2）速度分析
对式（22）求导一次，整理得：
l’1cosθ1 - l’2cosθ2 = E2 图5 l’1sinθ1 - l’2sinθ2 = F2 (25)
其中：E2 =u’ + A6θ’1 – A8θ’2 ，F2 = v’ - A5θ’1 – A7θ’2 ，A5 = l1cosθ1 + h1sinθ1 ， A6 = l1sinθ1 - h1cosθ1 ，A7 = l2cosθ2 - h2sinθ2 ，A8 = l2sinθ2+ h2cosθ2 。
由（25）解得：
l’1=（F2 cosθ2 - E2sinθ2）/ D8
l’2=（F2 cosθ1 - E2sinθ1) / D8 (26)
P3点的速度为对式（24）求导得： x’3 = x’1 + l’1cosθ1 + A6θ’1
y’3 = y’1 + l’1sinθ1 - A5θ’1 (27)
3） 加速度分析
对式（25）求导一次，整理得： l’’1cosθ1 - l’’2cosθ2 = E3
l’’1sinθ1 - l’’2sinθ2 = F3 (28)
2 2
其中：E3 = u’’ + 2A3l’1θ’1 + A5θ’1+ A6θ’’1–2A4l’2θ’2–A7θ’2– A8θ’’2 ，
2 2
F3 = v’’ - 2A1l’1θ’1 + A6θ’1- A5θ’’1 +2A2l’2θ’2–A8θ’2+ A7θ’’2 。 解（28）式得：
l’’1=（F3 cosθ2 – E3sinθ2） / D8
l’’2=（F3 cosθ1 – E3sinθ1） / D8 (29)
P3点的加速度为对式（27）求导得：
2
x’’3 = x’’1 + A1l’’1 - 2A3l’1θ’1 - A5θ’1- A6θ’’1
2
y’’3 = y’’1 + A3l’’1 - 2A1l’1θ’1 - A6θ’1- A5θ’’1 (30) 由上述式子可设计出 PRP杆组运动分析子程序（见程序单）。
6．RPP杆组运动分析子程序
图6所示RPPⅡ级杆组中，已知导路1参考点P1和外转动副P2的运动，h为外副P2
至导路2的垂直距离，导路1的方位角、角速度、角加速度（θ1，θ’1，θ’’1）已知，导路1与导路2间的夹角为?。要求确定导路1，2移动的位移、速度及加速度（l1，l2，l’1，l’2，l’’1，l’’2）以及导路中心P3，P4点的运动（x3，x4，x’3，x’4，x’’3，x’’4，y3，y4，y’3，y’4，y’’3， y’’4）。
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1）位置分析
推导l1，及l2的方程式：
x1+l1cosθ1+l2cos（θ1+?）= x2+hsin（θ1+?） y1+l1sinθ1+l2sin（θ1+?）= y2-hcos（θ1+?）
整理得：
l1cosθ1 + l2cos（θ1+?）= E1
l1sinθ1 + l2sin（θ1+?）= F1 (31) 其中：E1 = u + A1h，F1 = v –A2h，
A1 =sin（θ1+?），A2 =cos（θ1+?）。 由于θ1 ，? 均已知，由此解得： l1 =（E1 sin（θ1+?）- F1 cos（θ1+?））/ D8 l2 =（F1 cosθ1 - E1sinθ1）/ D8 (32)
其中：D8 =A1A4-A2A3=sin?，A3 =sinθ1 ，A4 =cosθ1 图6
P3、P4点的位置为：
x3 = x1 + l1 cosθ1 ，y3 = y1 + l1 sinθ1 x4 = x2 + h sin（θ1+?），y4 = y2 - hcos（θ1+?） (33) 当给定P1、P2点的位置，杆长h的大小和导路的方向角θ1、? 后，RPP杆组可能有两种形式，即图6中的实线和虚线两种形式，这可用h为“+”（实线机构）和h为“-”（虚线机构）来确定。
此外，从式（32）可以看出，为保证机构能够正常运动，两导路之间的夹角? 不能为0，再考虑到加工和装配等因素以及摩擦的存在，工程实际中，一般要求?sin??? 0.1。
2）速度分析
对式（31）求导一次，整理得： l’1cosθ1 + l’2cos（θ1+?）= E2
l’1sinθ1 + l’2sin（θ1+?）= F2 (34)
其中：E2 =u’ +θ’1（A2h + A3l1 + A1l2），F2 = v’ -θ’1（A1h - A4l1 - A2l2）。 由式（34）解得：
l’1 =（E2 sin （θ1+?）- F2 cos（θ1+?））/ D8
l’2 =（F2 cosθ1- E2 sinθ1 ) / D8 (35)
P3、P4点的速度为对式（33）求导得：
x’3 = x’1 + A4l’1 – A3l1θ’1，y’3 = y’1 + A3l’1 + A4l1θ’1
x’4 = x’2 + A2 hθ’1 ，y’4 = y’2 + A1 hθ’1 (36)
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3） 加速度分析
对式（34）求导一次，整理得： l’’1cosθ1 + l’’2cosθ2 = E3
l’’1sinθ1 + l’’2sinθ2 = F3 (37)
2
其中：E3 = u’’ +θ’’1（A2h +A3l1 +A1l2）-θ’1（A1h -A4l1 - A2l2）+ 2θ’1（A3l’1 +A1l’2）
2
F3 = v’’ +θ’’1（A1h -A4l1 -A2l2）+θ’1（A2h –A3l1 – A1l2）- 2θ’1（A4l’1 +A2l’2） 解（37）式得：
l’’1 =（E3 sin （θ1+?）- F3 cos（θ1+?））/ D8
l’’2 =（F3 cosθ1 – E3sinθ1）/ D8 (38) P3、P4点的加速度为对式（36）求导得：
2
x’’3 = x’’1 + A4l’’1 - A3l1θ’’1 - 2A3l’1θ’1–A4l1θ’1
2
y’’3 = y’’1 + A3l’’1 + A4l1θ’’1 + 2A4l’1θ’1–A3l1θ’1
2
x’’4 = x’’2 + A2 hθ’’1–A1 hθ’1
2
y’’4 = y’’2 + A1 hθ’’1 + A2 hθ’1 (39) 由上述式子可设计出 RPP杆组运动分析子程序（见程序单）。
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''机械原理平面机构运动分析子程序
（含单杆，RRR，RRP，RPR，PRP， RPP杆组）
Public Const PI = 3.1415926 '定义常量
''定义全局变量
Public l As Single, l 1 As Single, l v1 As Single, l a1 As Single Public l 2 As Single, l v2 As Single, l a2 As Single Public r As Single, af As Single，dt As Single Public ct As Single, cv As Single, ca As Single Public ct1 As Single, cv1 As Single, ca1 As Single Public ct2 As Single, cv2 As Single, ca2 As Single
Public u As Single, v As Single, u1 As Single, v1 As Single, u2 As Single, v2 As Single Public x1 As Single, y1 As Single, xv1 As Single, yv1 As Single, xa1 As Single, ya1 As Single
Public x2 As Single, y2 As Single, xv2 As Single, yv2 As Single, xa2 As Single, ya2 As Single
Public x3 As Single, y3 As Single, xv3 As Single, yv3 As Single, xa3 As Single, ya3 As Single
Public x4 As Single, y4 As Single, xv4 As Single, yv4 As Single, xa4 As Single, ya4 As Single
''定义中间变量
Public w As Single
Public a1 As Single, a2 As Single, a3 As Single, a4 As Single Public a5 As Single, a6 As Single, a7 As Single, a8 As Single
Public c As Single, d As Single, d7 As Single, d8 As Single, h1 As Single, h2 As Single Public e As Single, e1 As Single, e2 As Single, e3 As Single Public f As Single, f1 As Single, f2 As Single, f3 As Single Public g As Single, h As Single, i1 As Single Public k As Single, k1 As Single, k2 As Single Public n As Single, n7 As Single Public m As Integer, kp As Integer
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'''''各公共子程序
''单杆运动分析子程序
Public Sub SSL() x2 = x1 + l * Cos(ct) y2 = y1 + l * Sin(ct)
x3 = x1 + r * Cos(ct + af) y3 = y1 + r * Cos(ct + af) If (kp = 1) Then
xv2 = xv1 - l * Sin(ct) * cv yv2 = yv1 + l * Cos(ct) * cv
xa2 = xa1 - l * Sin(ct) * ca - l * Cos(ct) * cv * cv ya2 = ya1 + l * Cos(ct) * ca - l * Sin(ct) * cv * cv xv3 = xv1 - (y3 - y1) * cv yv3 = yv1 + (x3 - x1) * cv
xa3 = xa1 - (y3 - y1) * ca - (x3 - x1) * cv * cv ya3 = ya1 + (x3 - x1) * ca - (y3 - y1) * cv * cv End If End Sub
''RRR杆组运动分析子程序 Public Sub RRR() u = x2 - x1 v = y2 - y1 u1 = xv2 - xv1 v1 = yv2 - yv1 u2 = xa2 - xa1 v2 = ya2 - ya1
c = (u * u + v * v + l 2 * l 2 – l 1 * l 1) / 2 / l 2 k = v * v + u * u - c * c If (k < 0) Then
MsgBox \机械原理\Else
n7 = v + m * Sqr(k) d7 = u – c
If (Abs(d7 < 0.0000001) Then ct2 = PI Eles
ct2 = 2 * Atn(n7 / d7) End If
If (d7 < 0 And n7 > 0) Then ct2 = ct2 + 2 * PI Else
If (d7 < 0 And n7 < 0) Then ct2 = ct2 - 2 * PI
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机械原理基本杆组分析法
