机械原理大作业-连杆机构运动分析计算说明书.docx

机械原理大作业计算说明书机械原理大作业（一）连杆机构运动分析计算说明书作业名称： 连杆机构运动分析 设计题目： 第21题 院 系： 机电学院 班 级： * 设 计 者： * 学 号： * 指导教师： 陈明 丁刚 设计时间： 2015年5月 一、 运动分析题目如图1所示机构，已知机构各构件的尺寸为ab=170mm，=90，ac=110mm，cd=200mm，ce=320mm，ef=650mm，fg=500mm，h=380mm，构件1的角速度为1=10rad/s,试求构件7上点g的位移、速度和加速度，并对计算结果进行分析。图1二、 建立机构运动分析数学模型1、 建立以点e为原点的固定平面直角坐标系e-x,y,如图2所示。图22、对机构进行结构分析该机构由级机构ab、rpr级基本杆组bcd、rpr级基本杆组def、rrp级基本杆组fg组成。如图3所示：图33、数学模型（1）原动件ab（级机构）已知原动件ab的转角 1=0-2原动件ab的角速度 1=10rad/s原动件ab的角加速度 1=0运动副a的位置坐标 xa=110mm ya=320mm a点与机架相连，故该点速度和加速度均为0，即：运动副a的速度 vxa=0 vya=0运动副a的加速度 axa=0 aya=0原动件ab长度 lab=170mm可求出运动副b的位置坐标 xb=xa+labcos 1 yb=xa+labsin 1运动副b的速度 vxb= vxa -1 lab sin 1 vyb= vya+1 lab cos 1运动副b的加速度 axb= axa-12 lab cos 1-1lab sin 1 ayb=aya-12 lab sin 1+1lab cos 1（2） bcd（rpr级杆组）由（1）知c点位置坐标、速度、加速度运动副c点位置坐标 xc=0 yc=320mm c点与机架相连，即该点速度和加速度均为0,即：运动副c的速度 vxc=0 vyc=0运动副c的加速度 axc=0 ayc=0杆cd长 lcd=200mm 可求得bc杆相对于x轴正方向转角 2=arctanb0s0+a0c0a0s0-b0c0式中：a0=xb-xcb0=yb-ycc0=li+lk=0s0=a02+b02-c02化简得 2=arctanyb-ycxb-xccd杆相对于x轴正方向转角 3=2+/2求导可得bc杆角速度2、角加速度2和cd杆角速度3、角加速度3。根据同一构件上点的运动分析方法，可求出运动副d的位置坐标： xd=xc+lcdcos 3 yd=yc+lcdsin 3运动副d的速度 vxd= vxc 3 lcd sin 3 vyd= vyc+3 lcd cos 3运动副d的加速度 axd= axc-32 lcd cos 3-3lcd sin 3 ayd=ayc-32 lcd sin 3+3lcd cos 3（3） def（rpr级杆组）由（2）知d点位置坐标、速度、加速度运动副e点位置坐标 xe=0 ye=0e点与机架相连，即该点速度和加速度均为0,即：运动副e的速度 vxe=0 vye=0运动副e的加速度 axe=0 aye=0杆ef长 lef=650mm 可求得ef杆相对于x轴正方向转角 4=arctanb1s1+a1c1a1s1-b1c1式中：a1=xd-xeb1=yd-yec1=li+lk=0s1=a12+b12-c12化简得 4=arctanyd-yexd-xe求导可得ef杆角速度4、角加速度4。可求出运动副f的位置坐标 xf=xe+lefcos 4 yf=xe+lefsin 4运动副f的速度 vxf= vxe 4 lef sin 4 vyf= vyf+4 lef cos 4运动副f的加速度 axf= axe-42 lef cos 4-4lef sin 4 ayf=aye-42 lef sin 4+4lef cos 4（4） fg（rrp级杆组）由（3）知f点位置坐标、速度、加速度杆eflfg=500mm杆fg与x轴夹角5=arcsinyg-yflfg求导可得fg杆角速度5、角加速度55=（-q1sinj+q2cosj）/q35=（-q4sinj+q5cosj）/q3式中：j=0lj=0q1=vxk-vxf-5(s*sinj+ljcosj)q2= vyk - vyf + 5(s*cos5-ljsinj)q3= lfgsin5sinj+ lfgcos5cosjq4= 52 lfg cos5 52 s cos5- 2 vs 5 sin5q5= 52 lfg sin5 52 s sin5 + 2 vs 5 cos5（其中k为导轨参考点，保持固定不动）化简得：5= -vyf / (lfg cos5)5= (-axf +5 2lfg sin5) / (lfg cos5)得运动副g点位置坐标 xg=xf+lfgcos5 yg=700mm运动副g点速度 vxg= vxf 5 lfg sin 5 vyg = 0运动副g的加速度 axg= axf-52 lfg cos 5-5lfg sin 5 ayg=ayf-52 lfg sin 5+5lfg cos 5三、 计算流程框图四、 vb编写程序段1308102班 于洪鹏 制作学号：1130810210日期：2015/5/17option explicit 定义各点运动参数变量dim xa as double 点a的坐标，速度，加速度dim ya as doubledim vxa as doubledim vya as doubledim axa as doubledim aya as doubledim xb as double 点b的坐标，速度，加速度dim yb as doubledim vxb as doubledim vyb as doubledim axb as doubledim ayb as doubledim xc as double 点c的坐标，速度，加速度dim yc as doubledim vxc as doubledim vyc as doubledim axc as doubledim ayc as doubledim xd as double 点d的坐标，速度，加速度dim yd as doubledim vxd as doubledim vyd as doubledim axd as doubledim ayd as doubledim xe as double 点e的坐标，速度，加速度dim ye as doubledim vxe as doubledim vye as doubledim axe as doubledim aye as doubledim xf as double 点f的坐标，速度，加速度dim yf as doubledim vxf as doubledim vyf as doubledim axf as doubledim ayf as doubledim xg as double 点g的坐标，速度，加速度dim yg as doubledim vxg as doubledim vyg as doubledim axg as doubledim ayg as doubledim lab as double 杆ab的长度dim lcd as double 杆cd的长度dim lef as double 杆ef的长度dim lfg as double 杆fg的长度dim f1 as double 杆ab的角位移dim f2 as double 杆bc的角位移dim f3 as double 杆cd的角位移dim f4 as double 杆ef的角位移dim f5 as double 杆fg的角位移dim fj1 as double 循环变量dim w1 as double 杆ab的角速度dim w2 as double 杆bc的角速度dim w3 as double 杆cd的角速度dim w4 as double 杆ef的角速度dim w5 as double 杆fg的角速度dim e1 as double 杆ab的角加速度dim e2 as double 杆bc的角加速度dim e3 as double 杆cd的角加速度dim e4 as double 杆ef的角加速度dim e5 as double 杆fg的角加速度dim a0 as double bcd中的a0dim b0 as double bcd中的b0dim c0 as double bcd中的c0dim s0 as double bcd中的s0dim g1 as double bcd中的中间变量dim g2 as doubledim g3 as doubledim s1 as doubledim a1 as double def中的a1dim b1 as double def中的b1dim c1 as double def中的c1dim g4 as double def中的中间变量dim g5 as doubledim g6 as doubledim s2 as doubledim pi as double 圆周率dim pa as double 角度与弧度转换的系数dim i as double 循环变量private function arcsin(byval x as double) as double 定义arcsin函数 dim temp as double if x = 0 then temp = 0 else temp = atn(x / (sqr(1 - x * x) end if arcsin = tempend functionprivate sub form_load() 常量赋值 form1.windowstate = 2 lab = 170 lcd = 200 lef = 650 lfg = 500 w1 = 10 e1 = 0 xa = 110 ya = 320 vxa = 0 vya = 0 axa = 0 aya = 0 xc = 0 yc = 320 vxc = 0 vyc = 0 axc = 0 ayc = 0 xe = 0 ye = 0 vxe = 0 vye = 0 axe = 0 aye = 0 yg = 700 pi = 4 * atn(1) pa = pi / 180 fj1 = 0 timer1.interval = 20 timer1.enabled = falseend subprivate sub command1_click() 点g的位移 command2.setfocus set picture1.picture = nothing picture1.scale (-20, 960)-(400, -40) picture1.line (-20, 0)-(400, 0) x轴 picture1.line (0, 960)-(0, -40) y轴 for i = -20 to 400 step 50 x轴坐标 picture1.drawstyle = 2 picture1.line (i, 960)-(i, -40) picture1.currentx = i - 10: picture1.currenty = 0 picture1.print i next i for i = -40 to 960 step 40 y轴坐标 picture1.drawstyle = 2 picture1.line (-20, i)-(400, i) picture1.currentx = -20: picture1.currenty = i picture1.print i next i for fj1 = 0 to 360 step 0.01 f1 = fj1 * pa call ab call bcd call def call fg picture1.pset (fj1, xg), vbred 绘制位移图像 next fj1end subprivate sub command2_click() 点g的速度 command3.setfocus set picture2.picture = nothing picture2.scale (-20, 35000)-(400, -2000) picture2.line (-20, 0)-(400, 0) x轴 picture2.line (0, 35000)-(0, -2000) y轴 for i = -20 to 400 step 50 x轴坐标 picture2.drawstyle = 2 picture2.line (i, 35000)-(i, -2000) picture2.currentx = i - 10: picture2.currenty = 0 picture2.print i next i for i = -2000 to 35000 step 2000 y轴坐标 picture2.line (-20, i)-(400, i) picture2.currentx = -20: picture2.currenty = i picture2.print i next i for fj1 = 0 to 360 step 0.01 f1 = fj1 * pa call ab call bcd call def call fg picture2.pset (fj1, vxg), vbred 绘制速度图像 next fj1end subprivate sub command3_click() 点g的加速度 command4.setfocus set picture3.picture = nothing picture3.scale (-20, 2000000)-(400, -2000000) picture3.line (-20, 0)-(400, 0) x轴 picture3.line (0, 2000000)-(0, -2000000) y轴 for i = -40 to 400 step 50 x轴坐标 picture3.drawstyle = 2 picture3.line (i, 2000000)-(i, -2000000) picture3.currentx = i - 10: picture3.currenty = 0 picture3.print i next i for i = -2000000 to 2000000 step 200000 y轴坐标 picture3.line (-40, i)-(400, i) picture3.currentx = -25: picture3.currenty = i + 5 picture3.print i next i for fj1 = 0 to 360 step 0.01 f1 = fj1 * pa call ab call bcd call def call fg picture3.pset (fj1, axg), vbred 绘制加速度图像 next fj1end subprivate sub ab() ab构件运动分析子程序 xb = xa + lab * cos(f1) yb = ya + lab * sin(f1) vxb = vxa - w1 * lab * sin(f1) vyb = vya + w1 * lab * cos(f1) axb = axa - w1 2 * lab * cos(f1) - e1 * lab * sin(f1) ayb = aya - w1 2 * lab * sin(f1) + e1 * lab * cos(f1)end subprivate sub bcd() rpr级杆组bcd运动分析子程序 if xb xc and yb yc then 第一象限 f2 = atn(yb - yc) / (xb - xc) elseif xb = yc then 第二象限 f2 = atn(yb - yc) / (xb - xc) + pi elseif xb xc and yb xc and yb yc then y轴正向 f2 = 0.5 * pi elseif xb = xc and yb xe and yd ye then 第一象限 f4 = atn(yd - ye) / (xd - xe) elseif xd = ye then 第二象限 f4 = atn(yd - ye) / (xd - xe) + pi elseif xd xe and yd xe and yd ye then y轴正向 f4 = 0.5 * pi elseif xd = xe and yd ye then y轴负向 f4 = 1.5 * pi else end if g4 = (xd - xe) * cos(f4) + (yd - ye) * sin(f4) s2 = (vxd - vxe) * (xd - xe) + (vyd - vye) * (yd - ye) / g4 w4 = (vyd - vye) * cos(f4) - (vxd - vxe) * sin(f4) / g4 g5 = axd - axe + w4 2 * (xd - xe) + 2 * s2 * w4 * sin(f4) g6 = ayd - aye + w4 2 * (yd - ye) - 2 * s2 * w4 * cos(f4) e4 = (g6 * cos(f4) - g5 * sin(f4) / g4 xf = xe + lef * cos(f4) yf = ye + lef * sin(f4) vxf = vxe - w4 * lef * sin(f4) vyf = vye + w4 * lef * cos(f4) axf = axe - w4 2 * lef * cos(f4) - e4 * lef * sin(f4) ayf = aye - w4 2 * lef * sin(f4) + e4 * lef * cos(f4)end subprivate sub fg() rrp级杆组fg运动分析子程序 f5 = arcsin(yg - yf) / lfg) w5 = -vyf / (lfg * cos(f5) e5 = (-ayf + w5 2 * lfg * sin(f5) / (lfg * cos(f5) xg = xf + lfg * cos(f5) yg = yf + lfg * sin(f5) vxg = vxf - w5 * lfg * sin(f5) vyg = vyf + w5 * lfg * cos(f5) axg = axf - e5 * lfg * sin(f5) - w5 2 * lfg * cos(f5) ayg = ayf + e5 * lfg * cos(f5) - w5 2 * lfg * sin(f5)end subprivate sub command4_click() 开始/暂停 timer1.enabled = not timer1.enabled if timer1.enabled then command4.caption = 暂停 else command4.caption = 开始 end ifend subprivate sub timer1_timer() 动画程序 picture4.autoredraw = true set picture4.picture = nothing picture4.scale (-500, 800)-(1300, -100) picture4.line (-500, 0)-(1300, 0) x轴 picture4.line (0, 800)-(0, -100) y轴 for i = -500 to 1300 step 50 x轴坐标 picture4.drawstyle = 2 picture4.drawwidth = 1 线宽1 picture4.line (i, 800)-(i, -100) picture4.currentx = i - 10: picture4.currenty = 0 picture4.print i next i for i = -100 to 800 step 50 y轴坐标 picture4.drawstyle = 2 picture4.drawwidth = 1 线宽1 picture4.line (-500, i)-(1300, i) picture4.currentx = -25: picture4.currenty = i + 5 picture4.print i next i f1 = f1 + 0.005 * pi call ab call bcd call def call fg picture4.drawstyle = 1 实线 picture4.drawwidth = 2 线宽2 picture4.circle (xa, ya), 10 画铰链a picture4.circle (xb, yb), 10 画铰链b picture4.circle (xc, yc), 10 画铰链c picture4.circle (xd, yd), 10 画铰链d picture4.circle (xe, ye), 10 画铰链e picture4.circle (xf, yf), 10 画铰链f picture4.circle (xg, yg), 10 画铰链g picture4.line (xa, ya)-(xb, yb) ab picture4.line (xc + 350 * cos(f2), yc + 350 * sin(f2)-(xc, yc) bc picture4.line (xc, yc)-(xd, yd) cd picture4.line (xe, ye)-(xf, yf) ef picture4.line (xf, yf)-(xg, yg) fg picture4.line (-50, 700)-(1200, 700) g导轨 for i = 0 to 8 表示g导轨的虚线 picture4.line (1180 - 30 * i, 700)-(1180 - 30 * i - 20, 700 - 20) next i picture4.line (xg - 50, yg - 25)-(xg + 50, yg + 25), , b 滑块g picture4.line (xb - sqr(25 2 + 50 2) * cos(f2 + atn(1 / 2), yb - sqr(25 2 + 50 2) * sin(f2 + atn(1 / 2)-(xb - sqr(25 2 + 50 2) * cos(f2 - atn(1 / 2), yb - sqr(25 2 + 50 2) * sin(f2 - atn(1 / 2) 滑块b picture4.line (xb - sqr(25 2 + 50 2) * cos(f2 - atn(1 / 2), yb - sqr(25 2 + 50 2) * sin(f2 - atn(1 / 2)-(xb + sqr(25 2 + 50 2) * cos(f2 + atn(1 / 2), yb + sqr(25 2 + 50 2) * sin(f2 + atn(1 / 2) picture4.line (xb + sqr(25 2 + 50 2) * cos(f2 + atn(1 / 2), yb + sqr(25 2 + 50 2) * sin(f2 + atn(1 / 2)-(xb + sqr(25 2 + 50 2) * cos(f2 - atn(1 / 2), yb + sqr(25 2 + 50 2) * sin(f2 - atn(1 / 2) picture4.line (xb + sqr(25 2 + 50 2) * cos(f2 - atn(1 / 2), yb + sqr(25 2 + 50 2) * sin(f2 - atn(1 / 2)-(xb - sqr(25 2 + 50 2) * cos(f2 + atn(1 / 2), yb - sqr(25 2 + 50 2) * sin(f2 + atn(1 / 2) picture4.line (xd - sqr(25 2 + 50 2) * cos(f4 + atn(1 / 2), yd - sqr(25 2 + 50 2) * sin(f4 + atn(1 / 2)-(xd - sqr(25 2 + 50 2) * cos(f4 - atn(1 / 2), yd - sqr(25 2 + 50 2) * sin(f4 - atn(1 / 2) 滑块d picture4.line (xd - sqr(25 2 + 50 2) * cos(f4 - atn(1 / 2), yd - sqr(25 2 + 50 2) * sin(f4 - atn(1 / 2)-(xd + sqr(25 2 + 50 2) * cos(f4 + atn(1 / 2), yd + sqr(25 2 + 50 2) * sin(f4 + atn(1 / 2) picture4.line (xd + sqr(25 2 + 50 2) * cos(f4 + atn(1 / 2), yd + sqr(25 2 + 50 2) * sin(f4 + atn(1 / 2)-(xd + sqr(25 2 + 50 2) * cos(f4 - atn(1 / 2), yd + sqr(25 2 + 50 2) * sin(f4 - atn(1 / 2) picture4.line (xd + sqr(25 2 + 50 2) * cos(f4 - atn(1 / 2), yd + sqr(25 2 + 50 2) * sin(f4 - atn(1 / 2)-(xd - sqr(25 2 + 50 2) * cos(f4 + atn(1 / 2), yd - sqr(25 2 + 50 2) * sin(f4 + atn(1 / 2) for i = 0 to 30 picture4.line (xc, yc)-(xc + (30 - i) * cos(f2), yc + (30 - i) * sin(f2) picture4.line (xc + (30 - i) * cos(f2), yc + (30 - i) * sin(f2)-(xc + (30 - i) * cos(f3), yc + (30 - i) * sin(f3) picture4.line (xc + (30 - i) * cos(f3), yc + (30 - i) * sin(f3)-(xc, yc) next i picture4.line (0, 0)-(-20, -40) 铰链e picture4.line (0, 0)-(20, -40) picture4.line (-30, -40)-(30, -40) for i = 0 to 3 picture4.line (30 - 15 * i, -40)-(30 - 15 * i - 10, -40 - 10) next i picture4.line (0, 320)-(-20, 280) 铰链c picture4.line (0, 320)-(20, 280) picture4.line (-30, 280)-(30, 280) for i = 0 to 3 picture4.line (30 - 15 * i, 280)-(30 - 15 * i - 10, 280 - 10) next i picture4.line (110, 320)-(90, 280) 铰链a picture4.line (110, 320)-(130, 280) picture4.line (80, 280)-(140, 280) for i = 0 to 3 picture4.line (140 - 15 * i, 280)-(140 - 15 * i - 10, 280 - 10) next iend subprivate sub command5_click() 退出 endend sub五、 计算结果1、程序运行截图运动动画2、部分计算结果如下表所示：ab角位置(度)g位置(mm)g速度(mm/s)g加速度(mm/s2)0497.4937186-1517.857143-356.23028921494.8440185-1518.473706-350.33936222492.1932513-1519.080201-344.69453763489.5414339-1519.677063-339.30096064486.8885829-1520.264734-334.1638335484.234714-1520.843667-329.28841716481.5798419-1521.414323-324.68004037478.9239807-1521.977173-320.34409968476.2671436-1522.532696-316.28606639473.6093429-1523.081384-312.51149110470.9505903-1523.623735-309.026008611468.2908962-1524.16026-305.835343412465.6302704-1524.691477-302.945314613462.9687217-1525.217917-300.361841514460.306258-1525.74012-298.090949715457.6428861-1526.258636-296.138776616454.9786121-1526.774028-294.511577517452.3134409-1527.286868-293.215732218449.6473763-1527.797741-292.257751119446.9804215-1528.307241-291.644281920444.3125781-1528.815975-291.382116921441.6438471-1529.324564-291.478199522438.9742281-1529.833639-291.939632223436.3037196-1530.343843-292.773683724433.6323193-1530.855833-293.987797125430.9600233-1531.370279-295.589597526428.2868267-1531.887865-297.586900927425.6127236-1532.409288-299.987722628422.9377066-1532.93526-302.800285929420.2617671-1533.466505-306.033031530417.5848952-1534.003766-309.69462731414.9070798-1534.547798-313.793976532412.2283085-1535.099374-318.340230833409.5485673-1535.659281-323.342797734406.867841-1536.228324-328.811352535404.186113-1536.807326-334.75584