Freedom(局部自由度)

1、The Theory of Machines and Mechanisms Chapter 1. Structure AnalysisSun ZhihongZ62373317 62373319Room307,No.3 Teaching BuildingMain Topics of Today3.DOF of a mechanism4.Conditions for a mechanism to have determined motion5.Matters needing attention when calculating DOF3.DOF of a mechanism lWhat is DO

2、F of a mechanism:The number of links that have independent motion.lFormula:F=3n-(2PL+Ph)Where ： n number of moving links PL number of lower pairs Ph number of higher pairs3.DOF of a mechanismExample 1n=3Pl=4Ph=0F=3n-(2PL+Ph) =9-8 =13.DOF of a mechanismExample 2n=2Pl=2Ph=1F=3n-(2Pl+Ph) =6-(4+1) =14.C

3、onditions for a mechanism to have determined motion1.DOF F 1 2.The DOF of the mechanism should be equal to the numbers of the driving links.Example:F=0 F=1 F=21.When two links are connected by more than one sliding pairs which parallel to each other, they should be seen as one sliding pair.5.Matters

4、 needing attention when calculating DOF2.When two links are connected by more than one revolute pairs whose axes are coincide, they should be seen as one sliding pair.5.Matters needing attention when calculating DOF3.Passive Degree of Freedom(局部自由度) The degree that does not influence other links mot

5、ion. It should be omitted when calculate DOF.DOF=32-(22+11) =15.Matters needing attention when calculating DOF4.When two links are connected by more than one higher pairs whose common normal passing through the points of contact coincide, they should be seen as only one higher pair. F=32-(22+11)=1On

6、e revolute pairOne higher pair5.When two links are connected by more than one higher pairs whose common normal passing the points of contact are not coincide, they should not be omitted. 5.Matters needing attention when calculating DOFThe two higher pairs in left picture equal to one revolute pair.

7、The two higher pairs in the right picture equal to one higher pair.5.Matters needing attention when calculating DOF6.Compound hinge(復(fù)合鉸鏈) more than one links connect with each other by joints at one point, it is called compound hinge. The number of joint is (m-1), m means the number of links.N=7, Pl

8、=10 Ph=0F=21-20=1Compound hinges5.Matters needing attention when calculating DOF7. Redundant Constraints -When the distance between two points on two links remains constant during the motion of the mechanism, adding one link and two revolute pairs with their centers at these two points will create a

9、 redundant constraint。5.Matters needing attention when calculating DOF7. Redundant Constraints: If the revolute pair connects two points at two links which have exactly same locus, the revolute pair will introduce one redundant constraint.5.Matters needing attention when calculating DOF7. Redundant Constraints The symmetrical structure or duplicated structure which does not influence the transmission of motion in mechanism, they will introduce redundant constraint and should be omitted.ExercisePassive DOFCompound hingeRedundant constraintRedundant constraintSo