Harbin Institute of Technology机械原理大作业一课程名称：机械原理设计题目：连杆机构运动分析院系：班级：设计者：学号：指导教师：设计时间：22题：如图所示机构，已知机构各构件的尺寸为AB=120mm, BC=180mm ，CD=350mm, CE=300mm, h=100mm, EF=400mm, x D =130mm, y D =140mm ，构件1的角速度为ω=10rad/s 。

试求构件2上E 点的轨迹及构件5上F 点位移、速度和加速度，并对计算结果进行分析。

一、建立直角坐标系以A 点为直角坐标系的原点建立直角坐标系X-Y ，二、机构结构分析该机构由原动件AB 、机架及两个II 级杆组RRR 、RRP 组成。

两个II 级杆组如图所示。

RRP: RRR:+三、各基本杆组运动分析 1.原动件AB如图所示，已知原动件杆1的转角︒︒=360-0ϕ，pi =δ，角速度s rad /101==ωϕ，角加速度0==εϕ ，运动副A 的位置坐标为0,0==A A y x ，速度为0,0==A A y x ，加速度为0,0==A A yx ，原动件杆1的长度mm l AB 120=。

位置分析：)cos(δϕ+=i AB B l x )sin(δϕ+=i AB B l y 速度分析：)sin(δϕ+⨯⨯-=i AB xB l w v )sin(δϕ+⨯⨯-=i AB yB l w v 加速度分析：)sin()cos(2δϕδϕ+-+-=i AB i AB xB el l w a )()sin(2δϕδϕ+++-=i AB i AB yB coa el l w a 将已知参数带入可求出yB xB yB xB B B a a v v y x ,,,,,。

2.II 级杆组（RRR ）C 点：已知B 点参数（x B ，y B ，v xB ，v yB ，a xB ，a yB ），D 点的参数（x B ，y B ，v xB ，v yB ，a xB ，a yB ），杆2的长度L i , 杆3的长度L j ,可求得杆2的运动参数（f 2,w 2,e 2).位置分析：)(cos )(cos D j f l x i f l x x j i B C +=+= （1） )(sin )(sin C j f l y i f l y y j D i B +=+= （2） 连立（1）、（2）求得:02020200arctan 2)(C A C B A B i f +-+±=其中： )(2B D 0x x l A i -= )(2B D 0y y l B i -=2B D 2B D 2220)()(,y y x x l l l l C BD j BD i -+-=-+= 求得分f(i)后，带入（1）、（2），便可求得 f(j) ,速度分析：1B D /)]()([G v v S v v C w yB yD j x x j i -+-=CC ,y x1B D /)]()([G v v S v v C w yB yD j x x i j -+-= 其中： )(sin ),(cos i f l S i f l C i i i i == )(sin ),(cos j f l S j f l C j j j j ==)(sin )(sin B C j f l w v i f l w v v j j xD i i x x -=-= )(cos )(cos B j f l w v i f l w v v j j yD i i y yD +=+= 加速度分析：132/)(G S G C G e j j i += 132/)(G S G C G e i i j += 其中： j j i i xB xD C w C w a a G 222-+-= j j i i y y S w S w a a G 22B D 3-+-= )(cos )(sin 2B C i f l w i f l e a a i i i i x x --= )(sin )(cos 2B C i f l w i f l e a a i i i i y y -+=E 点：通过杆组RR （AB ）的分析，可易知B 点的运动参数（x B ，y B ，v xB ，v yB ，a xB ，a yB ），通过对II 级杆组RRR （杆2、3）的分析可知杆2的运动参数（f 2(i),w 2(i),e 2(i)）即可得杆BE 的运动参数（f(i),w(i),e(i)),引用RR 杆组模块，可求的E 点的运动参数（x E ，y E ，v xE ，v yE ，a xE ，a yE ）。

其中RR 类模块中A 点参数为B 的运动参数，杆AB 的角位移，角速度，角加速度为BE 杆参数。

位置分析：)(cos i f l x x AB A B += )(sin i f l y y AB A B += 速度分析：)(sin i f l w v v AB xA xB ⨯⨯-= )(sin i f l w v v AB yA yB ⨯⨯+=加速度分析：)(sin )(cos 2i f el i f l w a a AB AB xA xB --= )(sin )(cos 2i f el i f l w a a AB AB yA yB +-=3.II 级杆组RRP通过RR 杆组（BE ） 可求得E 点参数（x E ，y E ，v xE ，v yE ，a xE ，a yE ）,杆EF 的长Li,取参考点K 为（0，100），可得到F 点的运动参数（s F ,v F ,a F )。

其中引用RRP 杆组，B 点参数为E 点参数，CD 杆Lj 取0，参考点K 的运动参数（x K ，y K ，v xK ，v yK ，a xK ，a yK ）,导路运动参数（fj,wj,ej)，可求得F 的位移，速度，加速度。

位置分析：)(sin )(cos )(cos C j f l j f s x i f l x x j K i D -+=+= )(cos )(sin )(sin C j f l j f s y i f l y y j K i D ++=+= 可求得)(arcsin)(j f l l A i f ijk ++=，其中： )(cos )()(sin )(0j f y y j f x x A K D K D ---= 带入上式即可解的x G ,y G ,s速度分析：321/)(cos )(sin Q j f Q j f Q w i +-=（ 321/)(sin )(cos Q i f l Q i f l Q v i i D +-=（ 其中： ))(cos )(sin (1j f l j f s w v v Q j j xD xK +--= ))(sin )(cos (2j f l j f s w v v Q j j yD yK -+-= )(cos )(cos )(sin )(sin 3j f i f l j f i f l Q i i +=)(sin i f l w v v i i xD xG -= )(cos i f l w v v i i yD yG += 加速度分析：354/))(cos )(sin (Q j f Q j f Q e i +-= 354/))(sin )(cos (Q j f l Q i f l Q s i i i --= 其中：)(sin 2))(sin )(cos ())(cos )(sin ()(cos 224j f w v j f l j f s w j f l j f s e j f l w a a Q j s j j j j i i xD xK ---+-+-=)(cos 2))(sin )(sin ())(sin )(cos ()(sin 225j f w v j f l j f s w j f l j f s e j f l w a a Q j s j j j j i i yD yK ++--++-=)(sin 2)(cos )(sin )(cos 2D j f w v j f sw j f se j f a a a j s j j s xK x ---+=)(cos 2)(sin )(cos )(sin 2D j f w v j f sw j f se j f a a a j s j j s yK y +-++= 四、计算编程Private S(3600) As Double Private v(3600) As Double Private a(3600) As Double Private xE(3600) As Double Private yE(3600) As DoublePrivate Sub Form_Load() Dim i As Single Dim pi As Double Dim pa As Double Dim RR1 As RR Dim RR2 As RR Dim RRR1 As RRR Dim RRP1 As RRP Dim d1 As DoubleSet RR1 = New RR Set RR2 = New RR Set RRR1 = New RRR Set RRP1 = New RRP pi = 3.1415926 pa = pi / 180For i = 0 To 3600RR1.xA = 0: RR1.yA = 0 RR1.vxA = 0: RR1.vyA = 0 RR1.axA = 0: RR1.ayA = 0RR1.f = i * pa / 10: RR1.delt = 0 RR1.w = 10: RR1.e = 0 RR1.L = 120 RR1.cald1 = Sqr((RR1.xB - 130) ^ 2 + (RR1.yB + 140) ^ 2) If d1 > 530 Or d1 < 170 ThenS(i) = 0: v(i) = 0: a(i) = 0: xE(i) = 0: yE(i) = 0 GoTo S Else End IfRRR1.xB = 130: RRR1.yB = -140 RRR1.vxB = 0: RRR1.vyB = 0RRR1.axB = 0: RRR1.ayB = 0RRR1.xD = RR1.xB: RRR1.yD = RR1.yBRRR1.vxD = RR1.vxB: RRR1.vyD = RR1.vyBRRR1.axD = RR1.axB: RRR1.ayD = RR1.ayBRRR1.Li = 350: RRR1.Lj = 180RRR1.M = 1RRR1.calRR2.xA = RR1.xB: RR2.yA = RR1.yBRR2.vxA = RR1.vxB: RR2.vyA = RR1.vxBRR2.axA = RR1.axB: RR2.ayA = RR1.ayBRR2.f = RRR1.fj: RR2.delt = 0RR2.w = RRR1.wj: RR2.e = RRR1.ejRR2.L = 120RR2.calxE(i) = RR2.xB: yE(i) = RR2.yBRRP1.xB = RR2.xB: RRP1.yB = RR2.yBRRP1.vxB = RR2.vxB: RRP1.vyB = RR2.vyBRRP1.axB = RR2.axB: RRP1.ayB = RR2.ayBRRP1.Li = 400: RRP1.Lj = 0RRP1.fj = 0: RRP1.wj = 0: RRP1.ej = 0RRP1.xK = 0: RRP1.yK = 100:RRP1.vxK = 0: RRP1.vyK = 0RRP1.axK = 0: RRP1.ayK = 0RRP1.M = 1RRP1.calS(i) = RRP1.ss: v(i) = RRP1.vss / 1000: a(i) = RRP1.ass / 1000 S: Next iEnd SubPrivate Sub Command1_Click() 'D点轨迹Picture1.Scale (-500, 500)-(500, -500)Picture1.Line (-500, 0)-(500, 0) 'XPicture1.Line (0, 500)-(0, -500) 'YFor i = -500 To 500 Step 100 'X轴坐标Picture1.DrawStyle = 2Picture1.Line (i, 500)-(i, -500)Picture1.CurrentX = i - 10: Picture1.CurrentY = 0Picture1.Print iNext iFor i = -500 To 500 Step 100 'Y轴坐标Picture1.DrawStyle = 2Picture1.Line (-500, i)-(500, i)Picture1.CurrentX = -10: Picture1.CurrentY = iPicture1.Print iNext iFor i = 0 To 3600Picture1.PSet (xE(i), yE(i))Next iEnd SubPrivate Sub Command2_Click() 'G点位移Picture2.Scale (-10, 700)-(380, -100)Picture2.Line (-10, 0)-(380, 0) 'XPicture2.Line (0, 700)-(0, -100) 'YFor i = -10 To 380 Step 30 'X轴坐标Picture2.DrawStyle = 2Picture2.Line (i, 700)-(i, -100)Picture2.CurrentX = i - 10: Picture2.CurrentY = 0 Picture2.Print iNext iFor i = -100 To 700 Step 100 'Y轴坐标Picture2.DrawStyle = 2Picture2.Line (-10, i)-(380, i)Picture2.CurrentX = -10: Picture2.CurrentY = iPicture2.Print iNext iFor i = 0 To 3600Picture2.PSet (i / 10, S(i))Next iEnd SubPrivate Sub Command3_Click() 'G点速度Picture3.Scale (-10, 10)-(380, -10)Picture3.Line (-10, 0)-(380, 0) 'XPicture3.Line (0, 10)-(0, -10) 'YFor i = -10 To 380 Step 30 'X轴坐标Picture3.DrawStyle = 2Picture3.Line (i, 10)-(i, -10)Picture3.CurrentX = i - 10: Picture3.CurrentY = 0 Picture3.Print iNext iFor i = -10 To 10 Step 2 'Y轴坐标Picture3.DrawStyle = 2Picture3.Line (-10, i)-(380, i)Picture3.CurrentX = -10: Picture3.CurrentY = iPicture3.Print iNext iFor i = 0 To 3600Picture3.PSet (i / 10, v(i))Next iEnd SubPrivate Sub Command4_Click() 'G点加速度Picture4.Scale (-10, 25)-(380, -15)Picture4.Line (-10, 0)-(380, 0) 'XPicture4.Line (0, 25)-(0, -15) 'YFor i = -10 To 380 Step 30 'X轴坐标Picture4.DrawStyle = 2Picture4.Line (i, 25)-(i, -15)Picture4.CurrentX = i - 10: Picture4.CurrentY = 0 Picture4.Print iNext iFor i = -15 To 25 Step 5 'Y轴坐标Picture4.DrawStyle = 2Picture4.Line (-10, i)-(380, i)Picture4.CurrentX = -10: Picture4.CurrentY = iPicture4.Print iNext iFor i = 0 To 3600Picture4.PSet (i / 10, a(i))Next iEnd Sub五、计算结果E点轨迹F位移11F速度F 加速度（单位m/(s 2))。