平面机构的自由度及其计算中英文对照

Planar mechanism of freedom1.Degree of freedom of planar mechanisms and its calculationWhen a body in plane motion who is no other object constraint,it can move in the xoy plane coordinate system with a point along the X axis, Y axis direction, but also can revolve around a vertical to xoy plane a shaft is rotated, the 3 modes of motion can be no contact, the mutual movement is independent of. Component has a number of independent movement which known as components of the degrees of freedom. Therefore, a planar motion of the member has 3 degrees of freedom.When the member is formed between the pair, as the independence movement was restricted, so the degree of freedom of mechanism will be reduced.On the structure of the independence movement and the restrictions are called constraints.As mentioned before, the kinematic chain, if an institution as a rack, and when the other one (or several) members according to a given motion during exercise, the remaining members have been identified, such as mechanism kinematic chains. Obviously cannot move or irregular move movement of the chain are not mechanism.In order to design the mechanism movement and movement uncertainty, we must discuss the degrees of freedom of mechanism and mechanism has identified the movement conditions.Mechanism has to determine the motion required by a given independent movement of the number of parameters, called the degree of freedom of mechanism.In planar mechanisms, each member in planar motion, as shown in Figure 1-1, as planar motion of the member 1 has not been associated with component 2 kinematic pair, assuming that member 2 consolidation in the xoy coordinate system, member 1 relative to the member 2 has a total of 3 degrees of freedom (along the X, Y axis movement and around and sports plane perpendicular to the axis of rotation), now two member connected pair, due to the two member into contact with each other to provide certain constraints so that its degrees of freedom is reduced, and the reduction of the number is equal to the movement pair the number of constraints.Because the two components of kinematic pair, still need to ensure that can produce a certainrelative motion of planar mechanism kinematic pairs, so the constraints to a maximum of 2, while the rest of the number of degrees of freedom for a minimum of 1.Figure1-1 Degree of freedom of planar mechanism diagramAs shown in Figure 1-2, two members movable side, members can only along the X axis moving relatively, namely mobile side introduces two constraint, retains one degree of freedom.As shown in Figure 1-3 two member to form a rotary pair, retaining only the 1 rotating movements, also introduced 2 constraints, retained the 1 degrees of freedom.To sum up, the planar low-pair were reduced in two degrees of freedom.Figure 1-2 Mobile accessoryFigure 1-3 Rotation pairAs shown in Figure 1-4,two component plane higher pair, introduces 1 constraint, retained the 2 degrees of freedom (two component parts can be along the tangent direction of sliding of instantaneous contact point, and can rotate around the instantaneous contact point.).Figure 1-4 High sideAssumptions about the composition of planar mechanism there are a total of n activity component, when each member does not constitute a pair when there are a total of 3n degrees of freedom.When each member movement pair connection, because the movement pair constraint and the system degrees of freedom are correspondingly reduced, reducing the number of which is equal to the kinematic pair into bondage number.In two components in planar mechanism, kinematic pair can have lower and higher pairs.If the body of the components to form P L low side and p hhigh side, so it will introduce (2p l+p h) constraints, so the degree of freedom of mechanism for:F=3n-(2p l+p h)=3n-2p l-p h2. The condition that Mechanism has identified the movementAccording to certain requirements for movement of the transfer and transformation mechanism, when the driver according to a given motion during exercise, the body of the remaining component motion also is completely determined.Therefore, to judge whether a mechanism with the determined motion except with the degree of freedom of mechanism is related with mechanism, also given driver number.Then we analyse several examples.As shown in Figure 1-5, four bar mechanism whose n = 3, P L = 4, p h = o.Then calculated F = 1, so given a movement parameters (given a driver, such as a given member one angular ), then the rest of component displacement is determined.That is to say, the degree of freedom for the institution in 1 with a driving component can be determined motion.Figure 1-5 Four bar mechanismAs shown in Figure 1-6, five bar mechanism, whose n = 4, PL = 5, pH = 0, then F = 2, with two degrees of freedom.If only given a driver, for example, a given member 1 displacement θ, then the remaining components movement and can not be identified.When the 1 member holds the position of AB, member 2, 3, 4 can occupy position BCDE, can also hold the position of BC/D/E, or other location.However, if we are given a driver, such as a member of 4 angular displacement α, which at the same time given 2 independence movement parameters, see not hard, the five rodmechanism components of motion is completely determined.Therefore, it must be given two driver, can determine the movement.Figure 1-6 Five bar mechanismAs shown in Figure 1-7, kinematic chain n = 2, P L = 3, p h = 0, then F = 0, we can see the degrees of freedom equal to zero for the kinematic chain can not generate relative motion.Figure 1-7 Kinematic chainTo sum up, mechanism has a determined motion conditions are: the degree of freedom of mechanism is greater than zero and the number of degrees of freedom must be equal to the number of driver.3.Calculation of degrees of freedom of mechanism should be paid attention to it.In the calculation of degrees of freedom of mechanism, often encounter is calculated according to the formula of degree of freedom of mechanism and the actual number of degrees of freedom does not fit the situation.This is because in the calculation of degree of freedom of mechanism, there are some issues that should be paid attention to because of the failure to handle correctly, will now be the attention of the major issues as follows.（1）C ompound hingeMore than two members in the same side are connected by rotating, constitute the so-called composite hinge.By the M components of compound hinge, which is composed of the rotating pair number should be (m-1), therefore, in the calculation of degrees of freedom of mechanism, should pay attention to the existence of a compound hinge.（2）L ocal degrees of freedomIf the body in certain components produced by the partial exercise does not affect the other components of the movement, we put this does not affect the overall freedom of motion, called local degrees of freedom.In the calculation of degree of freedom of mechanism, should be the mechanism of removing no local degrees of freedom.Partial freedom while not affecting the whole body movement, but the roller can make the high side contact sliding friction into rolling friction, reduce wear, so the actual machinery often have local degrees of freedom appear.（3）V irtual constraintOn the motion of mechanism does not actually play a role of restriction constraints is called a virtual constraint.In the calculation of degree of freedom ofmechanism, should be the mechanism to construct virtual constraint component together with the attached motion pair removed at all.Virtual constraint as compound hinge and local degrees of freedom that stick out a mile, here are some common virtual constraint exists.①If there are two members in the mechanism through a rotating pair connection, when the rotating pair apart, two member connected to the locus of points coincide with each other, then the rotating pair into a virtual constraint.②In the motion process, if the two member is the distance between two points is always the same, then the two to two rotating pairs and a member, will thus introduce a virtual constraint.③If two members in some form a moving pair, and the moving side movement relative to agree, or two members in some form a rotation pair, and the rotational movement relative to an axis coincident side.In this case the calculation of degrees of freedom of mechanism, should only be considered a motion by the introduction of the constraints, the remaining side so throughout the campaign into the constraint as a virtual constraint to omit.平面机构的自由度及其计算1.平面机构的自由度一个不受其他物体约束的自由构件在作平面运动时，可以在平面Xoy坐标系中随其上某一点沿x轴、y轴方向移动，同时还可以绕垂直于xoy平面的某根轴旋转，这3种运动方式之间可以没有任何的联系，即相互之间的运动是独立的。