远动学 曲柄连杆机构 AB杆作平面运动 平面运动的分解 (请看动画)
26 曲柄连杆机构 AB杆作平面运动 平面运动的分解 （请看动画）
means 8 9-3 velocity of any point in a plane figure 1. pole-based method (composition method) VBA The velocity of point A in figure SvA and the rotational velocity o of the B VA figure are given, find vB Select a as the pole, and fix the moving reference system to point A The motion of the moving system is translation. Consider the moving point b, its motion can be viewed as the composition of the translation, the convected motion, and the rotation, the relative motion v, =VB;Ve=VA; V=vba, magnitude @. AB, direction 1 AB, point to the rotation direction v=v tV. Employ the theorem of velocity composition the velocity at point b can be expressed as VR=v B 4+D BA 27
27 §9-3 velocity of any point in a plane figure Employ the theorem of velocity composition , a e r v = v + v the velocity at point B can be expressed as B A BA v = v +v v v ;v v ;v v , a = B e = A r = B A The velocity of point A in figure S and the rotational velocity of the figure are given, find . Select A as the pole, and fix the moving reference system to point A. The motion of the moving system is translation. Consider the moving point B, its motion can be viewed as the composition of the translation, the convected motion, and the rotation, the relative motion point to the rotation direction. A v B v 1. pole-based method (composition method) magnitude AB,direction ⊥ AB
远动学 §9-3平面图形内各点的速度 基点法(合成法) 已知:图形S内一点A的速度v4, 14 图形角速度o求:VB 取A为基点,将动系固结于A点, 动系作平动。 取B动点,则B的运动可视为牵连运动为平动和相对运动 为圆周运动的合成v=vB;2=下A;=B4,大小OAB,方向⊥AB 指向与转向一致. 根据速度合成定理p=下+下,则B点速度为 V=V+y B BA 28
28 §9-3 平面图形内各点的速度 根据速度合成定理 , a e r v = v + v 则Ｂ点速度为： B A BA v = v +v 一．基点法（合成法） 取B为动点, 则B点的运动可视为牵连运动为平动和相对运动 为圆周运动的合成 v =v ;v =v ;v =v , 大小AB,方向⊥AB, a B e A r BA 已知：图形S内一点A的速度 ， 图形角速度 求： 指向与 转向一致． 取A为基点, 将动系固结于A点, 动系作平动。 A v B v
Kinematics That is, the velocity of any point in the figure is obtained as the geometric sum of the velocity of the pole and the relative rotational velocity with respect to the pole. Such a method of finding the velocity is called pole-based method, or composition method, which is a basic method to find the velocity of a point in a figure 2. Velocity projection method Since point A and b are arbitrarily selected the equation =v+VBA gives the relationship between the velocities of any two point in the figure. Noting that vri LAB projecting this equation to AB, gives B」AB =lv A JAB theorem of velocity projection e, the velocity projections of any two point in a figure on the line linking these two points are identical. This method for find the velocity of a point is called velocity projection method 29
29 Since point A and B are arbitrarily selected, the equation gives the relationship between the velocities of any two point in the figure. Noting that , projecting this equation to AB，gives B A BA v = v +v vBA⊥AB B AB A AB v = v ——theorem of velocity projection I. e., the velocity projections of any two point in a figure on the line linking these two points are identical．This method for find the velocity of a point is called velocity projection method． That is , the velocity of any point in the figure is obtained as the geometric sum of the velocity of the pole and the relative rotational velocity with respect to the pole. Such a method of finding the velocity is called pole-based method, or composition method, which is a basic method to find the velocity of a point in a figure ． 2．Velocity projection method
远动学 即平面图形上任一点的速度等于基点的速度与该点随图形绕 基点转动的速度的矢量和.这种求解速度的方法称为基点法, 也称为合成法.它是求解平面图形内一点速度的基本方法 速度投影法 由于A,B点是任意的,因此VB=v4+vB表示了图形上任 意两点速度间的关系.由于恒有vA⊥AB,因此将上式在AB 上投影,有 B⊥AB A JAB 速度投影定理 即平面图形上任意两点的速度在该两点连线上的投影彼此相 等.这种求解速度的方法称为速度投影法 30
30 由于A, B点是任意的，因此 表示了图形上任 意两点速度间的关系．由于恒有 ，因此将上式在AB 上投影，有 B A BA v = v +v vBA⊥AB B AB A AB v = v —速度投影定理 即 平面图形上任意两点的速度在该两点连线上的投影彼此相 等．这种求解速度的方法称为 速度投影法． 即平面图形上任一点的速度等于基点的速度与该点随图形绕 基点转动的速度的矢量和．这种求解速度的方法称为基点法， 也称为合成法．它是求解平面图形内一点速度的基本方法． 二．速度投影法