【20160321】Special Cases of the Mobility Equation D) E9 S$ Z9 ~7 f( c9 Q
1 g" U% E8 ? {Mobility is an extremely important property of amechanism. Among other facets, itgives insight into the number of actuators required to operate a mechanism. However, to obtain correct results, special care must be taken in using the Gruebler's equation. Some specialconditions are presented next.* W$ Z9 Q' c) [8 Z* r! I% B
自由度计算中有些特殊情况需要格外注意。
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2 S/ h4 w' d0 _6 s# G1 tCoincident Joints
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Some mechanisms have three links that are all connected at a common pin joint, as shown in Figure 1.28. This situation brings some confusion to kinematic modeling. Physically, one pin may be used to connect all three links. However, by definition, a pin joint connects two links.
! t* J8 A% }/ a2 M7 C' U: R同一销钉连接三个杆件的情况，需要算作两个销钉。因为按照定义，一个销钉连接两个杆件。
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+ w6 [: w4 _ G9 e; lExceptions to the Gruebler's Equation
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2 l5 P8 b Y6 U% H) W% lAnother special mobility situation must be mentioned. Because the Gruebler's equation doesnot account for link geometry, in rare instances it can lead to misleading results. One such instance is shown in Figure 1.31.
* ~ B! s5 ]+ B$ U' g4 ^0 O自由度计算公式也有例外，比如由几何因素引起的错误结果，一个例子如图所示。& C8 R, R/ [1 d& ?
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Notice that this linkage contains five links and six pin joints. Using Gruebler's equation, thislinkage has zero degrees of freedom. Of course, this suggests that the mechanism is locked. However, if all pivoted links were the same size, and the distance between thejoints on the frame and coupler were identical, this mechanism would be capable of motion, with one degree of freedom. The center link is redundant, and because it is identical in length to the other two links attached to the frame, it does not alter the action of the linkage.% {1 V1 J1 r' T8 ?; u; p
5个杆件6个销钉，按自由度计算公式其自由度为零。这意味着机构锁定，然而若所有转轴等长，并且与机架相连的销钉到连杆的距离相等，这个机构是可以运动的，有1个自由度。中间的曲柄是多余的，并不影响机构的运动。
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Idle Degrees of Freedom
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/ n4 e- K6 M/ V# U: ?8 X1 XIn some mechanisms, links exhibit motion which does not influence the input and output relationship of the mechanism. These idle degrees of freedom present another situation where Gruebler's equation givesmisleading results. An example is a cam with a roller follower as shown in Figure 1.32. Gruebler's equationspecifies two degrees of freedom (4 links, 3 pins, 1 higher-order joint). With an actuated cam rotation, the pivoted link oscillates while the roller follower rotates about its center. Yet, only the motion of the pivoted link serves as the output of the mechanism. The roller rotation is an idle degree of freedom and not intended to affect the output motion of the mechanism. It is a design feature which reduces friction and wear on the surface of the cam. While Gruebler's equation specifies that a cam mechanism with a roller follower has a mobility of two, the designer is typically only interested in a single degree of freedom. Several other mechanisms contain similar idle degrees of freedom.
8 D7 Q! I( S( O0 B+ d0 K, n$ u多余自由度，有的机构中含有这样的杆件，其运动对输出运动不产生影响， 则其为多余自由度。如图机构含4个杆件，3个销钉，1个高副约束，输入端凸轮转动，输出端杆件摆动，中间滚轮从动件绕其中心转动。然而只有杆件的摆动是机构的输出，滚轮的滚动是多余自由度，不影响机构输出。这样设计是为了减小凸轮表面的摩擦。自由度计算公式给出，该机构有2个自由度，然而事实上我们只对一个感兴趣。还有其他例子，不作赘述。7 x+ }8 @1 A# \& \6 A5 D/ U1 c
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楼主: 黑森林的鹿
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发表于 2016-3-21 08:22:26
