(1)=w1,w(2)=w3W(3)=w4,w(4)=w5DB(K)=DB(K)w1K=l,NB(K)=-B(k,II)w1(II)+DB(K)II=l,N打印結(jié)果結(jié)束四、計算源程序#include#include#include#define PI 3.141

11、5926#define N 4void Solutionangle(double 18,double ); /*矢量法求角位移*/void Solutionspeed(double NN,double N,double 18,double ); /*角速度求解*/void Solutionacceleration(double NN,double NN,double N,double 18);/*角加速度求解*/void GaussianE(double NN,double N,double N);/*高斯消去*/void FoundmatrixA(double 18,double NN);/

12、*創(chuàng)建系數(shù)矩陣A*/void FoundmatrixB(double 18,double ,double N);/*創(chuàng)建系數(shù)矩陣B*/void FoundmatrixDA(double 18,double NN);/*創(chuàng)建矩陣DA*/void FoundmatrixDB(double 18,double ,double N);/*創(chuàng)建矩陣DB*/*定義全局變量*/double l1=26.5,l2=105.6,l3=67.5,l4=87.5,l5=47.2,l6=37.8;double l2g=65.0,xg=153.5,yg=41.7,inang=90*PI/180,as1=1.0;/*主函

13、數(shù)*/int main() int i,j; FILE *fp; double shuju3618; double psvalue18,aNN,daNN,bN,dbN,ang1; /*建立文件，并制表頭*/ if(fp=fopen(數(shù)據(jù).txt,w)=NULL) printf(Cannt open this file.n); exit(0); fprintf(fp,n The Kinematic Parameters of Point 5n); fprintf(fp, ang2 ang3 ang5 ang6); fprintf(fp, as2 as3 as5 as6); fprintf(fp,

14、 aas2 aas3 aas5 aas6); fprintf(fp, xe ye vex vey aex aeyn); /*計算數(shù)據(jù)并寫入文件*/ for(i=0;i36;i+) ang1=i*PI/18; Solutionangle(psvalue,ang1); FoundmatrixB(psvalue,ang1,b); FoundmatrixA(psvalue,a); Solutionspeed(a,b,psvalue,ang1); FoundmatrixDA(psvalue,da); FoundmatrixDB(psvalue,ang1,db); Solutionacceleration

15、(a,da,db,psvalue); for(j=0;j4;j+) shujuij=psvaluej*180/PI; for(j=4;j18;j+) shujuij=psvaluej; fprintf(fp,n); for(j=0;j18;j+) fprintf(fp,%12.3f,shujuij); fclose(fp); /*輸出數(shù)據(jù)*/ for(i=0;i36;i+) ang1=i*PI/18; printf(n輸出ang1=%d時的求解n,i*10); printf(angle angspeed angacceleration :n); for(j=0;j4;j+) printf(%l

16、ft,shujuij); printf(n);for(j=4;j8;j+) printf(%lft,shujuij); printf(n); for(j=8;j12;j+) printf(%lft,shujuij); printf(n); for(j=12;j18;j+) printf(%lft,shujuij); printf(n); return 0;/*矢量法求角位移*/void Solutionangle(double value18,double ang1) double xe,ye,A,B,C,phi,alpha,csn,ang5g,d2,d,ang2,ang3,ang5,ang6

17、; A=2*l1*l3*sin(ang1); B=2*l3*(l1*cos(ang1)-l4); C=l2*l2-l1*l1-l3*l3-l4*l4+2*l1*l4*cos(ang1); ang3=2*atan(A+sqrt(A*A+B*B-C*C)/(B-C); if(ang30) /*限定ang3大小*/ ang3=2*atan(A-sqrt(A*A+B*B-C*C)/(B-C); ang2=asin(l3*sin(ang3)-l1*sin(ang1)/l2); xe=l4+l3*cos(ang3)+l2g*cos(ang2-inang); ye=l3*sin(ang3)+l2g*sin(

18、ang2-inang); phi=atan2(yg-ye),(xg-xe); d2=(yg-ye)*(yg-ye)+(xg-xe)*(xg-xe); d=sqrt(d2); csn=(l5*l5+d2-l6*l6)/(2.0*l5*d); alpha=atan2(sqrt(1.0-csn*csn),csn); ang5g=phi-alpha; ang5=ang5g-PI; ang6=atan2(ye+l5*sin(ang5g)-yg,xe+l5*cos(ang5g)-xg); value0=ang2;value1=ang3;value2=ang5;value3=ang6; value12=xe

19、;value13=ye; /*限定角度大小*/ int i; for(i=0;i2*PI) valuei-=2*PI; while(valuei0) valuei+=2*PI; /*角速度求解*/void Solutionspeed(double a2NN,double b2N,double value18,double ang1) double ang2,ang3; ang2=value0;ang3=value1; double p2N; GaussianE(a2,b2,p2); value4=p20; value5=p21; value6=p22; value7=p23; value14=

20、-l3*value5*sin(ang3)-l2g*value4*sin(ang2-inang); value15=l3*value5*cos(ang3)+l2g*value4*cos(ang2-inang);/*角加速度求解*/void Solutionacceleration(double a3NN,double da3NN,double db3N,double value18) int i,j; double ang2,ang3; ang2=value0;ang3=value1; double bkN=0; double p3N; for(i=0;iN;i+) for(j=0;jN;j+)

21、 bki+=-da3ij*value4+j; bki+=db3i*as1; GaussianE(a3,bk,p3); value8=p30; value9=p31; value10=p32; value11=p33; value16=-l3*value9*sin(ang3)-l3*value5*value5*cos(ang3)-l2g*value8*sin(ang2-inang)-l2g*value4*value4*cos(ang2-inang); value17=l3*value9*cos(ang3)-l3*value5*value5*sin(ang3)+l2g*value8*cos(ang

22、2-inang)-l2g*value4*value4*sin(ang2-inang);/*高斯消去法解矩陣方程*/void GaussianE(double a4NN,double b4N,double p4N) int i,j,k; double a4gNN,b4gN,t; for(i=0;iN;i+) for(j=0;jN;j+) a4gij=a4ij; for(i=0;iN;i+) b4gi=b4i; /*使主對角線上的值盡可能大*/ if(a4g00a4g11) for(j=0;jN;j+) t=a4g0j;a4g0j=a4g1j;a4g1j=t; t=b4g0;b4g0=b4g1;b

23、4g1=t; if(a4g22a4g33) for(j=0;jN;j+) t=a4g2j;a4g2j=a4g3j;a4g3j=t; t=b4g2;b4g2=b4g1;b4g3=t; /*初等行變換*/ for(j=0;jN;j+) for(i=0;iN;i+) if(i!=j) for(k=0;kN;k+) if(k!=j) a4gik-=a4gij/a4gjj*a4gjk; b4gi-=b4gj*a4gij/a4gjj; a4gij=0; for(i=0;iN;i+) b4gi/=a4gii; p40=b4g0; p41=b4g1; p42=b4g2; p43=b4g3;/*創(chuàng)建系數(shù)矩陣A*

24、/void FoundmatrixA(double value518,double a5NN) double ang2,ang3,ang5,ang6; ang2=value50;ang3=value51;ang5=value52;ang6=value53; a500=-l2*sin(ang2);a501=l3*sin(ang3); a510=l2*cos(ang2);a511=-l3*cos(ang3); a520=-l2*sin(ang2)-l2g*sin(ang2-inang); a522=l5*sin(ang5);a523=l6*sin(ang6); a530=l2*cos(ang2)+

25、l2g*cos(ang2-inang); a532=-l5*cos(ang5);a533=-l6*cos(ang6); a502=a503=a512=a513=a521=a531=0;/*創(chuàng)建系數(shù)矩陣B*/void FoundmatrixB(double value618,double ang1,double b6N) b60=b62=l1*sin(ang1)*as1; b61=b63=-l1*cos(ang1)*as1;/*創(chuàng)建矩陣DA*/void FoundmatrixDA(double value718,double da7NN) double ang2,ang3,ang5,ang6,a

26、s2,as3,as5,as6; ang2=value70;ang3=value71;ang5=value72;ang6=value73; as2=value74;as3=value75;as5=value76;as6=value77; da700=-l2*as2*cos(ang2);da701=l3*as3*cos(ang3); da710=-l2*as2*sin(ang2);da711=l3*as3*sin(ang3); da720=as2*(-l2*cos(ang2)-l2g*cos(ang2-inang); da722=as5*l5*cos(ang5);da723=as6*l6*cos(

27、ang6); da730=as2*(-l2*sin(ang2)-l2g*sin(ang2-inang); da732=as5*l5*sin(ang5);da733=as6*l6*sin(ang6); da702=da703=da712=da713=da721=da731=0;/*創(chuàng)建矩陣DB*/void FoundmatrixDB(double value818,double ang1,double db8N) db80=db82=l1*as1*cos(ang1); db81=db83=l1*as1*sin(ang1);5、 計算結(jié)果數(shù)據(jù)轉(zhuǎn)角ang2ang3ang5ang6as2as3036.

28、79969.573210.375349.905-0.434-0.4341032.70966.003212.118345.238-0.379-0.2762029.27864.073211.589339.939-0.306-0.1113026.59763.731209.276334.605-0.2310.0394024.63664.755205.562329.184-0.1630.1615023.30166.865200.836323.398-0.1060.2566022.4969.79195.54317.027-0.0580.3257022.11373.301190.166310.051-0.0

29、190.3748022.09977.209185.201302.6670.0150.4059022.39681.365181.043295.1970.0440.42410022.96885.644177.918287.9660.070.43111023.7989.946175.87281.230.0940.42812024.84694.183174.793275.1490.1170.41813026.12398.28174.485269.8190.1390.414027.615102.17174.7265.2920.160.37715029.314105.794175.174261.610.1

30、80.34716031.211109.099175.659258.8050.1990.31317033.293112.039175.928256.8990.2170.27418035.542114.577175.803255.8880.2320.23219037.932116.679175.164255.730.2450.18820040.431118.319173.95256.3370.2540.1421042.996119.475172.161257.5830.2580.09122045.574120.129169.838259.3250.2560.0423048.103120.26167

31、.054261.4310.248-0.01424050.51119.848163.901263.7990.232-0.06925052.711118.867160.497266.3870.207-0.12826054.609117.285157.001269.2340.171-0.18927056.095115.063153.65272.50.124-0.25628057.048112.159150.817276.5220.064-0.32629057.34108.528149.138281.893-0.008-0.40130056.841104.141149.701289.595-0.093

32、-0.47731055.44399.006154.274301.031-0.188-0.54932053.08493.203164.892317.269-0.284-0.60833049.79786.931180.855335.709-0.371-0.6434045.75580.55195.897348.494-0.432-0.62735041.28174.575205.485352.141-0.455-0.558as5as6aas2aas3aas5aas6xe0.463-0.9350.2320.833-0.867-1.2149.9940.278-1.1080.3860.953-0.1670.

33、119150.0760.166-1.1350.4370.9180.0680.667148.80.096-1.1080.4150.7850.1280.835146.4760.058-1.0670.3590.6210.120.839143.3830.051-1.0220.2990.4650.070.772139.7330.071-0.970.2480.333-0.0160.667135.683-0.525-0.7230.2070.2260.239-0.24131.364-0.462-0.7480.1780.140.47-0.05126.897-0.366-0.740.1570.070.6020.1

34、42122.4-0.258-0.7020.1430.0120.6240.287117.991-0.153-0.6430.133-0.0380.5610.379113.784-0.065-0.5720.127-0.0810.4430.431109.8870-0.4940.123-0.1190.2990.462106.3990.039-0.4110.119-0.1530.1490.484103.3990.052-0.3250.114-0.1830.0040.503100.9520.041-0.2360.106-0.209-0.1250.51699.0970.01-0.1460.096-0.231-

35、0.2290.51597.851-0.037-0.0570.082-0.25-0.2980.49197.21-0.0920.0240.062-0.265-0.3320.4497.151-0.1510.0950.038-0.277-0.3320.36797.634-0.2070.1520.008-0.288-0.3070.28498.613-0.2570.194-0.027-0.299-0.2660.206100.039-0.2990.225-0.069-0.311-0.2120.148101.868-0.330.248-0.118-0.326-0.1450.122104.068-0.3480.

36、27-0.173-0.344-0.0560.143106.626-0.3470.302-0.235-0.3660.0760.232109.546-0.3170.357-0.305-0.3910.2860.42112.853-0.2390.457-0.379-0.4170.6390.755116.584-0.0790.634-0.454-0.4351.2511.311120.7740.2210.931-0.518-0.4322.2682.138125.4240.7321.38-0.555-0.3893.5692.909130.4651.4921.882-0.538-0.2762.480.8681

37、35.6971.8781.689-0.441-0.07-2.4-5.689140.7591.3940.549-0.2520.229-4.672-7.471145.1460.807-0.445-0.0040.564-2.538-3.887148.338yevexveyaexaey11.2074.869-27.149-52.40826.5456.973-3.703-20.892-44.82242.8634.009-10.61-12.997-34.28745.5292.408-15.753-5.565-25.03838.531.97-19.490.229-18.1627.5982.373-22.1944.072-13.03516.6413.288-24.0916.141-8.7957.4284.434-25.2816.796-4.8650.4465.6-25.7926.423-0.988-4.3716.638-25.6275.3822.879-7.2637.458-