平面运动分析analysis竞赛用

1、Theory of Machines and Mechanisms(机械原理)Chapter1 IntroductionChapter2 Structural Analysis of Planar MechanismsChapter3 Kinematic Analysis of MechanismsChapter4 Planar Linkage MechanismsChapter 5 Cam MechanismsChapter 6 Gear MechanismsChapter 7 Gear TrainsChapter 8 Other Mechanisms in Common UseChapte

2、r 9 Balancing of MachineryChapter 10 Motion of Mechanical Systems and Its RegulationChapter 11 Efficiency of MachineChapter 3Kinematic Analysis of Mechanisms本章重点： 平面机构速度和加速度分析的图解法 （包括基点法和重合点法）。本章难点： 重合点法中哥氏加速度的正确确定。3.1 Tasks and Methods of Kinematic Analysis3.2 Velocity Analysis by the Method of ins

3、tant Centres3.1 Tasks and Methods of Kinematic Analysis不考虑引起机构运动外力的影响，仅仅研究已知原动件运动规律的条件下，输出构件的运动情况.Task: to find positions, velocities and accelerations or angular positions, angular velocities and angular accelerationsPosition: to determine whether all links will interfere(干涉) with each other,to fin

4、d locus(轨迹)Velocity: to calculate the stored kinetic energy(动能) or power(功率) P. Acc.：To calculate the dynamic forcesmethod graphical method (图解法): 直观，精度不高 analytical method (解析法) : 精度高，计算烦琐 experimental method (实验法) : 需专门的仪器 Instant(瞬时的) centre method for velocityVector(矢量) equation method3.2 Veloci

5、ty Analysis by the Method of instant Centres3.2.1 Definition of the Instant Centre 刚体2相对于另一刚体1（固体坐标系）作平面运动，在任一瞬时，该平面运动都可看成绕某一相对静止点的转动，该点称为速度瞬时中心（瞬心） instant centerP12 VA2A1刚体2上的A点相对于刚体1上的A点的相对速度， VA2A1AP.VB2B1同理。 Suppose that the positions of points A and B, the directions of VA2A1 and VB2B1 are kno

6、wn.可通过VA2A1，VB2B1求P12点。 VA2A1AP. VB2B1BP. instant centerP12 One of bodies is staticabsolute instant center Both of them are movingrelative instant centerAttention:a pair of coincident(重合) points, the absolute(绝对) velocities of which are the same, in both magnitude(大小) and direction.具有相同的绝对速度的重合点 。 i

7、nstant centerrelative velocity is zero.两构件上相对速度是零的重合点3.2.2 Number of Instant Centers of a Mechanism发生相对运动的任意两构件之间都有一个瞬心 knumber of links including the frameinstant centerthe center of revolutes3.2.3 Location of the Instant Center of two links connected by a kinematic pair(1) Revolute Pair若两构件组成回转副，则

8、回转副中心为其速度瞬心；(2) Sliding Pair Instant center:lies at infinity in either directionPerpendicular to the guide-way. Attention：The common normal(公法线) may pass through any point !(3) Higher Pair:Pure-rolling PairInstant centerthe point of contact (4)Higher Pair :rolling & sliding PairInstant centerlies so

9、mewhere on the common normal（公法线） through the point of contact3.2.4 Theorem of Three Centres (Aronhold-Kennedy Theorem)Any three links have three instant centers.They must lie on a straight line CVc 2Vc 3P12P13AB123233.2.5 Applications of Instant CentersExample1: Locate all instant centers for the r

10、evolute four-bar linkage. (1) locate all instant centers for the mechanism(2) find the ratio 2/4Find：P12、P23、P34和P14；Solution：再由三心定理可知：(1) locate all instant centers P12 ， P14P24P23 ， P34P12 ， P23P13P14 ， P34(2) find the ratio 2/4P24在P12、P14的同一侧，2和4方向相同。P24在P12、P14之间，2和4方向相反。P24为构件2和构件4的速度瞬心，两构件在P24

11、处应有相等的绝对速度，即:Example2:For the following Slider-Crank Mechanism，Given: lAB, lBC,，1 locate all instant centers for the mechanism ；the velocity of follower link3 V3 。Solution：(1) Find Instant centerP13(2) Determine V3Example3In the cam mechanism as shown in the following fig. the cam2 rotates anti-cloc

12、kwise at a constant speed ，Determine the velocity of the follower2 for the position shown. (1) Find Instant center P23P23应在P12 ， P13的连线上P23P23 在接触点的公法线上(2) Determine V3Solution：3.2.6 Advantages and Disadvantages of the Method of Instant CentersExcellent tool in simple mechanisms. difficult to find Instant Center in a complex mechanismit can not be used in acceleration analysis.Attentions (this chapter