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黄河科技学院毕业设计(文献翻译) 第 7 页 混合振动筛动力学分析摘要：一种新型的多自由度振动筛和高效率的多自由度机械动力学原理介绍。其突出的特点是有一个额外的高频率和振幅振动时间短。它能有效地增加物料破碎概率，消除致盲光圈，以及筛分效率高。一系列的力学方程的参数。建立了振动波形图进行仿真计算。关键词：振动筛；筛分效率；混沌动力学分析1 简介精确筛选煤的过程是一种提高产品质量结构的煤炭生产和提高经济效益和社会节能效益的有效方法。目前，关键问题是精确筛选过程抑制潮湿原煤的颗粒大小、表面积大小，水引起的孔径和致盲。普通振动筛完成筛选这个任务是困难的。现有的湿法筛选机很难使用粉煤干法筛分潮湿原煤。因此，在最近几年的机械工程和矿物加工工程，重点是在研究了加工的难筛物料。因为筛选机是很容易被蒙蔽的筛选，这个话题在国内和国外被广泛而深入的研究。在本文中，我们打算开发一个新型多自由度混合振动筛。2 混合振动筛的工作原理及结构图1是一个混合振动筛的结构，振动器构成部分1，2，3，4，和5。长杆1和3导致加速度振动周期长，短杆2和4加速度振动周期短，叠加的振动使材料松散获得较高的筛分效率。为了使物料筛容易，筛箱应该倾斜，大角度（约30）为粘性材料。振动筛，组件1为主动元件。驱动转矩，筛箱和材料形成一个动态系统。当电机驱动系统运动时，筛箱将有一个混合运动。这一运动将有效地促进筛选效率激励频率和设计。1、 曲柄 2、短杆1 3、连杆 4、短杆2 5 支撑杆图1 混合振动筛的动力示意图 图1所示的混合振动自由度是F=35(260)=3。根据经典机构的定义，充要条件是指定的运动是与原来的数目相等的运动的程度。如果一些自由运动是比原来的更大的数量，我们不能把它称为机制。然而，随着机构动力学的发展，机制的概念已经扩展。如果我们认为对于空间运动副或弹性元件在分析动态的组成部分，一些自由运动数量远远大于原来的组件，然后机制是动力机制。当一些原有的元件数小于自由运动，位置跟随功能的大规模的机制，惯性矩，和外部力量。适当的选择尺寸时，输出的运动机制可能是复合运动的长周期振动后，短周期振动。该机构有三个自由度的运动，一个产生长期的幅度振动筛网，其他两个创造高频率和混合振动。目前，混合现象被认为是一个最复杂的运动动态系统，其中包括各种动态系统。混合是非线性动态行为，产生固定点和周期点，达到特定形式的“障碍”通过乘法过程。对于非线性动力学，人们用线性模型方法来进行对真实系统简化的动态分析与设计。然而，这种线性近似并不总是可行的，忽视非线性因素，往往造成不可接受的误差分析与计算。近年来，人们认识到，如果他们想设计和生产高品质的系统，他们必须掌握非线性系统的动态行为。振动筛取决于振动的丝网材料投入、碰撞、分离、滚动或滑动，从而实现筛箱通过相对碰撞之间的材料和丝网。有另外一个长周期振动可以通过短时间的概率增加碰撞之间的材料、材料与材料之间的网格，然后可以很容易地分散和筛选。这个新的混合振动筛的筛分效率可以达到目的。3 动态分析混合振动筛 如图1所示在建立的坐标系的各部分，曲柄长度是l1，角速度是1，A1点的转动惯量是JA；长连杆是l2，角位移是2，C点的转动惯量是JC；短杆2和4的长度是e1和e2，角位移是1和2，短杆4在D点的转动惯量是JD，E点在坐标上水平和垂直方向的距离是x5和y5。3.1 分解运动方程从图2中，我们可以得到分解的微分方程： (1) 图2 应力分析 图3 第一个偏心轴的应力分析 3.2 第一个偏心轴的运动方程 从图3中，我们可以得到第一偏心轴的微分方程： (2) (3) (4) 3.3 导杆的运动方程 从图4中，我们可以得到连杆的微分方程： 图4 连杆的应力分析 图5 偏心轴的应力分析 (5) (6) (7) 3.4 偏心轴的运动方程 从图5中，我们可以得到偏心轴的微分方程： (8) (9) (10) 3.5 筛箱的运动方程 (11) (12)图6 模型盒的应力分析 从约束条件，我们可以得到封闭机制的矢量方程： (13) (14) (15) (16) (17) (18) (19) 一阶导数的时间变量方程是从公式（14）到公式（19） (20) (21) (22) (23) (24) (25) 二阶导数的时间变量方程是从公式（20）到公式（25） (26) (27) (28) (29) (30) (31) 根据消费设备欧拉公式（13） (32) (33) (34) 第一、二导数的时间变量方程的分别在（32）和（33） (35) (36) (37) (38) 加速筛箱框符合对角移动 (39)4 模拟曲线分析根据上述公式，应用程序，模拟运动的轨迹，我们可以得到曲线，并选择一些进行进一步分析。图7 当e1=e2=0mm时，筛箱的运动轨迹 图8 当e1=e2=1mm时，筛箱的运动轨迹 图9 当e1=e2=3mm时，筛箱的运动轨迹 图10 当e1=e2=6mm时，筛箱的运动轨迹 根据数字7，8，9，和10，水平方向（x）表示时间，垂直方（y）表示位移。为了在动力学方法的基础上测试出正确的解决方案，如图7所示，我们假设的短杆长度是e1=e2=0mm。在转速恒定在这种情况下，本运动曲线的筛箱单和长幅往复运动。其运动轨迹固定，不存在混合现象，表明从类似于动态方法中获得动力学结果。因此，无论是通过动态方程和仿真都是准确的。如图8所示，在短杆长度是e1=e2=1mm，虽然可以看到高谐波运动，但不明显；筛选粘性材料，材料之间崩溃的概率小。如图9所示，在短杆长度是e1=e2=3mm，高谐波运动是明显的，原周期运动不会受损，混合运动是显而易见的。因此，性质的高谐波运动可以增加率崩溃，材料易分散。应在增加粘性材料、提高粘度和致盲作出努力，。如图9所示，在短杆长度是e1=e2=6mm，高谐波运动是非常明显的，但频率和振幅开始减少。平衡的运动被摧毁，它不再有积极努力提高粘度和盲目。5 结论一种新型的多自由度振动筛及高效多自由度的提出，使长期使用的振幅振动频率高、振幅叠加短振动。理论上，它可以有效地增加的材料或材料丝网，分散的粘性材料，和单独的材料网之间碰撞的概率。因此，它能有效的避免粘合材料之间的粘合和消除致盲孔径。根据MATELAB运动曲线，在它有可能获得高频率和振幅的振动的基础上，长期振幅要适当的选择短杆长度以达到更好的屏蔽作用的粘性材料。参考文献1 刘C，设计和试验研究筛选机构，煤炭学报，3（2004）364 - 366。2 刘C，动态特性的翻转筛箱，其工艺参数的研究,中国矿业大学学报，29（2000）290-292。3 赵Y和刘C，干法筛分的理论和应用，科学出版社，1999。单位代码 0 2 学 号 100305001 分 类 号 TH6 密 级 秘密 毕业设计 文献翻译 院（系）名称工学院机械系 专业名称机械设计制造及其自动化 学生姓名马春阳 指导教师 杨汉嵩2012年 03 月 10 日The 6th International Conference on Mining Science & TechnologyDynamic analysis of a chaotic vibrating screenSong Yan*, Jiang Xiao-hong, Song Juan, Zhang Jian-xunChina University of Mining & Technology, Xuzhou 221116, ChinaAbstract A new type of multi-degree-of-freedom and highly efficient vibrating screen based on multi-degree of freedom mechanics principle of dynamics is presented. Its prominent character is to have an additionally high frequency and short amplitude vibration on long amplitude vibration. And it can efficiently increase probability of material crashing, eliminate blinding aperture,and get high screening efficiency. A series of mechanics Equ.s are set up and parameter vibrating wave charts are gained by emluator of Matlab.Keywords: vibrating screen; dynamic analysis; screening efficiency; chaos1. IntroductionThe precisely screening process of coal is an effective way to improve the quality and structure of coal production and to increase economic efficiency and social energy saving benefit. At present, the key problem of restraining the precisely screening process of moist raw coal is the small size of particles, big specific surface area, and blinding aperture caused by water. It is difficult for ordinary vibrating screen to complete this screening task. Existing wet screening machines make it difficult to use fine-coal dry screening to screen the wet raw coal. Therefore, in recent years for the mechanical engineering and mineral process engineering, the focus is on the research into proscessing the difficult screening materials. As the screening machine is very easy to be blinded when screening, this topic has been extensively and deeply studied both at home and abroad. In this paper, we intend to develop a new type of multi-degree-of-freedom chaotic vibrating screen.2. Structure and working principle of chaotic vibrating screenFigure 1 is the structure of a chaotic vibrating screen. Vibrator is constituted of components 1, 2, 3, 4, and 5.Long bars 1 and 3 cause acceleration vibration of long period, short bars 2 and 4 cause acceleration vibration of short period, the superposition of the two vibrations make the material loose and get a high screening efficiency.In order to make the material screen easier, the box of screen should be tilted for a large angle (about 30) for viscous material. The vibrating screen, component 1 is an initiative component. Driving torque, components, box of the screen and material form a dynamic system. When the motor drives the power system into motion, box of thescreen will have a chaotic motion. This motion will effectively promote screening efficiency if incentive frequency and bars are designed suitably.1 winch; 2 short bar 1; 3 connecting rod 2; 4 short rod; 5 stander5Fig. 1. Diagram of dynamics of the chaotic vibrating screenThe degree of freedom of the chaotic vibration shown in Fig. 1 is F35-(260)=3. According to the definition of classic institutions, the necessary and sufficient condition of the specified movement is that the number of the original is equal to the number of the degree of motion. If the number of freedom of motion is greater than the number of the original, we can not call it mechanism. However, with the development of the mechanism dynamics,the concept of mechanism has become extended. If we think about the space of kinematic pair or elasticity of components when analyzing dynamic of components, the number of the freedom of motion is far greater than the number of the original components, then the mechanism is dynamic mechanism. When the number of original components is less than the number freedom of motion, the location of the follower is the function of the mass of the mechanism, moment of inertia, and external force. When the size is suitably selected, the output movement of the mechanism may be the compound movement of long period vibration followed with short period vibration. This mechanism has three freedom degrees of motion, one generates long amplitude vibration on screen mesh, the other two create high frequency and chaotic vibration. At present, chaotic phenomenon is considered to be one of the most complex motions in dynamic system, which includes all kinds of dynamic system. Chaos is a nonlinear dynamic behavior, which generate fixed point and periodic point, and reach specific form of disorder through multiplicative process. As for nonlinear dynamics, people used to make the linear model to approach to true system, simplify dynamic analysis and design. However, this linear approximation is not always feasible, the nonlinear factors whichare overlooked often cause unacceptable error in analysis and calculation. In recent years, people realized that, ifthey want to design and produce high-quality system, they must command the nonlinear dynamic behavior of the system.Vibrating screens depend on the vibrating of the screen mesh making materials to throw, collide, separate, and roll or slid so that it can implement screen through relative collision between materials and screen mesh. To have an additionally long period vibration on short period vibration can increase the probability of collision between materials and materials and between materials and screen meshs, then the materials can be easily decentralized and screened. This new chaotic vibrating screen can achieve the purpose of screening efficiency.3. Dynamic analysis of chaotic vibrating screenIn building coordinate system of every component shown in figure 1, given that the length of crack 1 is l1, angular velocity is 1, rotational inertia about point A1 is JA; the length of connecting bar is l2, angular displacement is 2, rotational inertia about point C is JC; the lengths of short bars 2 and 4 is e1 and e2 , angular displacement is 1 and 2，rotational inertia of short bar 4 about point D is JD, horizontal and vertical distance between point E on the screen box and the origin of the coordinate is x5 and y5.3.1. Motion equations of crackFrom figure 2, we can get the rotational differential equation of the crack: (1)Fig. 2. Stress analysis model of the crack Fig. 3. Stress analysis model of the first eccentric shaft 3.2. Motion equations of the first eccentric shaftFrom figure 3, we can get differential equations of the first eccentric shaft: (2) (3) (4)3.3. Motion equations of the guide barFrom figure 4, we can get differential equations of the connecting bar:Fig. 4. Stress analysis model of the connecting bar Fig. 5. Stress analysis model of the second eccentric shaft (5) (6) (7)3.4. Motion equations of the second eccentric shaftFrom figure 5, we can get the differential equations of the second eccentric shaft: (8) (9) (10)3.5. Motion equations of the box (11) (12)Fig. 6. Stress analysis model of the boxFrom constrain conditions, we can get vector closed equations of the mechanism: (13) (14) (15) (16) (17) (18) (19)The first derivative on time of every variable is got from Equ. (14) to Equ. (19) (20) (21) (22) (23) (24) (25)The second derivative on time of every variable is got from Equ. (20) to Equ. (25) (26) (27) (28) (29) (30) (31)Expend Equ. (13) according to Eulers formula (32) (33) (34)The first and the second derivatives with respect to time are got respectively in Equ. (32) and Equ. (33) (35) (36) (37) (38)The acceleration of the screen box moving diagonally satisfy (39)4. Simulating curves and analysis According to the above formulas, using MATLAB to program, simulating the movement trajectory, we can get curves, and choose some of them for further analysis.Fig. 7. When e1=e2=0mm,the movement trajectory of screen box Fig. 8. When e1=e2=1mm,the movement trajectory of screen boxFig. 9. When e1=e2=3mm,the movement trajectory of screen boxFig. 10. When e1=e2=6mm,the movement trajectory of screen box According to figures 7, 8, 9, and 10, the horizontal direction (x) represent time, the vertical direction (y) represent displacement. In order to test the correctness of the solutions based on dynamics method, we suppose that the length of short bars be e1=e2=0mm. Given that the rotational speed is a constant in this situation, as shown in figure 7, the movement curve of the screen box is single and long amplitude reciprocating motion. Its movement trajectory is fixed and there is no chaotic phenomena, indicating that the result obtained from dynamic method is similar to theresult obtained from kinetic method. Therefore, both the dynamic equations and simulation through MATLAB are accurate. As shown in figure 8, when the length of the bars is e1=e2 =1mm, the character of the high harmonic movement can be seen but not obvious; for screening viscous material, the probability of crashing among materials is small. As shown in figure 9, when the length of the bars is e1=e2= 3mm, the character of the high harmonic movement is obvious, the original character of the periodic movement isnt damaged, and the chaotic movement is obvious. Therefore, the character of the highly harmonic movement can increase the rate of the crashing and make the materials easy to be dispersed. For increasing viscous materials, an obvious effort should be made to improve the viscosity and blinding. As shown in figure 9, when the length of the bars is e1=e2=6mm, the character of the high harmonic movement is very obvious, but the frequency and the amplitude begin to reduce. The balance of the movement is destroyed, it no longer has the positive effort to improve the viscosity and blind.5. Conclusion A new type of multi-degree-of-freedom and high efficient vibrating screen based on multi-degree of freedom is presented, which makes use of long amplitude vibrating superimposing high frequency and short amplitude vibration. In theory, it can efficiently increase probability of crashing among materials or between materials andscreen mesh, scatter viscous materials, and separate materials from screen mesh. Therefore, it will effectively avoid bonding between materials and eliminate blinding aperture. According to movement curves got from MATELAB, it is possible to get a high frequency and short amplitude vibration on the basis of long amplitude as long as the length of bars is suitably chosen so as to achieve better screening effect for viscous material.References 1 C. Liu, Design and experimental research of screening machine of two degrees of freedom. Journal of Coal. 3 (2004) 364-366. 2 C. Liu, Dynamic characteristics of the flip screen and researches of its process parameters. China University of Mining Journal. 29 (2000) 290-292. 3 Y. Zhao and C. Liu, Theory and application of dry screening. The Science Press, 1999. The 6th International Conference on Mining Science & Technology Dynamic analysis of a chaotic vibrating screen Song Yan*, Jiang Xiao-hong, Song Juan, Zhang Jian-xun China University of Mining & Technology, Xuzhou 221116, China Abstract A new type of multi-degree-of-freedom and highly efficient vibrating screen based on multi-degree of freedom mechanics principle of dynamics is presented. Its prominent character is to have an additionally high frequency and short amplitude vibration on long amplitude vibration. And it can efficiently increase probability of material crashing, eliminate blinding aperture, and get high screening efficiency. A series of mechanics Equ.s are set up and parameter vibrating wave charts are gained by emluator of Matlab. Keywords: vibrating screen; dynamic analysis; screening efficiency; chaos 1. Introduction The precisely screening process of coal is an effective way to improve the quality and structure of coal production and to increase economic efficiency and social energy saving benefit. At present, the key problem of restraining the precisely screening process of moist raw coal is the small size of particles, big specific surface area, and blinding aperture caused by water. It is difficult for ordinary vibrating screen to complete this screening task. Existing wet screening machines make it difficult to use fine-coal dry screening to screen the wet raw coal. Therefore, in recent years for the mechanical engineering and mineral process engineering, the focus is on the research into proscessing the difficult screening materials. As the screening machine is very easy to be blinded when screening, this topic has been extensively and deeply studied both at home and abroad. In this paper, we intend to develop a new type of multi-degree-of-freedom chaotic vibrating screen. 2. Structure and working principle of chaotic vibrating screen Figure 1 is the structure of a chaotic vibrating screen. Vibrator is constituted of components 1, 2, 3, 4, and 5. Long bars 1 and 3 cause acceleration vibration of long period, short bars 2 and 4 cause acceleration vibration of short period, the superposition of the two vibrations make the material loose and get a high screening efficiency. In order to make the material screen easier, the box of screen should be tilted for a large angle (about 30) for viscous material. The vibrating screen, component 1 is an initiative component. Driving torque, components, box of the screen and material form a dynamic system. When the motor drives the power system into motion, box of the * Corresponding author. Tel.: +86-13776797600. E-mail address: songyan. 187 -/09/$ See front matter 2009 Published by Elsevier B.V. doi:10.1016/eps.2009.09.2358 5220/locate/procediaProcedia Earth and Planetary Science 1 (2009) 15251531Procedia Earth and Planetary Science screen will have a chaotic motion. This motion will effectively promote screening efficiency if incentive frequency and bars are designed suitably. ? ? 1 winch; 2 short bar 1; 3 connecting rod 2; 4 short rod; 5 stander5 Fig. 1. Diagram of dynamics of the chaotic vibrating screen The degree of freedom of the chaotic vibration shown in Fig. 1 is F35-(260)=3. According to the definition of classic institutions, the necessary and sufficient condition of the specified movement is that the number of the original is equal to the number of the degree of motion. If the number of freedom of motion is greater than the number of the original, we can not call it mechanism. However, with the development of the mechanism dynamics, the concept of mechanism has become extended. If we think about the space of kinematic pair or elasticity of components when analyzing dynamic of components, the number of the freedom of motion is far greater than the number of the original components, then the mechanism is dynamic mechanism. When the number of original components is less than the number freedom of motion, the location of the follower is the function of the mass of the mechanism, moment of inertia, and external force. When the size is suitably selected, the output movement of the mechanism may be the compound movement of long period vibration followed with short period vibration. This mechanism has three freedom degrees of motion, one generates long amplitude vibration on screen mesh, the other two create high frequency and chaotic vibration. At present, chaotic phenomenon is considered to be one of the most complex motions in dynamic system, which includes all kinds of dynamic system. Chaos is a nonlinear dynamic behavior, which generate fixed point and periodic point, and reach specific form of disorder through multiplicative process. As for nonlinear dynamics, people used to make the linear model to approach to true system, simplify dynamic analysis and design. However, this linear approximation is not always feasible, the nonlinear factors which are overlooked often cause unacceptable error in analysis and calculation. In recent years, people realized that, if they want to design and produce high-quality system, they must command the nonlinear dynamic behavior of the system. Vibrating screens depend on the vibrating of the screen mesh making materials to throw, collide, separate, and roll or slid so that it can implement screen through relative collision between materials and screen mesh. To have an additionally long period vibration on short period vibration can increase the probability of collision between materials and materials and between materials and screen meshs, then the materials can be easily decentralized and screened. This new chaotic vibrating screen can achieve the purpose of screening efficiency. 3. Dynamic analysis of chaotic vibrating screen In building coordinate system of every component shown in figure 1, given that the length of crack 1 is l1, angular velocity is 1, rotational inertia about point A1 is JA; the length of connecting bar is l2, angular displacement is 2, rotational inertia about point C is JC; the lengths of short bars 2 and 4 is e1 and e2 , angular displacement is 1 and 2，rotational inertia of short bar 4 about point D is JD, horizontal and vertical distance between point E on the screen box and the origin of the coordinate is x5 and y5. 3.1. Motion equations of crack / Procedia Earth and Planetary Science 1 (2009) 15251531S. Yan et al. 1526e1 C 1 F32y F12xF12ym2g F32xB B1J&22xm & &22ym & &2 From figure 2, we can get the rotational differential equation of the crack: 11111A21x21yd1sincos()JFlFlM= +& (1) Fig. 2. Stress analysis model of the crack Fig. 3. Stress analysis model of the first eccentric shaft 3.2. Motion equations of the first eccentric shaft From figure 3, we can get differential equations of the first eccentric shaft: 111B32x132y1sincosJFeFe(2)= +& 2232x12xm xFF=& (3) 2212y32y2m yFFmg= +& (4) 3.3. Motion equations of the guide bar From figure 4, we can get differential equations of the connecting bar: Fig. 4. Stress analysis model of the connecting bar Fig. 5. Stress analysis model of the second eccentric shaft 2222222C343x43y0.5cossincosJmg lFlFl= +& (5) 334323xxm xFF=& (6) 3343y23y3m yFFm g=& (7) l1 A 1 B 1 F21x F21y F61y F61x Md，1 1A& &Jm3g F23y C D 3 F23x 2F43y F43x C2J&33ym & &33xm & &S l2 De2 4 E F54x F54y F34y F34x 44xm & &m4g 44ym & &2 2& &DJ 1527/ Procedia Earth and Planetary Science 1 (2009) 15251531S. Yan et al. 3.4. Motion equations of the second eccentric shaft From figure 5, we can get the differential equations of the second eccentric shaft: 22D254x254y2sincosJFeFe=+& (8) 4454x34xm xFF=& (9) 4434y54y4m yFFm g=& (10) 3.5. Motion equations of the box 5545sin Nxm xFF=& (11) 55455. cos. yNm yFFm g=& (12) Fig. 6. Stress analysis model of the box From constrain conditions, we can get vector closed equations of the mechanism: 1122iiii i/2i0121552eeeeee leyxel+= + (13) 11 2cos xl= (14) 112sin yl= (15) 11131coscos xle=+ (16) 11131sinsin yle=+ (17) 1112241coscos cos xlel=+ (18) 1112241sinsin sin ylel=+ (19) The first derivative on time of every variable is got from Equ. (14) to Equ. (19) 1112sin xl= & (20) 1112cos yl=& (21) 1111311sinsin xle= & (22) 1111131coscos yle=+& (23) m5g E F45x F45y FN 55ym & &55xm & & 1528/ Procedia Earth and Planetary Science 1 (2009) 15251531S. Yan et al. 1111122241sinsinsin xlel= +& (24) 1111122241coscos cos ylel=+& (25) The second derivative on time of every variable is got from Equ. (20) to Equ. (25) 21111121cossin xll= & (26) 21111121sincos yll= +& (27) 221111111131111cossincossin xllee= & (28) 221111111131111sincossincos yllee= +& (29) 221111111141111cossincossinxllee= +&2222222cossin ll+& (30) 221111111141111sincossincos yllee+= +& 2222222 sincos ll& (31) Expend Equ. (13) according to Eulers formula 1122iiiii/2i0121552eeeeee leyxel+= + (32) 111222152coscoscoscos lexel+=+ (33) 111222512sinsinsinsin yleel+=+ (34) The first and the second derivatives with respect to time are got respectively in Equ. (32) and Equ. (33) 1111122222152sinsinsinsin (35)lexel =& 1111122222512coscoscoscos yleel+=+& (36) 22111111111111cossincossinllee =& 222222222222522cossincossin xeell& (37) 221111111111511sincossincosyllee+=& 22222222222222sincossincos eell+& (38) The acceleration of the screen box moving diagonally satisfy 55tanyx=& (39) 1529/ Procedia Earth and Planetary Science 1 (2009) 15251531S. Yan et al. 4. Simulating curves and analysis According to the above formulas, using MATLAB to program, simulating the movement trajectory, we can get curves, and choose some of them for further analysis. Fig. 7. When e1=e2=0mm,the movement trajectory of screen box Fig. 8. When e1=e2=1mm,the movement trajectory of screen box Fig. 9. When e1=e2=3mm,the movement trajectory of screen box Fig. 10. When e1=e2=6mm,the movement trajectory of screen box According to figures 7, 8, 9, and 10, the horizontal direction (x) represent time, the vertical direction (y) represent displacement. In order to test the correctness of the solutions based on dynamics method, we suppose that the length of short bars be e1=e2=0mm. Given that the rotational speed is a constant in this situation, as shown in figure 7, the movement curve of the scr
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