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MECHANISMS AND MACHINE THEORYAurelian Vadean , Dimitri Leray , Jean GuillotAdeapartment of Mechanical Engineering, Ecole Polytechnique de Montreal, P.O. Box 6079, Station Centre-Ville,Montreal, Qubec, Canada H3C 3A7bLaboratoire de Genie Mecanique de Toulouse - COSAM, INSA Toulouse, 135 Avenue de Rangueil,Toulouse Cedex 4, Automotive sub-actuators tooth side clearance adjustment optimization techniques1.Introduction to Mechanism：The function of a mechanism is to transmit or transform motion from one rigid body to another as part of the action of a machine. There are three types of common mechanical devices that can be used as basic elements of a mechanism.1、Gear system, in which toothed members in contact transmit motion between rotating shafts. 2、Cam system, where a uniform motion of an input member is converted into a nonuniform motion of the output member. 3、Plane and spatial linkages are also useful in creating mechanical motions for a point or rigid body. A kinematic chain is a system of links, that is, rigid bodies , which are either jointed together or are in contact with one another in a manner that permits them to move relative to one another. If one of the links is fixed and the movement of any other link to a new position will cause each of the other links to move to definite predictable position, the system is a constrained kinematic chain. If one of the links is held fixed and the movement of any other link to a new position will not cause each of the other links to move to a definite predictable position then the system is an unconstrained kinematic chain,A mechanism or linkage is a constrained kinematic chain, and is a mechanical device that has the purpose of transferring motion and/or force from a source to an output. A linkage consists of links (or bars), generally considered rigid, which are connected by joints, such as pin Cor revolute) or prismatic joints, to form open or closed chains (or loops). Such kinematic chains, with at least one link fixed, become mechanisms if at least two other links remain mobility, or structures if no mobility remains. In other words, a mechanism permits relative motion between its rigid links; a structure does not. Since linkages make simple mechanisms and can be designed to perform complex tasks, such as nonlinear motion and force transmission they will receive much attention in mechanism study.Mechanisms are used in a great variety of machines and devices. The simplest closed-loop linkage is the four-bar linkage, which has three moving links (plus one fixed link) and four pin joints. The link that is connected to the power source or prime mover and has one moving pivot and one ground pivot is called the input link. The output link connects another moving pivot to another ground pivot. The coupler or floating link connected the two moving pivots, thereby coupling the input to the output link.The four-bar linkage has some special configurations created by making one or more links infinite in length. The slider-crank (or crank and slider) mechanism is a four-bar chain with a slider replacing an infinitely long output link. The internal combustion engine is built based on this mechanism. Other forms of four-link mechanisms exist in which a slider is guided on a moving link rather than on a fixed link. These are called inversions of the slider-crank, produced when another link (the crank, coupler, or slider) is fixed link.Although the four-bar linkage and slider-crank mechanism are very useful and found in thousands of applications, we can see that these linkages have limited performance level. Linkages with more members are often used in more demanding circumstances. However it is often difficult to visualize the movement of a multiloop linkage, especially when other components appear in the same diagram. The first step in the motion analyses of more complicated mechanisms is to sketch the equivalent kinematic or skeleton diagram. The skeleton diagram serves a purpose similar to that of the electrical schematic or circuit diagram .Organization movement analysis second step: Draws a graphic chart, is must determine the organization the number of degrees of freedom. Based on degree of freedom, but Italy refers needs certain independent inputs the movement number, by determined organization all components are opposite in the ground position. The people have thousands of different types conceivably the link motion gear. You may imagine a bag containing massive link motion gear the component: Two pole groups, three pole groups, four pole groups and so on, as well as components, rotation, motion, cam follower, gear, tooth chain, chain wheel, leather belt, belt pulley and so on. (Sphere movement, screw vice-as well as the permission three dimensional relative motion other connections not yet includes, here, discusses in parallel planes merely plane motion). Moreover you conceivable put these components various types link motion gear possibility which forms in the same place. How exists helps the people to control forms these organizations the rule? In fact, the majority organization duty is requests a sole input to transmit to a sole output. Therefore the single degree of freedom organization uses most one kind of organization type. For example, namely may see by the intuition: Four pole organizations are a single degree of freedom link motion gear. The picture motion diagram and the determination organization degree of freedom process, is the movement analysis and the synthesis process first stage. In the movement analysis, adds on its characteristic according to the organization geometry shape which possibly knew (for example input angle, speed, angle acceleration and so on) studies the determination concrete organization. On the other hand, the movement synthesis is designs an organization to complete the duty process which an institute requests. In this, chooses the new organization the type and the size is a movement synthesis part. Conceives the relative motion ability, can guess the reason that designs an organization the reason and makes the improvement to a concrete design ability is like this a successful organization scientists symbol. Although these abilities come from the congenital creativity, however more is because has grasped the technology which enhances from the practice. 1.1The movement analysis： simple one of most useful organizations is four pole organizations. In on following elaboration majority of content centralism discussion link motion gear, but this procedure is also suitable for the more complex link motion gear. We already knew four pole organizations have a degree of freedom. About four pole organizations, has the useful more contents which must know? Indeed is some! These pull the Xiao husband criterion including the standard, the transformation concept, the blind spot position (divergence point), branch office, transmission angle, with theirs movement characteristic, including position, speed and acceleration. Four pole organizations may have one kind of being called as crank rocker organization form, one kind of double rocking lever organization, one kind of double crank (tension bar) does the organization, which one form send in is called as the organization, is decided in two pole movement scopes which (fixed component) connects with the rack. The crank rocker organization input component, the crank may revolve through 360 and the continuous rotation, but outputs the component to make the undulation merely (i.e. swing member). As an exceptional case, in the parallel four pole organization, inputs the pole the length to be equal to outputs the pole the length, the go-between length and the fixed link (rack) length, also is equal. Its input and the output all may make the complete alternation rotation or transform the being called as antiparallel quadrangle organization the overlapping structure. The standard pulls the Xiao husband criterion (theorem) to indicate that,If in four pole organizations, between two poles can do willfully relatively rotates continuously, that, its longest pole length is smaller than sum of with the shortest pole length or is equal to sum of the other two pole length.Should pay attention: The same four pole organization, may have the different form, which pole is this decided in was stipulated (i.e. makes fixed link) as the rack. The movement transformation process is in the fixed organization transmission chain different member has the different organization rate process. Besides has about the component rotation scope knowledge, but also must have how causes the organization before the manufacture on energy “the revolution” the good measure, that will be very useful. Hardenbergh (Hartenberg) speaks of: “The revolution” is terminology, its significance passes to outputs the component the movement validity. It meant the revolution is steady, in which can in output in the component to have a strength or the torque biggest force component is effective. Not only although the final output strength or the torque are the connecting rod geometric figure functions, moreover also is generally the power or the force of inertia result, that is frequently big to like static strength several times. In order to analyze the idling or in order to easy to obtain how can cause any organization “the revolution” the index, the transmission angle concept is extremely useful. In organization movement period, the transmission angle value is changing. The transmission angle 0 may occur in the special position. Will output the pole but in this special position the movement with not to exert inputs on the pole the strength many to have nothing to do with greatly. In fact, as a result of the movement vice-friction influence, the general basis practical experience, with the transmission angle planning board which is bigger than the rating. The weight link motion gear transmission movement ability matrix foundation definition already studied. A determining factor value (it includes regarding some assigns organization graph, position output movement variable to input variable derivative) is a this link motion gear in concrete position mobility criterion. If the organization has a degree of freedom (e.g. four pole organizations), then stipulated a location parameter, if the input angle, completely determined this organization stops position (neglect branch offices possibility). We may study one about four pole organization component absolute angular position analysis expression. When analyzes certain positions and (or) certain different organization time, this will be must be much more useful than the geometric figure analysis program, because this expression will cause the automated computation easy to program. The realization organization speed analysis relative velocity law is the speed polygon is one of several effective methods. This end (goes against) the spot to represent on the organization all spots, has the zero speed. From this the line which stipples respectively to the speed polygon in is representing the absolute speed which this organization photograph well should select respectively. In a line connection speed polygon random two points represents is taking on this organization two corresponding spot relative velocity. Other method is the instantaneous center law, namely the instantaneous center law, this method is extremely useful moreover is frequently when the complex link motion gear analysis quick method. The instantaneous center is a spot, this spot in that flash, on between the organization two components does not have the relative motion. In order to discover known organization certain instantaneous centers the position, Kennedy the (Kennedy) three center theories extremely are useful. It is said that,Each other relative motion three object three instantaneous centers are surely in a straight line. The organization various components acceleration is makes one be interested, because it affects the force of inertia, subsequently affects the machine part the stress, the bearing load, the vibration and the noise. Because the final goal is the machine and the organization force of inertia analysis, the all acceleration various components all should the disposable picture - - in the organization fixed component inertial coordinate system express in the identical coordinate system. Should pay attention: Is opposite in rotates on the vice-rotation rigid body an acceleration component usually to have two fixedly. A force component direction cuts in this path, its direction is same with this object angle acceleration direction, and is called the tangential acceleration. Its existence is completely because the angular speed rate of change causes. Another component, always aims at the object the center of rotation, is called the standard the centripetal acceleration, because this component the velocity vector direction has the change to exist. The movement comprehensiveGanization is forms many mechanisms the basic geometry structural units, these mechanisms including automatic packaging, printer, mechanical toy, textile machinery and other machineries and so on. The typical organization must design causes the movement which the rigid component relative datum component produces hoped. The organization movement design is the movement synthesis, first step frequently designs the entire machine first. When consideration stress, must ask dynamics aspect question, the bearing load, the stress, the lubrication and so on the similar question, but the major problem is the machine structure question. The movement scientist defines the kinematics as “the development facility movement and the foundation organization method”. This definition first part involves the kinematic analysis. The known organization, its constitution state of motion determined by the kinematic analysis. The narration movement analysis duty contains the organization between the main dimension, the component links mutually with the input movement technical characteristic or the actuation method. The goal is must discover the displacement, the speed, the acceleration, the impact or the beat (two step accelerations), with various components higher order acceleration which possibly occurs as well as describes the diameter mark and the movement which realizes by certain components. The definition second part of available following two aspect explained ：1. research produces with the aid of the organization assigns the movement the method. 2. research construction to be able to produce assigns the motion the method, but in two plans, the movement is assigns the organization is the foundation. This is the movement synthesis essence. Such movement synthesis involves to for assigns the performance the organization system design. The movement synthesis aspect may sum up as following two kinds: 1. types are comprehensive. The stipulation requests the performance, how is one kind of type organization appropriate? (Tooth gear train, link motion gear? Cam gear?)How many components but should the organization have? How many degrees of freedom needs? How outline structure is hoped? . About the member number and the degree of freedom consideration was usually considered is in the type synthesis is been called as for a quantity synthesis branch domain. 2. sizes are comprehensive. The movement synthesis second predominant type is the best method which determined through the goal law. The size synthesis attempts to determine the organization the important size and the starting position, this organization is conceives beforehand for the realization stipulation duty and the anticipated performance. Of the so-called important size meanings are refer about two poles, three poles and so on between the length or the pole are away from, angle between number of articles and spool thread, cam contour size, cam follower diameter, eccentricity, gear quota and so on. Expected the organization type possibly is the crank slide organization, four pole organizations, the tape reel from the moving parts cam gear, but or is non-has some kind of structure shape more complex link motion gear because by the analysis situs method which the inferior analytic method determined. Is comprehensive regarding the movement, in the convention has three duties: Function production, path production and movement production. Inputs and outputs the component in the function production organization the rotation or the migration must be the interdependence. Regarding arbitrary function y=f(x), a movement synthesis duty possibly is designs a link motion gear to cause the input and the output establishes the relations in order to cause in the xoxxn-1 scope to input according to x movement, but outputs according to the y=f(x) movement. In the input and in the output gyroscopic motion situation, the corner phi and phi respectively is x and the y linear simulation. When inputs rotates to an independence x value, in one “black box” in the organization, causes to output which the component to change to corresponds in the value which by function y=f(x) decided. This may consider is the mechanical analogy computer simple situation. Each kind of different organization all may contain in this “the black box” in, however produces regarding the arbitrary function non-error, four pole organizations are helpless, possibly matches merely in the limited precision with it. It widely uses in the industry, because four pole organizations in the construction and the service all are simple. In the path production organization, in “floats the walking beam” on a spot to have to draw one to be opposite in a fixed coordinate system determination path. If this path spot is both must and have to be related with the time correlation with the position, this duty is called it the predetermined cyclical path production. A path production organization example is the design throws the baseball or the tennis four pole organization. In this case, will select P the path will be this: Picks a ball in the predetermined position, and transmits in the predetermined time cycle along the predetermined diameter mark the ball, can achieve the appropriate speed and the direction. In the mechanism design has many situations, both must guide the rigid body in these situations through a series of stipulations, the independent position which limits, and must limit in the reduction when independent position number, to the vehicle speed and (or) the acceleration restrains, that is necessary. Movement production or rigid body guiding organization request: A complete object must guide passes a predetermined movement sequence. Took the object which guides usually is “the fluctuation component” not only a part, that is the target point P path, also is and inserts in this object through this spot the line rotation. For example, this possibly represents in the automated machinery a carrier, but that has a predetermined path in a carrier on spot this carrier also to have a predetermined angle position. The predetermined way charger cableway bucket movement is the movement production organization another example. The cableway bucket end path has the limit. Because its port must realize the excavation path, is following close on the path which must realize promotes and falls in torrents. The cableway bucket angle position to guaranteed fights the material to fall in torrents from the correct position similarly is (but actually) important.The cam and the gearcam gear is changes one kind of movement Cheng Ling one kind of movement the convenience installment. This kind of machine part has the curved surface or the trough surface, this curved surface or the trough surface with passes to from the moving parts appropriate match merge the movement from the moving parts. The cam movement (usually is rotation) is transmitted for does from the moving parts the undulation or the migration, or both have. Because various geometric solid and the massive cams with unify from the moving parts, therefore the cam is one kind of extremely numerous function multi-purpose machine parts. Although the cam and from the moving parts may for the movement, the path and the function production designs, but it mainly is uses in using the cam and takes the function production component from the moving parts. According to the cam shape, the most universal cam type is: Disc transmission cam (two dimensional, namely plane) and cylindrical cam (three dimensional, namely space) organization. May use several methods from the moving parts to classify: According to from the moving parts movement, for example the migration or the undulation classifies, according to the translation type (straight line) from the moving parts movement is along the radial direction from the cam shaft center bias and the basis from the moving parts contact face shape (for instance plane, rollarounds, spot - - knife point type, spherical surface, plane curve or space-like surface). Regarding one to the heart translation roller from the moving parts disk cam, may draw and cam surface contacting also with the wheel axle concentric most small circle is the base circle. The follower spot produces the pitch line rollarounds center spot. The angle of pressure is the roller center path course line and passes the rollarounds center between the pitch line normal included angle moreover is the transmission angle coangle. The neglect frictional influence, this normal direction with the cam with from the moving parts the contact force direction is the superposition consistent. In a link motion gear, the angle of pressure the change is precisely likely the cam transmits in the circulation generating process the movement action one kind of measurement which goes from the moving parts. The big angle of pressure will produce exerts from the moving parts pole side force, because of the friction force existence, that inevitably will limit from the moving parts in the guide channel. Need the intermittent motion in automated machinery many applications. As soon as a typical example will request one to include the rise to stand still a returns and the possible another idle time cycle, each stage will pass through the angle which will assign, will follow an institute to request from the moving parts displacement, this displacement or will measure by the centimeter. Designers work designs this cam correspondingly. First must do the decision-making is must choose the cam from the moving parts type. The stipulation application possible to request the cam and unifies from the moving parts. Transforms includes for policy-making certain factors: Geometry shape condition, dynamic condition, environmental condition and economic agent. Once the cam with was designated from the moving parts movement vice-type, then surely designated from the moving parts movement. Therefore, the speed, the acceleration and in certain situations, really are the extreme from the moving parts displacement further plan to be important. The gear is draws support in gear teeth success meshing transmits the movement the machine part. Gear from a gyro-axle to another gyro-axle transmission movement or transmission movement to a transmission rack. In the most applications all (or often decides torque by the constant angle transmission ratio to compare) exists. In the constant angle transmission ratio application is surely the axial transmission. In various useful gear type foundation, the input axis and the output shaft need or need parallel mutually in a straight line all not any limit. Because uses the non-round gear, the non-linear angle transmission ratio also is very useful. In order to maintain the constant angular speed, each gear tooth profile must obey the gear meshing the basic rule: In order to a pair of tooth can transmit the constant angle transmission ratio, they contact the tooth profile the shape to have to be must like this: The common normal passes in two