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1、5.3 Characteristics(特性) Analysis of Four-bar Linkages,through belt mechanism or gears. Therefore a designer must ensure(确保) that one side link is a crank.,5.3.1 Grashof Criterion准则 (Condition for having a crank),In a revolute four-bar mechanism, the input motion is usually obtained through a side li
2、nk driven by an electric motor directly or indirectly,Suppose we wish to design a crank-rocker mechanism ABCD, in which the side link AB is an input crank.,in BCD must obey (服从) the triangle inequality(不等式）,If the RRR Assur group can be assembled(装配) onto the basic mechanism by the two outer revolut
3、es B and D, the lengths of the three sides,-(5-1),The distance f is a variable(可变的) value during the motion of the mechanism.,(5-2),(5-3),(5-2),Again, from the inequalities (5-2), we can conclude that the sum of the shortest and the longest links must be less than the sum of the remaining(剩余) two li
4、nks. This is called Grashof criterion(准则) or the Condition for having a crank.,Thus from the inequalities (5-3), we can see that the crank in a crank-rocker mechanism must be the shortest link.,(5-3),上述条件表明：当四杆机构各杆的长度满足杆长 条件时，有最短杆参与构成的转动副都是周转副 （A、B副），而其余的转动副则是摆转副（C、 D副）。 于是，四杆机构有曲柄的条件是各杆的长度应满 足杆长条件，
5、且其最短杆为连架杆或机架。,The Grashof criterion can be expressed as: LMAX +LMIN Lb +Lc. A linkage mechanism which satisfies the Grashof criterion is sometimes called a Grashof linkage mechanism.,If LMAX +LMIN Lb +Lc, the linkage mechanism is an non-Grashof linkage mechanism, in which no link can rotate through
6、360o relative to any other link and all inversions(倒置) are double-rocker mechanisms.,an non-Grashof linkage mechanism,In a non-Grashof linkage mechanism, no link can rotate through 360o relative to any other link.,However, in a Grashof double-rocker mechanism, the coupler can rotate 360o with respec
7、t to other links.,5.3.2 Quick Return Characteristics（急回特性）,曲柄摇杆机构摇杆的两极限位置是在两状态下（曲柄与 连杆拉直共线和重合共线）用作图法画出两极限位 置从动件的行程角运动过程分析工作行程 和空回行程角速度不同（极位夹角）急回特性 的应用如何衡量急回引入K0，K1 曲柄滑块机构的急回特性其他,C1DC2 is called the angular stroke(行程) of the rocker, denoted as max.,从动件位于两极限位置时，对应曲柄的一个位置与另一位置的反向所夹的角度C1AC2 ，称为 极位夹角,记为
8、.,极位夹角可能小于90，也可能大于90 ，一般范围是（0 ，180 ）,2、急回运动,主动件a,时间：,转角：,运动：,从动件c,时间：,转角：,运动：,从动件c的平均角速度：,当曲柄等速回转的情况下，通常把从动件往复运动速度快慢不同的运动称为急回运动。,通常把从动件往复运动平均速度的比 值(大于1)称为行程速比系数，用K表示。,3. 行程速比系数K,A crank-rocker mechanism with special dimensions may not have quick return characteristics.,AB= C1C2 /2. =0 and k=1. This
9、crank-rocker mechanism has no quick-return characteristics.,Since =0o, an in-line(对心) slider-crank mechanism has no quick-return characteristics.,In the offset slider-crank mechanism, the distance C1C2 is the stroke H of the slider. C2AC1 is the angle .,If the driving crank AB rotates counter-clockw
10、ise with constant angular velocity, the slider will take a longer time in its rightward(向右) stroke than in its leftward(向左) stroke.,In Fig.4-27, the counter-clockwise stroke of the follower rocker should be the working stroke(工作行程), and the clockwise stroke should be the return stroke(回程).,working s
11、troke, then the rotation direction of the crank should be reversed(倒转).,If the clockwise stroke is needed to be a,In an oscillating guide-bar mechanism, two limiting positions CD1 and CD2 of the follower,guide-bar CD occur when the driving crank AB is perpendicular(垂直于) to the oscillating guide-bar
12、CD.,Note: The limiting positions of the follower guide-bar CD do not occur when the driving crank AB is horizontal(水平的).,D1CD2 is the angular stroke max of the follower.,For this linkage mechanism, happens(碰巧) to be equal to max. The coefficient of travel speed variation K, or the time ratio, is K=(
13、180o+)/(180o-).,5.3.2 Pressure Angle(压力角) and Transmission Angle(传动角) ,不考虑运动副的摩擦及构件重力的影响,5.3.2 Pressure Angle(压力角) and Transmission Angle(传动角) ,5.3.2 Pressure Angle(压力角) and Transmission Angle(传动角) ,5.3.2 Pressure Angle(压力角) and Transmission Angle(传动角) ,1、压力角,从动件上某点的受力方向与从动件上该点速度方向的所夹的锐角。,2、传动角，F与Fr
14、夹角，,（经常用衡量机构的传动质量）,当 BCD90o, 时=BCD.,当 BCD 90o, 时 =180o- BCD.,Only the tangential(切向的) component(分量) F t can create the output torque(转矩) on the driven link DC. The radial(径向的) component F r only increases pivot(枢轴) friction(摩擦) and does not contribute to the output torque.,For this reason, it is des
15、irable that is not too great or is not too small., 和 在运动过程中是变化的.,许用压力角（最大压力角） =40o, 许用传动角（最小传动角） =50o .,min =minmin, min.,For the same kinematic chain, the positions and the values of and will change, if a different link is chosen as the driver.,For the same kinematic chain, the positions and the va
16、lues of and will change, if a different link is chosen as the driver., and must be drawn on the driven link!,If the crank is an input link and the slider is an output, then the acute angle(锐角) between the coupler BC and the slider path is at that position.,If the crank is an input link and the slider is an output, then the acute angle(锐角) between the coupler BC and the slider pa
