平面机构的自由度及其计算中英文对照.doc

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 certain relative 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 PL low side and ph high side, so it will introduce (2pl+ph) constraints, so the degree of freedom of mechanism for:F=3n-(2pl+ph)=3n-2pl-ph 2. 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, PL = 4, ph = 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 mechanism As 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 , 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 , which at the same time given 2 independence movement parameters, see not hard, the five rod mechanism components of motion is completely determined.Therefore, it must be given two driver, can determine the movement.Figure 1-6 Five bar mechanism As shown in Figure 1-7, kinematic chain n = 2, PL = 3, ph = 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） Compound hinge More 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） Local degrees of freedom If 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） Virtual 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 of mechanism, 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. If 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. In 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. If 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。构件所具有的独立运动的数目称为构件的自由度。由此可知，一个作平面运动的构件具有3个自由度。当构件之间组成运动副后，由于独立运动受到了限制，因而机构的自由度将随之减少。对构件的独立运动所加的限制称为约束。如前所述，在运动链中，若以某一构件作为机架，而当其另一个（或几个）构件按给定的运动规律运动时，其余各构件都得到确定的运动，则这样的运动链便成为机构。显然不能运动或无规则乱动的运动链都不是机构。为了所设计的机构能能够运动并且有运动的确定性，必须探讨机构自由度和机构具有确定运动的条件。机构具有确定运动时所必需给定的独立运动参数数目，称为机构的自由度。在平面机构中，各构件只作平面运动，如图1-1所示，当做平面运动的构件1尚未与构件2构成运动副时，假设构件2固结在xoy坐标系上，构件1相对于构件2共具有3个自由度（沿x，y轴的移动及绕与运动平面垂直的轴线的转动），现将两构件连接而构成运动副，由于两构件相互接触并提供某些约束使其自由度减少，而且减少的数目就等于该运动副引入的约束的数目。又因为两构件组成运动副后，仍需保证能产生一定的相对运动，故平面机构中运动副引入的约束数目最多为2个，而剩下的自由度的数目最少为1个。图1-1 平面机构自由度示意图 图1-2中的两构件组成移动副后，构件间只能沿x轴作相对移动，也就是移动副引入了2个约束，保留了1个自由度。同样图1-3中的两构件组成转动副后，只保留了一个旋转运动，也引入了2个约束，保留了1个自由度。综上所述，平面低副均减少两个自由度。1-2 移动副1-3 转动副在图1-4中的两构件组成平面高副后，引入了1个约束，保留了2个自由度（两构件间既可以沿瞬时接触点的公切线方向滑动，又可绕瞬时接触点转动）。1-4 高副 假设组成平面机构共有n个活动构件，当各构件尚未构成运动副时共有3n个自由度。当各构件用运动副连接后，由于运动副的约束而使系统的自由度相应地减少，减少的数目将等于运动副引入的约束数。在平面机构中，两构件构成的运动副可以有低副和高副。若该机构中各构件间共构成了pl个低副和ph个高副，那么它将共引入（2pl+ph）个约束，于是该机构的自由度为：F=3n-（2pl+ph）=3n-2pl-ph2. 机构具有确定运动的条件为了按照一定的要求进行运动的传递及变换，当机构的原动件按给定的运动规律运动时该机构中其余构件的运动也都应是完全确定的。因此，判断一个机构是否具有确定的运动除了与该机构的自由度有关外，还与机构给定的原动件数目有关。下面分析几个例子。如图1-5所示的四杆机构，n=3，pl=4，ph=0。得F=1，所以只要给定一个运动参数（即给定一