[英語(yǔ)學(xué)習(xí)]第4次課--Chapterppt課件

1、Review of the Latest LectureLinksKinematic PairsTypes of Kinematic pairsKinematic ChainMechanismTypes of MechanismsThe Kinematic Diagram of a MechanismTopic 7. Degree of Freedom of a MechanismDefinition The number of independent(獨(dú)立的獨(dú)立的) parameters needed to define uniquely(獨(dú)一獨(dú)一地地) the locations of a

2、ll moving links within mechanism with respect to(相對(duì)于相對(duì)于) the frame is the degree of freedom (DOF) of a mechanism.LinksKinematic Pairs MechanismDOFconstrainsRemain DOFLinksKinematic PairsMechanismDOFconstrainsRemain DOF3N(2PL+PH)F=Each unconstrained(無(wú)約束的) link has 3 DOF. Each planar lower pair elimin

3、ates(消除) two DOF and each planar higher pair eliminates one DOF. DOF=3N-2PL-PHTopic 7 Degree of Freedom of a MechanismQ: Conditions for a Mechanism to have Motion ?A: DOF= 1DOF=3N-2PL-PH Where: N=Numbers of moving links (not include the frame!) PL=Numbers of planar lower pair PH= Numbers of planar h

4、igher pair Topic 7 Degree of Freedom of a MechanismConditions for a Mechanism to have a Determined Motion機(jī)構(gòu)有確定運(yùn)動(dòng)的條件ABCD1234123F=1=3 Provide one independent parameter，all moving links can have determined motionsTopic 7 Degree of Freedom of a MechanismABCD1234441A15EB2D32CC3D Provide two independent p

5、arameters，can not move at all. In extreme(極端) cases, the weakest link in the chain may be broken.Topic 7 Degree of Freedom of a MechanismABCD1234441A15EB2D32CC3DIf the number of driving links is less than the DOF of the mechanisms, some driven(從動(dòng)的) links will not have determined motion.Topic 7 Degre

6、e of Freedom of a MechanismABCDE123451432F=2=4 Provide two independent parameters，all moving links have determined motion(提供二個(gè)獨(dú)立運(yùn)動(dòng) ，一切構(gòu)件有確定相對(duì)運(yùn)動(dòng))Topic 7 Degree of Freedom of a MechanismABCD1234123F=1=3N=3，PL=4， PH=0F=3N-2PL-PH =33 24 =1 Topic 7 Degree of Freedom of a MechanismABCDE123451432F=2=4N=4，

7、PL=5， PH=0F=3N-2PL-PH =34 -25 =2 Topic 7 Degree of Freedom of a Mechanism F=1 F= Number of the driving linksThe condition for a mechanism to have a determined (確定的) motion is:NOTE：Independent(獨(dú)立的) parameters(參數(shù)) are supplied only by the driving links. The driving links are always connected to the fr

8、ame by lower pairs, one driving link (together with the corresponding lower pair) will provide only one independent parameter.Topic 7 Degree of Freedom of a MechanismExample 1N=4, PL=6F=3N-2PL-PH =34-26=0N=2, PL=3F=3N-2PL-PH =32-23=0N=3, PL=5F=3N-2PL-PH =33-25=-1 truss(桁架)ACDEF12345Topic 7 Degree of

9、 Freedom of a MechanismExample 2N=2; PL=2PH=1F=3N-2PL-PH =3x2-2x2-1x1 =1N=5; PL=7F=3N-2PL-PH =3x5-2x7 =1N=2; PL=2PH=1F=3N-2PL-PH =3x2-2x2-1x1 =113245Topic 7 Degree of Freedom of a Mechanism123456ACDEFGH F=3N-2PL-Ph=36 -28 = 2 兩自在度的剎車(chē)機(jī)構(gòu)可使兩片剎車(chē)片均勻地抱緊在輪轂上，自動(dòng)調(diào)理剎車(chē)片的均載，剎車(chē)效果比單一剎車(chē)片單自在度的更好。Topic 7 Degree of F

10、reedom of a MechanismPoints for the Calculation of DOFIn the development of the structural formula of mechanism Eq.： F=3N-2PL-PHno consideration was given to the link dimensions. It is not surprising to find many exceptions to the formula in practical cases with special geometric features.Topic 7 De

11、gree of Freedom of a Mechanism Compound Hinge(復(fù)合鉸) If the axes(軸) of two revolutes coincide(重合), they constitute a compound hinge.The number of revolutes in a compound hinge is equal to one less than the number of links joined at that hinge.1 07253 23hlppnFTopic 7 Degree of Freedom of a MechanismNot

12、e：In many cases, compound hinge (復(fù)合鉸鏈) does not show clearly. Attention must be paid to it.1111222233334Topic 7 Degree of Freedom of a Mechanism All machine elements belonging to the same link in the kinematic diagram must be connected firmly by welding(焊接) symbols. Topic 7 Degree of Freedom of a Me

13、chanism In a mechanism having gears(齒輪) or cams(凸輪), careful attention must be paid to the existence (存在) of compound hinges.Topic 7 Degree of Freedom of a MechanismEx.1: Calculate the DOF of the gear-linkage mechanism(齒輪連桿機(jī)構(gòu)). 12345ABCDEFIn the mechanism, there are three moving gears(1, 2, and 3) a

14、nd two moving rods(桿)(4 and 5).Topic 7 Degree of Freedom of a MechanismC is a compound hinge of links 2、4、5D is a compound hinge of links 3、5、6. F=3N-2PL-PH=35 -26 -2=1 12345ABCDEFTopic 7 Degree of Freedom of a Mechanism2. Passive DOF(部分自在度) The DOF which does not change the output motion of the mec

15、hanism is a passive DOF. F=3N-2PL-PH=33-23-1=2123演示演示Topic 7 Degree of Freedom of a MechanismAny passive DOF should be deleted(刪除) by welding the roller(滾子) to the follower before the calculation of the DOF of mechanism. F=3N-2PL-PH=32 -22 -1=1123123動(dòng)畫(huà)動(dòng)畫(huà)動(dòng)畫(huà)動(dòng)畫(huà)Topic 7 Degree of Freedom of a MechanismLi

16、nk 4 exactly has the same kinematic function as other constraints. N=,PL=,PH=0F=3N-2PL-PH=3X-2X=3. Redundant Constraints(虛約束ABCDN=3,PL=4,PH=0F=3N-2PL-PH=3X3-2X4=1動(dòng)畫(huà)演示動(dòng)畫(huà)演示1234ABCDEFABCDEFTopic 7 Degree of Freedom of a Mechanism(1) When two links are connected by more than one parallel(平行的) sliding pa

17、ir, only one sliding pair can be counted during the calculation, others are redundant constraints and must not be counted.F Redundant constraints must not be counted during the calculation of DOFTopic 7 Degree of Freedom of a Mechanism(2) When two links are connected by more than one revolute pair w

18、hose axes coincide(重合), only one revolute pair is counted.AA Topic 7 Degree of Freedom of a Mechanism(3) When two links are connected by more than one higher pair whose common normals(公法線) passing through the contact points coincide(重合) ,only one higher pair is counted.3AOBnn12F=3N-2PL-PH =32 -22-1=

19、1 3 2 -23-2=-2Topic 7 Degree of Freedom of a MechanismHowever, if their common normals (公法線) do not coincide(重合), then both higher pairs should be counted. NoImagennnnnnnnAABBTopic 7 Degree of Freedom of a Mechanism(4).When the distance between two points on two links remains(堅(jiān)持) constant(常數(shù)) during

20、 the motion of the mechanism, adding one link and two revolutes with their centers at these two points will create a redundant constraintABCDEF12345A BE FC DE1AA B4C DFE FB2DC3Topic 7 Degree of Freedom of a MechanismDuring the motion of the mechanisms, the distance between two points A and B on two

21、links 2 and 4 remains constant, link 1, revolute A and revolute B create a redundant constraint25CDEF1BB2CE5DFAAA B = B C = B D4433B C = B D , A F A EF=3N-2PL-PH=33 -24=1 34 -26=0 Topic 7 Degree of Freedom of a Mechanism(5).When the locus(軌跡) of a point is a straight line, adding one link with one f

22、ixed guide way parallel to the straight line and one revolute with its centre at that point will create a redundant constraint. A4312BCEDA B = B C = B DBA4123CE5DFA4312BCEDA B = B C = B DBA4123CE5DFTopic 7 Degree of Freedom of a Mechanism(6) Symmetrical(對(duì)稱(chēng)的) structure In order to transmit(傳輸) more p

23、ower, many pinions(小齒輪) are distributed(分布) symmetrically in space. Only one pinion should be counted.123422Note：gear 1, gear 3, and frame 4 constitute(組成) a compound hinge(復(fù)合鉸鏈). F=3N-2PL-PH =33 -23-2=1 Topic 7 Degree of Freedom of a MechanismNoteRedundant constraints can improve the rigidity(剛度) o

24、f a mechanism, improve the force condition in links, etc., and are widely used. “Deleting the redundant constraints during the calculation of DOF does not mean that the redundant constraints should be omitted(省略) from real mechanisms.All redundant constraints require some special dimensions. Therefo

25、re, attention should be paid to manufacturing(制造) accuracy(精度) when any redundant constraint is used. Topic 7 Degree of Freedom of a MechanismEx.1：Calculate the DOF of the mechanism shown below.Topic 7 Degree of Freedom of a MechanismAnalysisThe spring(彈簧) should not be counted in the number of links. C is a compound hinge of links 2, 3, 4。 The roller has a passive DOF(部分自在度). There are two parallel(平行) sliding pairs E and E between the frame 8 and the slider 6. One of the sliding pairs is redundant(多余的).123345