理论力学刚体的平面运动9.ppt

1 Every rigid body has its own instantaneous velocity center and angular velocity that may be either with the body or in its extension, but not in other rigid bodies. For instance, in [Example 1], the instantaneous velocity center of rod AB lies in point P1, and that of rod BD in point P2. Note P1 is not a point on rod CB. ? 每个作平面运动的刚体在每一瞬时都有自己的速度瞬心和 角速度, 并且瞬心在刚体或其扩大部分上, 不能认为瞬心在 其他刚体上. 例如, [例1] 中AB的瞬心在P1点,BD的瞬心在P2 点, 而且P1也不是CB杆上的点 [Example 4] A slotted bar-sliding block mechanism [例4] 导槽滑块机构 Look at the animation 请看动画 [Example 4] In the mechanism show in the figure, OA= r , the crank rotates with uniform ?, and a block attached at the center C of rod AB can slid along the slotted bar O1D. AB=l. At the moment shown in the figure , point O, A and O1 in the same horizontal line , and OA?AB, ?AO1C= ?=30. Find: the angular velocity of O1D. [例4] 导槽滑块机构已知： 曲柄OA= r , 匀角速度? 转动, 连杆AB的中点C处连接一 滑块C可沿导槽O1D滑动, AB=l,图示瞬时 O,A,O1三点在同一水平线上, OA?AB, ?AO1C= ?=30。 求：该瞬时O1D的角速度． 解：OA, O1D均作定轴转动,AB作平面运动 Solution：OA and O1D rotate about their fixed axes and rod AB is in plane motion. Composition of motions method ?用合成运动方法 Fine the velocity of the contact point in O1D with block C. 求O1D杆上与滑块C 接触的点的速度 moving point is point C on rod AB (or block C ), 动点: AB杆上C (或滑块C ), moving system is rod O1D, static system is supports. 动系: O1D杆, 静系: 机架 ? 研究AB: 　　　 , 图示位置, 作瞬时平动, 所以 ? Consider AB: 　　　, AB is in instantaneous translation, therefore, Absolute motion: curvilinear motion 　　　　 , direction ? 绝对运动：曲线运动　　　　　，方向? Relative motion: rectilinear motion 　　 , direction// O1D 相对运动：直线运动，　　，方向// O1D Convicted motion: rotation, , direction? O1D 牵连运动：定轴转动，　　，方向? O1D ） ( 这是一个需要联合应用点的合成运动和刚体平面运动理论求解的综合性问题．注意这类题的解法，再看下例． This is a comprehensive problem, which can be solve by applying both composition of motions and plane motion. Pay attention to the solving method for such kind of problem