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1、4.3 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.,4.3.1 Grashof Criterion格拉霍夫准则 (Condition for having a crank),In a revolute four-bar mechanism, the input motion is usually obtained through a sid
2、e link 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) thetriangle inequality(不等式）,If the RRR Assur group can be assembled(装配) onto the basic mechanism by the two outer revo
3、lutes B and D, the lengths of the three sides,-(4-1),The distance f is a variable(可变的) value during the motion of the mechanism.,(4-2),(4-3),(4-2),Again, from the inequalities (4-2), 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
4、 links. This is called Grashof criterion(准则) or the Condition for having a crank.,Thus from the inequalities (4-3), we can see that the crank in a crank-rocker mechanism must be the shortest link.,(4-3),The Grashof criterion can be expressed as: LMAX +LMIN Lb +Lc, the linkage mechanism is an non-Gra
5、shof linkage mechanism, in which no link can rotate through 360o relative to any other link and all inversions(倒置) are double-rocker mechanisms.,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
6、can rotate 360o with respect to other links.,If LMAX +LMIN =Lb +Lc, the centre lines of the four links can become collinear(共线).,At these positions, the output behavior may become indeterminate(不确定的). These positions are called change-points. Such linkage mechanisms are called change-point mechanism
7、s.,The configuration AB2C2D is called a parallel-crank mechanism, while the configuration AB2C2D is called an antiparallel-crank mechanism.,In Fig.4-22, the change-points are handled by providing the duplicate(复制的) linkage 90 out of phase(相位). As a consequence(结果), each linkage carries the other thr
8、ough its change-points so that the output remains(保持) determinate(确定的) at all positions.,Table 4-1 Type criteria for the revolute four-bar mechanisms,From the above, we know that the Grashof criterion LMAX +LMIN Lb +Lc is only a necessary condition, not sufficient(充足的) condition for having a crank.,
9、To determine the type of a revolute four-bar mechanism, we must check not only whether the necessary condition is satisfied but also which link is the frame.,In an offset slider-crank mechanism, the sum of the length a of the crank AB and the offset e must be less than the length b of the coupler BC
10、, if the crank AB is to rotate 360o relative to the frame.,4.3.2 Pressure Angle(压力角) and Transmission Angle(传动角) ,4.3.2 Pressure Angle(压力角) and Transmission Angle(传动角) ,4.3.2 Pressure Angle(压力角) and Transmission Angle(传动角) ,4.3.2 Pressure Angle(压力角) and Transmission Angle(传动角) ,defined as the pressu
11、re angle(压力角) of the mechanism at that position.,The acute angle(锐角) between the directions of the force F and the velocity of the point receiving(接受) the force on the follower is,4.3.2 Pressure Angle(压力角) and Transmission Angle(传动角) ,The complement(余角) of the pressure angle is called transmission a
12、ngle(传动角) . The transmission angle is also the acute angle(锐角),between the coupler(连杆) and the follower.,If BCD90o, then =BCD.,If BCD90o, then =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 p
13、ivot(枢轴) friction(摩擦) and does not contribute to the output torque.,For this reason, it is desirable that is not too great or is not too small., and change during motion.,Thus we should find the extreme values of and .,The maximum value of should be less than the allowable(允许的) pressure angle =40o,
14、or the minimum value of should be larger than =50o .,BCD reaches its extreme(极值) when the driving crank and the frame link are collinear. min will occur in either of the two positions.,It is common practice to calculate both values and then pick(挑选) the worst case, i.e., min =minmin, min.,For the sa
15、me 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 values 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 path is at that position.,
