理论力学刚体和般运动.ppt

1 * 1 Theoretical mechanics 1 1 Chapter 10 General motion of a rigid body 第十章 刚体的一般运动 §10–1 Composition of rotations about two parallel axes §10–1 刚体绕平行轴转动的合成 1 Chapter 10 General motion of a rigid body 第十章　刚体的一般运动 §10-1　Composition of rotations about two parallel axes §10-1　刚体绕平行轴转动的合成 　Composition problem of rotations about parallel axes is often encountered in mechanical engineering. For instance, the planet gear wheel in a planet gear mechanism has plane motion. 刚体绕平行轴转动的合成问题在机械中经常遇到。例如，行星圆柱齿轮机构，行星轮作平面运动。 1 　In previous study, we dealt with a plane motion of a planet gear by decomposing it into a translation and a rotation. However, it is more convenient to view the plane motion of a planet gear as a composition of two rotations.　 　　前面所研究的平面运动是把它看成为平动和转动的合成运动，但是在分析行星轮系的传动问题时，将行星轮的平面运动看成为转动与转动的合成运动则比较方便。　 1 Take a planet gear mechanism as an example. 例如在行星轮系中 Static system is O1xy 静系：O1xy Moving system is O1xy 动系： O1xy 1 　　　 Relative motion: rotation about axis O2, 相对运动: 绕O2轴转动, ?r is the relative angular velocity. ?r为相对角速度。 1 Embroiling motion: rotation about axis O1, 牵连运动: 绕O1轴转动, ?e is the embroiling angular velocity.　　　　 ?e为牵连角速度。　　　　　 （翻页请看动画） （Look for the animation on the next page） 1 1 1 The figure shows that Differentiating it with respect to t gives: 由图看出 　对 t 求导： At moment t, it is in position O2A; At moment t + ? t, it is in position O2A‘. ｔ时刻，O2A 位置； t + ? t 时刻, O2A位置 1 In conclusion: The absolute angular velocity ?a of the plane figure (the planet gear) equals to the algebraic sum of the embroiling angular velocity ?e and the