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外文文献Proof that hinged four-bar mechanism will cause unstable motionThe unstable mechanism has two equilibrium points within its range of motion, and they are important in many systems, such as valves, switches and beats. The unstable mechanism is difficult to design because of the combination of energy storage and action characteristics. This paper studies unstable mechanism, such as four-bar mechanism, which has torsional elastic force at the joint. In theory, rigid mechanism has been improved to ensure the rotation of unstable mechanism. With this knowledge, designers can solve the problem of motion and energy demand of a large number of unstable mechanisms. An example is given to illustrate the theoretical role in the design of an unstable roduceAn activity agencies within the scope of its movement is two equilibrium position, it is required by many organizations, but there are many problems in the design activities institutions, especially the mechanism motion and energy accumulation characteristics. Moreover, motion and energy storage usually occur on a flexible rotating part. This paper discusses the necessity of designing a simple rotating mechanism to study the basic relationship between the motion of the mechanism and the unstable mechanism.Many people have discussed a lot of characteristics of rotating mechanism, including the design of motion mechanism. Recently, they have been particularly interested in micro-rotating mechanisms, which require that the power needed to control the switch is provided by the rotating mechanism and not maintained. Unstable micro-valves, micro-switches, micro-relays, even a small fiber switch have all proved this. It has been suggested that a rotating system be used to provide the elastic force for assembling small parts. This paper is an example of the structure of research institutions to ensure the implementation of unstable institutions.Problem studyAbove each of the rotating mechanism are stored in the process of movement and release energy, in fact, all of the unstable system requires some form of energy storage, because of the stable point occurred in the place of minimum energy. Unstable mechanical systems typically rely on the energy stored during tension to obtain unstable motion. The compliant manner in which the unstable mechanism behaves is subjected to an unstable execution of the motion, since the moving member allows the moving member to merge with the energy storage. In addition, there are many advantages, such as reducing the number of parts, reducing friction, recoil and loss.Unstable mechanical design, however, is not a mechanical, needs to analyze mechanism of rotation and storing energy, to solve this problem, many of the above mentioned mechanical with a simple beam for unstable motion. However, this method is simple, can let the designers flexible control sliding power or the location of the steady state, especially for small beams often rely on the rest of the bending strain and change a lot of parameters to reduce a little.The hinge model provides a simple way to simulate complex non-linear deflection mechanisms. It can roughly describe the force deflection characteristics of a mechanism connected by one or more bolts. The torsional elastic force of the joint simulates the stiffness of the component, as shown in figure 1. This type of model is bolted with short, curved spindles, ends bolted, or straight members bolted. The length of the connecting rod and the stiffness of the spring are transported in combination.Hinge model on accurate analysis and rotating mechanism and characteristics of energy storage using has been fully proved, but in order to study the current problems, people have realized that many types of institutions may be bending spring said connecting rod bolt coupling. Therefore, this paper will remind us to check the rotation and operation of the mechanism at one or more joints with fixed structure with bending spring, and then this; The results of the operation may be used in fixed or unstable structures. This depends on the implementation of the results or the designers requirements.Stability of unstable mechanism. The bending or bending of a part of a machine requires a strong movement of the spring. When there is no external force to ensure the position of the force mechanism, the mechanism is in equilibrium. If the system returns to its original position after a small disturbance, the mechanism is stable, but if a small disturbance causes the system to change its original position, it will be unstable. The potential and the stability of the mechanism can be linked by Lagranges theorem. If comply with the minimum potential, equilibrium position is stable, the theorem of led to more instability organization form, the definition of an unstable agencies within the scope of rotational including two minimum energy points.The potential equation of the hinged fixed model can be established simply.(1)Where k is the bending spring coefficient, and so is the turning Angle of the connecting rod, or the bending Angle of the rods. The potential of the mechanism is the sum of the potential stored in the rods. The equilibrium point can be found by determining the location of the machine. It is the first time that the offset is zero. The second offset at these points will determine the stability of the equilibrium position, and the positive value is consistent.Methods analysis of institutions No hinged four-bar linkage is shown in figure 2, figure in each of the four pole length is r1, r2, r3 and r4, four torsional spring coefficient k1, k2, k3, k4, an Angle of theta every rod and ground 1, 2, theta theta 3, 4, theta define the ground as the first lever, dont think torsional spring is distorted, position in an organization depends on theta 20, 30, theta theta 40, unstable structure design to ensure there are unstable structure. Therefore, it may be necessary to check each spring separately to determine whether there is a spring in the mechanism to ensure that the mechanism can execute motion. Its going to take a non-zero parameter, and everything else is going to be zero, and this potential equation might be different, its offset is going to be zero, and the solution is going to be in equilibrium. Therefore, the solution to the problem can be described as follows: find the position of the torsion spring in the general four-bar hinge mechanism, which has two balance points during the rotation process.Problem solution shows that simple design tool for processing unstable structure as a series of theorems guiding unstable structure, consists of a series of theorems of unstable institutions run results, proves theorem above solution.The theorem guides the movement of unstable structuresAccording to the Grashof criterion, the four-bar mechanism is divided into Grashof mechanism and non-grashof mechanism, grof mechanismThe criteria can be described mathematically:(2)Where s,l,p and q are respectively the longest and the shortest, and two rods whose length is in the middle. Grashof criterion 2 divides the equation intoWhere the inequality is satisfied is the mechanism, and vice versa. In addition, the side is the mechanism for the left and right sides of the equation. The transposition mechanism will be handled differently from other types of mechanisms, so there are three types of mechanisms: institutions, and the side is institutions and non-institutions.The Grashof inequality mechanismTheorem 1 if and only if the four-bar linkage of a torsion spring is located in the connection place opposite the shortest bar, and not bending spring instead of the opposite two inconsistent state in a straight line, its movement as unstable and the hinge bar model agency.Rule 1.1 if and only if the four pole Grashof institutions have a torsion spring is located in the shortest across the bar, and not bending spring instead of the opposite two inconsistent state in a straight line, it will not balance.Argument. Through to the general there is a connection of potential equation of four bar linkage analysis, prove theorem 1, the analysis on the solution of the equation of the minimum potential decide whether institutions rotation can reach each minimum value, because the previous demonstration of the accuracy of the hinge, the result is quite suitable for any organization. So rule 1 is the same argument as theorem 1.1.The above theorem can be used to determine which bolt connection should be at the same Angle in two positions by considering the rotation of Grashof mechanism. However, more rigorous arguments give designers more information about the way nature and stability are set.For any four-bar mechanism, the energy equation is the sum of each springs potentialType in theSelect delegate 2 as an independent variable, and the first offset is:Because the agency may be reversed in order to make it of each bar is as fixed on the ground, there is only one spring position need analysis, select position because of simple equation, and theta. 2 the independent variables did not appear in the expression of bits of four equations, if k4 is not zero, equations as follows:0 = (6)Equation of the first part theta 40 = 0, 4 - theta conformed institutions have two assembly method, that is to say, any length r1, r2, r3r and r4 rod, the fourth lever of the initial Angle of theta 40, there are two different mechanical position, assuming theta 40 does not conform to the requirements, institutions can be configured, as shown in figure 3, according to the accurate position equation can be soThe solution to the equation isType in theAnd the two sets of solutions will be the same, as in the case of the second and third rods, respectively.The second part of equation (6) has an offset ofIf the equation has two sets of solutions:2 = theta 3 theta.Theta 2 = theta 3 + PI.Therefore, when the second lever and third lever on the same straight line, the offset is zero, according to the equation (10) of the offset is zero, the second, three pole, also in the same line that is agency is modified gear.Interpretation of the solutionIt can be seen from the above analysis that the potential equation of the first offset of a spring on any member of a four-bar mechanism has four sets of solutions. The first two groups are given in equation (8), which indicates the stable position of the mechanism, and the other two groups of solutions are in equation (11), which indicates an unstable position, unless, as defined above, they are extreme values. At this point, equation (7) has a unique solution, the same as the total solution of equation (11). Therefore, the potential equation has at most two exact values during the entire rotation - a stable position and an unstable position. This proves that the spring of a four-bar mechanism is stable if the opposite pole is coaxial.Although a mechanism for any length of pole and the bending spring are likely to have two stable position, but the extreme value of in addition to the above discussion, some structures can not reach a steady state, that is to say, an organization can always in a stable position assembly. But its not necessarily stable after assembly. To prove this, think of a mechanism in an unstable position, where the opposite pole connected to the spring is in a straight line. That is, when the delegate 2= delegate 3, the organization reaches its balance point,And similarly, if there is a difference in the number of circles between now and tomorrow, the equation is zeroEquation (12) of the second condition and the conditions of equation (13) of the first can simultaneously with any proof of four bar linkage, known type of any two pole length less than or equal to the other two shots, and, to prove the inequality, can assemble an accord with inequality to institutions. The longest bar is also less than or equal to the sum of the other two barsS + p + q l (14)Where SLPQ is defined in equation (2), the algebraic inequality isL minus q is less than or equal to s plus p of 15.L - p s + q or lessL - s p + q or lessIn addition, since l is the longest rod, the following inequality can be obtained:-s p + q l (16)Q -s l + p| | l （14）式中slpq如方程（2）中定义的，代数不等式为 l-q s+p （15）l-p s+ql-s p+q另外，由于l为最长杆，可得以下不等式：p-sl+q （16） q-sl+p|p-q|l+s以上六个不等式证明的四杆机构的任意两杆长只差等于另外两杆只和，这满足方程(12)的第二式和方程(3 )的第一式。但是，一个不稳定机构必须满足两条件中的一个，得到一贯平衡位置中。要决定哪个机械结构不稳定，没个可能结构的杆长都要考虑。个别结果在说明使每个机构达到不稳定状态的条件之前，要详述三个有用的关系式。前两个是最长杆和中间杆的长度之和要大于等于中间两杆的长度之差， （17） （18） （19）方程（17）（18）（19）是对得到不稳定机构的条件的补充。以上证明了对于一个弹簧在任意一个联接处，这个四杆机构可能在两个稳定位置中的一个处装配。但是，如果能得到两个不稳定位置中的一个，弹簧就可以插入两个位置中间。这些不稳定位置与弹簧对面的两杆同线的状态相符，或者换句话说，就是它们的夹角相同或相差弧度。对于弹簧对面两杆的夹角相同的位置，方程（12）的第一个条件必须满足： () (20) 式中和是联接弹簧的两杆长度,和是与弹簧相对的杆长，为不稳定四杆机构的条件之一，同理，当机构的位置处于相对杆的角度差为时，就必须满足（13）中的第二个条件。 () (21)此式为机构不稳定条件二，分析一个弹簧联接引起的不稳定机构，每个弹簧必须满足以上两个条件中的一个。如果两个条件都满足，该弹簧引起的不稳定机构可以在两个方向上旋转时都能达到稳定状态；如果只满足一个条件，可以用在不稳定状态下挂索环实现两个稳定位置；如果两个条件都不满足，弹簧的位置不会引起不稳定状态。对于Grashof 机构，变位机构和Grashof机构，机构可以形成两条运动学链中的一条，或者可以组成机构的基本方法，例如图4，在（a）图中，最长杆和最短杆相邻。图（b）恰好相反，每个基本链都要考虑。推论以上讨论适合任何四杆机构，但是最后一部分论据只适合Grashof机构，我们首先考虑位置1的弹簧机构，图4（a）类型的Grashof机构： (22)式（22）违背了，因为相邻两杆的长度之和小于对杆只和，同理，也不满足，对于图4 (b)的Grashof类型 (23)式（23）违背了，由方程（17），是不满足的。弹簧在位置1的Grashof结构既不稳定也不满足运动学。用同样的方法，每个弹簧都要经过分析决定是否能够得到不稳定结构，对于Grashof机构结果，表1中有所显示，1a表示图4（a）中的位置1，1b表示图4(b)中弹簧位置1。表中可知，如果弹簧置于位置3或4时，机构就不稳定，这说明弹簧如果弹簧不在最短杆相邻位置，Grashof机构在满足条件的同时也会满足条件2，机构可以放入不稳定位置得到第二个稳定位置，以上是对定理1和准则1.1的证明非Grashof机构定理2 当且仅当铰链杆模型机构的不弯曲弹簧与其对面的两杆在一条直线上的状态不符时，它运动起来和任意一个联接处有扭转弹簧的非Grashof四杆机构一样不稳定。准则2.1 当且仅当非Grashof四杆机构的不弯曲扭转弹簧与其对面的两杆在一条直线上的状态不符时，弹簧在任意位置它都不会平衡。论证 已经准确的证明铰链杆模型，我们同时来证明订立和准则2.1，除了最后一部分外，以上所有的证明都适合于Grashof机构和非Grashof机构。因此可以证明订立和准则2.1说明弹簧在机械机构任意一个位置都满足方程(20)和(21)中的至少一个条件。以上材料证明了如果弹簧对面的两杆在为曲折位置同轴，机构不稳定。例如，弹簧位于a图位置1，根据已经用过的准则，Grashof不等式为： (24) 此式证明非Grashof机构满足，但是根据方程（19），不满足 。如果弹簧放在图b位置1，方程（17）