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Khurmi, J. Other Useful Links. Your Comments About This Post. Is our service is satisfied, Anything want to say? Cancel reply. Please enter your comment! Please enter your name here. You have entered an incorrect email address! Leave this field empty. Trending Today. With the motion of the link containing the slot and the relative sliding motion taking place in the slot as known quantities, we may wish to find the absolute l11otionof the sliding member.
It was for problems of this type that the apparent-displacement vector was defined in Section 2. A rigid link having some general motion carries a coordinate system xzyzzz attached to it. All points of link 2 move with the coordinate system. Also, during the same time interval, another point P3 of another link 3 is constrained in some manner to move along a known path with respect to link 2.
Although it is pictured in this way, the constraint may occur in a variety of different forms. Recalling the apparent-displacement equation 2. We note from its definition, Eq. Thus, in concept, it is the velocity of the moving point P3 as it would appear to an observer attached to the moving link 2 and making observations in coordinate system xzyzzz.
This concept accounts for its name. We also note that the absolute velocity is a spe- cial case of the apparent velocity where the observer happens to be fixed to the Xl YI Z I coordinate system. We can get further insight into the nature of the apparent-velocity vector by studying Fig.
This figure shows the view of the moving point P3 as it would be seen by the moving observer. Working in this coordinate system, suppose we locate the point C as the center of curvature of the path of point P3.
We now define the unit-vector tangent to the path 1: with positive sense in the direction of pos- itive movement. The plane defined by this tangent vector 1: and the center of curvature Cis called the osculating plane. In the cam-and-follower system shown in Fig. We see that if slip were not possible between links 2 and 3 at point P, the triangle P AB would form a truss; therefore, sliding as well as rotation must take place between the links.
Let us distinguish between the two points P2 attached to link 2 and P3 attached to link 3. Components could then be taken along directions defined by the common normal and common tangent to the surfaces at the point of direct contact.
Otherwise, either the two links would separate or they would interfere, both contrary to our basic assumption that contact persists. The velocity polygon for this system is shown in Fig. It is possible in other mechanisms for there to be direct contact between links without slip between the links. The cam-follower system of Fig. Henceforth we will restrict the use of the term rolling contact to situations where no slip takes place.
By "no slip" we imply that the apparent "slipping" velocity ofEq. By Eq. The graphical solution of the problem of Fig. Given W2, the velocity difference V P2B can be calculated and plotted, thus locating point P2 in the velocity polygon. Using Eq. This second approach would be necessary if we had not assumed rolling contact no-slip at P.
It will also be noticed that the word "relative" velocity has been carefully avoided. Instead we note that whenever the desire for using "relative" velocity arises, there are always two points whose velocities are to be "related"; also, these two points are attached either to the same or to two different rigid bodies. Therefore, we can organize all situations into the four cases shown in Table 3. In this table we can see that when the two points are separated by a distance, only the velocity difference equation is appropriate for use and two points on the same link should be used.
When it is desirable to switch to points of another link, then coincident points should be chosen and the appar- ent velocity equation should be used. Here, link 3 rotates about a point called an instant center located at infinity see Section 3. This has the effect of a connecting rod of infinite length, and the second terms of Eqs. Hence, for the Scotch yoke we have Thus the slider moves with simple harmonic motion. It is for this reason that the deviation of the kinematics of the slider-crank motion from simple harmonic motion is sometimes said to be due to "the angularity of the connecting rod.
As we saw, the complex-algebra formu- lation provides the advantage of increased accuracy over the graphical methods, and it is amenable to solution by digital computer at a large number of positions once the program is written.
On the other hand, the solution of the loop-closure equation for its unknown position variables is a nonlinear problem and can lead to tedious algebraic manipulations. Fortunately, as we will see, the extension of the complex-algebra approach to velocity analysis leads to a set of linear equations, and solution is quite straightforward. Recalling the complex polar form of a two-dimensional vector from Eq.
This analytical approach is referred to as the method of kinematic coefficients. The numeric values ofthe first-order kinematic coefficients can also be checked with the graphical approach of finding the loca- tions of the instantaneous centers of zero velocity. This method is illustrated here by again solving the four-bar linkage problem that was presented in Example 3. For the mechanism shown in Fig. The radius of the wheel is 10 em. The length of the input link 2 is 1. In particular, we shall find that an axis exists which is common to both bodies and about which either body can be considered as rotating with respect to the other.
We shall refer to them as instant centers of velocity or velocity poles. These instant centers are regarded as pairs of coincident points, one attached to each body, about which one body has an apparent rotational velocity, but no translation velocity, with respect to the other.
This property is true only instantaneously, and a new pair of coincident points becomes the instant center at the next instant. It is not correct, therefore, to speak of an instant center as the center of rotation, because it is generally not located at the center of curvature of the apparent point path which a point of one body generates with respect to the coordinate system of the other.
Even with this restriction, however, we will find that instant centers contribute substantially to understanding the kinematics of planar motion. The classic work covering its properties is R. The instant center can be located more easily when the absolute velocities of two points are given. Per- pendiculars to V A and Vc intersect at P, the instant center. Figure 3. The instant center between two bodies, in general, is not a stationary point.
It changes its location with respect to both bodies as the motion progresses and describes a path or locus on each. These paths of the instant centers, called centrodes, will be discussed in Section 3. Because we have adopted the convention of numbering the links of a mechanism, it is convenient to designate an instant center by using the numbers of the two links associated with it.
Thus P32 identifies the instant centers between links 3 and 2. This same center could be identified as P23, because the order of the numbers has no significance.
A mechanism has as many instant centers as there are ways of pairing the link numbers. Thus the number of instant centers in an n-link mechanism is According to Eg. Point P23, for example, is a point of link 2 about which link 3 appears to rotate; it is a point of link 3 which has no apparent velocity as seen from link 2; it is a pair of coinci- dent points of links 2 and 3 which has the same absolute velocities. A good method of keeping track of which instant centers have been found is to space the link numbers around the perimeter of a circle, as shown in Fig.
Then, as each in- stant center is identified, a line is drawn connecting the corresponding pair of link numbers. These two instant centers cannot be found simply by applying the definition visually. This theorem states that the three instant centers shared by three rigid bodies in relative motion to one another whether or not they are connected all lie on the same straight line.
The theorem can be proven by contradiction, as shown in Fig. Link 1 is a station- ary frame, and instant center Pl2 is located where link 2 is pin-connected to it. Similarly, Pl3 is located at the pin connecting links 1 and 3. The shapes of links 2 and 3 are arbitrary. The Aronhold-Kennedy theorem states that the three instant centers P12, Pl3, and P23 must all lie on the same straight line, the line connecting the two pins. Let us suppose that this were not true; in fact let us suppose that P23 were located at the point labeled P in Fig.
The directions are inconsistent with the definition that an instant center must have equal absolute velocities as a part of either link. The point P chosen therefore cannot be the instant center P This same contradiction in the directions of V P, and V P, occurs for any location chosen for point P unless it is chosen on the straight line through P12 and P In the last two sections we have considered several methods of locating instant centers of velocity.
They can often be located by inspecting the figure of a mechanism and visually seeking out a point that fits the definition, such as a pin-joint center. Also, after some instant centers are found, others can be found from them by using the theorem of three centers. Section 3.
The purpose of this section is to expand this list of techniques and to present examples. It is known as the Aronhold theorem in German-speaking countries and is called Kennedy's theorem in English-speaking countries. Consider the cam-follower system of Fig. The instant centers P12 and Pl3 can be located, by inspection, at the two pin centers.
However, the remaining instant center, P23, is not as obvious. According to the Aronhold-Kennedy theorem, it must lie on the straight line connecting P12 and Pl3, but where on this line?
After some reflection we see that the direction of the apparent velocity V Ad3 must be along the common tangent to the two mov- ing links at the point of contact; and, as seen by an observer on link 3, this velocity must appear as a result of the apparent rotation of body 2 about the instant center P This line now locates P23 as shown.
The concept illustrated in this example should be remembered because it is often useful in locating the instant centers of mechanisms involving direct contact. A special case of direct contact, as we have seen before, is rolling contact with no slip. Considering the mechanism of Fig. If the contact between links 1 and 4 involves any slippage, we can only say that instant center P14 is located on the vertical line through the point of contact.
How- ever, if we also know that there is no slippage-that is, if there is rolling contact-then the instant center is located at the point of contact. This is also a general principle, as can be seen by comparing the definition of rolling contact, Eq.
Another special case of direct contact is evident between links 3 and 4 in Fig 3. Here, as in Fig. The instant centers P13, P34, and P15, being pinned joints, are located by inspection. Also, Pl2 is located at the point of rolling contact. After these, all otherinstant. In the analysis and design of linkages it is often important to know the phases of the link- age at which the extreme values of the output velocity occur or, more precisely, the phases at which the ratio of the output and input velocities reaches its extremes.
Rosenauer, however, showed that this is not strictly true. The theorem states that at an extreme of the output to input angular velocity ratio of a four-bar linkage, the collineation axis is perpendicular to the coupler link.
During motion of the linkage, P24 travels along the line P12P14 as seen by the theorem of three centers; but at an extreme value of the velocity ratio, P24 must instantaneously be at rest its direction of travel on this line must be reversing. This occurs when the velocity of P24, considered as a point of link 3, is directed along the coupler link. This will be true only when the coupler link is perpendicular to the collineation axis, because PI3 is the instant center of link 3.
In this section we will study some of the various ratios, angles, and other parameters of mechanisms that tell us whether a mechanism is a good one or a poor one. Many such pa- rameters have been defined by various authors over the years, and there is no common agreement on a single "index of merit" for all mechanisms.
In addition, most depend on some knowledge of the application of the mech- anism, especially of which are the input and output links. It is often desirable in the analy- sis or synthesis of mechanisms to plot these indices of merit for a revolution of the input crank and to notice in particular their minimum and maximum values when evaluating the design of the mechanism or its suitability for a given application.
Thus, in the four-bar linkage of Fig. We also learned in Section 3. If we now assume that the linkage of Fig. Because friction and inertia forces are negligible, the input power applied to link 2 is the negative of the power applied to link 4 by the load; hence The mechanical advantage of a mechanism is the instantaneous ratio of the output force torque to the input force torque.
Here we see that the mechanical advantage is the negative reciprocal of the velocity ratio. Either can be used as an index of merit in judging a mechanism's ability to transmit force or power. The mechanism is redrawn in Fig. In Sections 1.
This angle is also often used as an index of merit for a four- bar linkage. Equation 3. If the transmission angle becomes too small, the mechanical advantage becomes small and even a very small amount of friction may cause a mechanism to lock or jam. In other mechanisms-for example, meshing gear teeth or a earn-follower system- the pressure angle is used as an index of merit.
The pressure angle is defined as the acute angle between the direction of the output force and the direction of the velocity of the point where the output force is applied. Pressure angles are discussed more thoroughly in Chap- ters 5 and 6. In the four-bar linkage, the pressure angle is the complement of the transmis- sion angle. Another index of merit which has been proposed6 is the determinant of the coeffi- cients of the simultaneous equations relating the dependent velocities of a mechanism.
In Example 3. For the original linkage, with link I fixed, this is the curve traced by PI3 on the coordinate system of the moving link 3; it is called the moving centrode. It is imagined here that links 1 and 3 have been machined to the actual shapes of the respective centrodes and that links 2 and 4 have been removed entirely. If the moving centrode is now permitted to roll on the fixed centrode without slip, link 3 will have exactly the same motion as it had in the original linkage. This remarkable property, which stems from the fact that a point of rolling contact is an instant center, turns out to be quite useful in the synthesis of linkages.
We can restate this property as follows: The plane motion of one rigid body with respect to another is completely equivalent to the rolling motion of one centrode on the other. The instantaneous point of rolling contact is the instant center, as shown in Fig.
Also shown are the common tangent to the two centrodes and the common normal, called the centrode tangent and the centrode normal; they are sometimes used as the axes of a coordinate sys- tem for developing equations for a coupler curve or other properties of the motion.
The centrodes of Fig. Another set of centrodes, both moving, is generated on links 2 and 4 when instant center P24 is considered. These two centrodes roll upon each other and describe the identical motion between links 2 and 4 which would result from the operation of the origi- nal four-bar linkage. This construction can be used as the basis for the development of a pair of elliptical gears.
E, vol. The angular acceleration of the crank link 2 is zero, and notice that the corresponding acceleration image is turned from 0 the orientation of the link itself.
On the other hand, notice that link 3 has a counterclock- wise angular acceleration and that its image is oriented less than from the orientation 0 of the link itself. Thus the orientation of the acceleration image depends on the angular ac- celeration of the link in question.
Let us now investigate the acceleration of such a point. To review, Fig. It serves the objectives of this section because it relates the accelerations of two coincident points on different links in a meaningful way. There is only one unknown among the three new components defined. The Coriolis and normal components can be calculated from Eqs. It is important to notice the dependence of Eq.
This path is the basis for the axes for the normal and tangential components and is also neces- sary for determination of p for Eq. Finally, a word of warning: The path described by P3 on link 2 is not necessarily the same as the path described by P2 on link 3. The path of P2 on link 3 is not at all clear.
As a result, there is a natural "right" and "wrong" way to write the apparent -acceleration equation for that situation. We defined the term rolling contact to imply that no slip is in progress and developed the rolling contact condition, Eq.
Here we intend to investigate the apparent accel- eration at a point of rolling contact. Consider the case of a circular wheel in rolling contact with another straight link, as shown in Fig. Although this is admittedly a very simplified case, the arguments made and the conclusions reached are completely general and apply to any rolling-contact situa- tion, no matter what the shapes of the two bodies or whether either is the ground link.
To keep this clear in our minds, the ground link has been numbered 2 for this example. Once the acceleration Ac of the center point of the wheel is given, the pole 0 A can be chosen and the acceleration polygon can be started by plotting Ac.
In relating the acceler- ations of points P3 and Pz at the rolling contact point, however, we are dealing with two coincident points of different bodies. Therefore, it is appropriate to use the apparent accel- eration equation. To do this we must identify a path that one of these points traces on the other body. Although the pre- cise shape of the path depends on the shapes of the two contacting links, it will always have a cusp at the point of rolling contact and the tangent to this cusp-shaped path will always be normal to the surfaces that are in contact.
Recall that link 2 of that four-bar linkage is driven at a constant angular velocity of In planar mechanisms this can be done by the methods presented below. When two rigid bodies move relative to each other with planar motion, any arbitrarily chosen point A of one describes a path or locus relative to a coordinate system fixed to the other. At any given instant there is a point A', attached to the other body, which is the cen- ter of curvature of the locus of A.
If we take the kinematic inversion of this motion, A' also describes a locus relative to the body containing A, and it so happens that A is the center of curvature of this locus. Each point therefore acts as the center of curvature of the path traced by the other, and the two points are called conjugates of each other. The distance be- tween these two conjugate points is the radius of curvature of either locus.
Figure 4. Let us think of the circle with center C' as the fixed centrode and think of the circle with center C as the moving centrode of two bodies experiencing some particular relative planar motion. In actuality, the fixed centrode need not be fixed but is attached to the body that contains the path whose curva- ture is sought.
Also, it is not necessary that the two centrodes be circles; we are interested only in instantaneous values and, for convenience, we will think of the centrodes as circles matching the curvatures of the two actual centrodes in the region near their point of contact P.
As pointed out in Section 3. Their point of contact P, of course, is the instant center of velocity. Because of these properties, we can think of the two circular centrodes as actually representing the shapes of the two moving bodies if this helps in visualizing the motion. The Hartmann construction provides one graphical method of finding the conjugate point and the radius of curvature of the path of a moving point, but it requires knowledge of the curvature of the fixed and moving centrodes.
It would be desirable to have graphical meth- ods of obtaining the inflection circle and the conjugate of a given point without requiring the curvature of the centrodes. Such graphical solutions are presented in this section and are called the Bobillier constructions. To understand these constructions, consider the inflection circle and the centrode normal Nand centrode tangent T shown in Fig.
Let us select any two points A and B of the moving body which are not on a straight line through P. Now, by using the Euler-Savary equation, we can find the two corresponding conjugate points A' and B'.
Then, the straight line drawn through P and Q is called the collineation axis. This axis applies only to the two lines AA' and BB' and so is said to belong to these two rays; also, the point Q will be located differently on the collineation axis if another set of points A and B is chosen on the same rays. Nevertheless, there is a unique relationship between the collineation axis and the two rays used to define it. This relationship is expressed in Bobillier 's theorem, which states that the angle from the centrode tangent to one of these rays is the negative of the angle from the collineation axis to the other ray.
In applying the Euler-Savary equation to a planar mechanism, we can usually find two pairs of conjugate points by inspection, and from these we wish to determine the inflection circle graphically. For example, a four-bar linkage with a crank 02A and a follower 04B has A and O2 as one set of conjugate points and Band 04 as the other, when we are inter- ested in the motion of the coupler relative to the frame. Given these two pairs of conjugate points, how do we use the Bobillier theorem to find the inflection circle?
Rays constructed through each pair intersect at P, the instant center of velocity, giving one point on the inflection circle. Then the collineation axis can be drawn as the line PQ. The next step is shown in Fig. Drawing a straight line through P parallel to A' B', we identify the point W as the intersection of this line with the line AB. Now, through W we draw a second line parallel to the collineation axis. We could now construct the circle through the three points I A, Is, and P, but there is an easier way.
Remembering that a triangle inscribed in a semicircle is a right triangle having the diameter as its hypotenuse, we erect a perpendicular to A P at I A and another perpendicular to B P at Is. The intersection of these two perpendiculars gives point I, the inflection pole, as shown in Fig. Because P I is the diameter, the inflection circle, the centrode normal N, and the centrode tangent T can all be easily constructed. To show that this construction satisfies the Bobillier theorem, note that the arc from P to I A is inscribed by the angle that lAP makes with the centrode tangent.
But this same arc is also inscribed by the angle PIsIA. Therefore these two angles are equal. But the line IslA was originally constructed parallel to the collineation axis. Therefore, the line PIs also makes the same angle f3 with the colliineation axis. Our final problem is to learn how to use the Bobillier theorem to find the conjugate of another arbitrary point, say C, when the inflection circle is given.
This ray serves as one of the two necessary to locate the collineation axis. For the other we may as well use the centrode normal, because I and its conjugate point 1', at infinity, are both known. For these two rays the collineation axis is a line through P parallel to the line Ie I, as we learned in Fig.
The balance of the construction is similar to that of Fig. Point Q is located by the intersection of a line through I and C with the collineation axis. The sign convention is as follows: If the unit normal vector to the point trajectory points away from the center of curvature of the path, then the radius of curvature has a positive value. If the unit normal vector to the point trajectory points toward the center of curvature of the path, then the radius of curvature has a negative value.
The coordinates of the center of curvature of the point trajectory, at the position under investigation, can be written as Consider a point on the coupler of a planar four-bar linkage that generates a path relative to the frame whose radius of curvature, at the instant considered, is p. For most cases, because the coupler curve is of sixth order, this radius of curvature changes continuously as the point moves.
In certain situations, however, the path will have stationary curvature, which means that where s is the increment traveled along the path.
The locus of all points on the coupler or moving plane which have stationary curvature at the instant considered is called the cubic of stationary curvature or sometimes the circling-point curve. It should be noted that sta- tionary curvature does not necessarily mean constant curvature, but rather that the contin- ually varying radius of curvature is passing through a maximum or minimum.
Here we will present a fast and simple graphical method for obtaining the cubic of sta- tionary curvature, as described by Hain. Then points A and B have stationary curvature-in fact, constant curvature about centers at A' and B'; hence, A and B lie on the cubic.
The first step of the construction is to obtain the centrode normal and centrode tangent. This construction follows directly from Bobillier's theorem. We also construct the centrode normal N. At this point it may be convenient to reorient the drawing on the working sur- face so that the T-square or horizontal lies along the centrode normal. Next we choose any point SG on the line G. Connecting ST with SN and drawing a perpendicular to this line through P locates point S, another point on the cubic of stationary curvature.
We now repeat this process as often as desired by choosing different points on G, and we draw the cubic as a smooth curve through all the points S obtained. Note that the cubic of stationary curvature has two tangents at P, the centrode- normal tangent and the centrode-tangent tangent. Then, half the distance PGT is the radius of curvature of the cubic at the centrode-normal tangent, and half the distance PG N is the radius of curvature of the cubic at the centrode-tangent tangent.
A point with interesting properties occurs at the intersection of the cubic of stationary curvature with the inflection circle; this point is called Ball's point.
A point of the coupler coincident with Ball's point describes a path that is approximately a straight line because it is located at an inflection point of its path and has stationary curvature. The constants M and N are found by using any two points known to lie on the cubic, such as points A and B of Fig. It so happens5 that M and N are, respectively, the diameters P GT and P G N of the circles centered on the cen- trode tangent and centrode normal whose radii represent the two curvatures of the cubic at the instant center.
Rosenauer and A. Goodman et al. Applied Kinematics, 2nd ed. The most important and most useful references on this subject are Rosenauer and Willis, Kine- matics of Mechanisms, Chapter 4; A. ASME, vol. Hartenberg and J. Hain, Applied Kinematics, pp. For a derivation ofthis equation seeA.
Denavit, Kinematic Synthesis of Linkages, , p. Draw a circle through C with center at C' and complete this circle with the actual path of C. We were given the design of a mechanism and we studied ways to determine its mobility, its position, its velocity, and its acceleration, and we even discussed its suitability for given types of tasks. However, we have said little about how the mecha- nism was designed-that is, how the sizes and shapes of its links are chosen by the designer.
The next several chapters will introduce this design point of view as it relates to mech- anisms. We will find ourselves looking more at individual types of machine components, and learning when and why such components are used and how they are sized. In this chap- ter, devoted to the design of cams, for example, we will assume that we know the task to be accomplished. However, we will not know, but will look for techniques to help discover, the size and shape of the cam to perform this task.
Of course, there is the creative process of deciding whether we should use a cam in the first place, or rather a gear train, or a linkage, or some other idea. This question often can- not be answered on the basis of scientific principles alone; it requires experience and imag- ination and involves such factors as economics, marketability, reliability, maintenance, es- thetics, ergonomics, ability to manufacture, and suitability to the task.
These aspects are not well-studied by a general scientific approach; they require human judgment of factors that are often not easily reduced to numbers or formulae. There is usually not a single "right" answer, and these questions cannot be answered by this or any other text or reference book. On the other hand, this is not to say that there is no place for a general science-based approach in design situations. Most mechanical design is based on repetitive analysis.
Therefore, in this chapter and in future chapters, we will use the principles of analysis pre- sented in the previous chapters. The coming several chapters will still be based on the laws of mechanics. The primary shift for Part 2 of this book is that the component dimensions will often be the unknowns of the problem, while the input and output speeds, for example, may be given information. In this chapter we will discover how to determine a earn contour which will deliver a specified motion.
A cam is a mechanical element used to drive another element, called the follower, through a specified motion by direct contact. Cam-and-follower mechanisms are simple and inex- pensive, have few moving parts, and occupy a very small space. Furthermore, follower mo- tions having almost any desired characteristics are not difficult to design. The versatility and flexibility in the design of earn systems are among their more at- tractive features, yet this also leads to a wide variety of shapes and forms and the need for terminology to distinguish them.
Cams are classified according to their basic shapes. Figure 5. By far the most common is the plate earn. For this reason, most of the remainder of this chapter specifically addresses plate cams, although the concepts presented pertain universally. Cam systems can also be classified according to the basic shape of the follower. This is not al- ways the case; and examples of inverse cams, where the output element is machined to a complex shape, can be found. Another method of classifying cams is according to the characteristic output motion allowed between the follower and the frame.
Thus, some cams have reciprocating trans- lating followers, as in Figs. Further classifica- tion of reciprocating followers distinguishes whether the centerline of the follower stem relative to the center of the earn is offset, as in Fig. In all cam systems the designer must ensure that the follower maintains contact with the cam at all times. This can be accomplished by depending on gravity, by the inclusion of a suitable spring, or by a mechanical constraint.
Mechanical constraint can also be introduced by employing dual or conjugate cams in an arrangement like that illus- trated in Fig. Here each cam has its own roller, but the rollers are mounted on a com- mon follower.
In spite of the wide variety of cam types used and their differences in form, they also have certain features in common which allow a systematic approach to their design. Usually a cam system is a single-degree-of-freedom device. It is driven by a known input motion, usually a shaft that rotates at constant speed, and it is intended to produce a certain desired periodic output motion for the follower.
In order to investigate the design of cams in general, we will denote the known input motion by aCt and the output motion by y. Reviewing Figs. These figures also show that y is a trans- lational distance for a reciprocating follower but is an angle for an oscillating follower. During the rotation of the cam through one cycle of input motion, the follower executes a series of events as shown in graphical form in the displacement diagram of Fig.
In such a diagram the abscissa represents one cycle of the input motion a one rev- olution of the cam and is drawn to any convenient scale. Since the variety is unbounded no standard solutions are shown here. Assemble the links in all possible combinations and sketch the four inversions of each. Do these linkages satisfy Grashof's law? Describe each inversion by name, for example, a crank- rocker mechanism or a drag-link mechanism. Drag-link mechanism Drag-link mechanism Ans. Crank-rocker mechanism Crank-rocker mechanism Ans.
Double-rocker mechanism Crank-rocker mechanism Ans. Draw the linkage and find the maximum and minimum values of the transmission angle. Locate both toggle positions and record the corresponding crank angles and transmission angles. Download full file from buklibry. For the instantaneous motion of the coupler link AB show: a the velocity pole I, the pole tangent T, and the pole normal N; b the inflection circle and the Bresse circle; c the acceleration center of the coupler link AB.
The instant center I 24 and the collineation axis are as shown in the figure.
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