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【20160321】Special Cases of the Mobility Equation5 g) ^5 O* |9 ]' S, t
8 P# M( g, p5 V O8 H/ B; RMobility 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.7 h" @% Z( K: g6 U: X5 B1 x I
自由度計(jì)算中有些特殊情況需要格外注意。) Y% Y9 c4 x, t
6 W: a( A+ X: }Coincident Joints
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! q% T$ N7 i; k+ s% o2 fSome 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.3 X: w) i; N$ j& Z/ N
同一銷釘連接三個(gè)桿件的情況，需要算作兩個(gè)銷釘。因?yàn)榘凑斩x，一個(gè)銷釘連接兩個(gè)桿件。
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' I9 c0 g+ }4 A1 U& V, wExceptions to the Gruebler's Equation
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- Q2 F- n S( n7 I# S1 _+ wAnother 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.
! A5 b2 ]. G1 P& N1 J2 I5 k自由度計(jì)算公式也有例外，比如由幾何因素引起的錯(cuò)誤結(jié)果，一個(gè)例子如圖所示。 Y* C7 q: @4 Z! Q) Y) j; O8 j
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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.
. y& e$ M8 M k+ T5個(gè)桿件6個(gè)銷釘，按自由度計(jì)算公式其自由度為零。這意味著機(jī)構(gòu)鎖定，然而若所有轉(zhuǎn)軸等長(zhǎng)，并且與機(jī)架相連的銷釘?shù)竭B桿的距離相等，這個(gè)機(jī)構(gòu)是可以運(yùn)動(dòng)的，有1個(gè)自由度。中間的曲柄是多余的，并不影響機(jī)構(gòu)的運(yùn)動(dòng)。$ m! [' g1 z/ K. ?
; l, J9 C4 L, {/ e7 hIdle Degrees of Freedom* ^$ a% m3 f, W! k( U: C
; ]; E# L8 w/ Y6 t! j, r; 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.$ e7 {- R3 E! A2 M. h2 o3 t
多余自由度，有的機(jī)構(gòu)中含有這樣的桿件，其運(yùn)動(dòng)對(duì)輸出運(yùn)動(dòng)不產(chǎn)生影響， 則其為多余自由度。如圖機(jī)構(gòu)含4個(gè)桿件，3個(gè)銷釘，1個(gè)高副約束，輸入端凸輪轉(zhuǎn)動(dòng)，輸出端桿件擺動(dòng)，中間滾輪從動(dòng)件繞其中心轉(zhuǎn)動(dòng)。然而只有桿件的擺動(dòng)是機(jī)構(gòu)的輸出，滾輪的滾動(dòng)是多余自由度，不影響機(jī)構(gòu)輸出。這樣設(shè)計(jì)是為了減小凸輪表面的摩擦。自由度計(jì)算公式給出，該機(jī)構(gòu)有2個(gè)自由度，然而事實(shí)上我們只對(duì)一個(gè)感興趣。還有其他例子，不作贅述。
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樓主: 黑森林的鹿
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發(fā)表于 2016-3-21 08:22:26
