Failure 4. If valid go to Step 6. Check that the power fail Defective buzzer on LED is lit. Page 98 Chapter 4: Troubleshooting Troubleshooting Tables 4.
Too much ambient Also, make sure that procedure light and sunlight observation lights are not at the highest settings, If not OK, replace power supply. If OK, replace Defective probe patient probe. Plug in replacement cable and part : re-test. Replace harness as necessary. Wrench Remove and check fuses F1, F4. Replace as Needle nose pliers, necessary. In addition, check the contacts on Warmer head the Warmer head harness.
Printed Circuit Board. Liquid Crystal Display. Digital Multi-Meter. An electronic measuring instrument that combines several functions in one unit. Digital Multimeter An electronic instrument that measures electrical resistance. Follow your local health and safety guidelines for manual handling of heavy objects when lifting and carrying the heater head.
For Wall Mount Warmer models, it is necessary to remove the heater head from the wall bracket to access the rear side of the unit for repairs.
Two of the screws that secure the duct are behind the power supply mounting plates. Heater alignment is also required after the installation of wall mount models. Refer to section 5. Disconnect wire ties from power supply mounting plate using 2 mm hex key. Disconnect ground wire from bracket using 7 mm socket wrench.
Using a 3mm hex key, remove the power supply bracket mounting screws. Electronics Enclosure Disassembly 5. Turn lamp off and allow 5 minutes to cool before replacing bulb. Use a 3 mm hex key to remove the single socket head screw that holds the procedure light in place.
This will allow the entire lamp to dangle by its connecting wires. Power Board Panel 5. Caution: Dispose of the battery in accordance with local toxic waste regulations. Display and Touch Panel 5. Loosen the 2 captive screws at the top of the enclosures rear panel, then tilt the panel down and lift the 2 tabs at the bottom of the panel up out of the slots that they seat in.
Do not pry them out use needle nose pliers and pull straight out. For bedded model, tilt the bed so the back is down and the front is all the way up. Disassemble the probe panel housing following instructions 5. Slide the decorative strip down, and remove it from the dovetail. Slide the upper housing forward to remove it from the dovetail rails. Make sure that you do not pinch the electrical wires. Ensure that foot switch connectors are secured with retaining clips.
Base, Legs, and Rails Service Manual Page Chapter 5: Repair Procedures Lower Unit Repairs Bedded and Freestanding Models Re-install the retaining plates in the rails such that the top of the plates are aligned with the top of the mounting block and M8 set screws are located on top see Figure Choose one: Harness Power Factor Correction M Label Set Giraffe Branding M Inductor mounting bracket M Label Set Panda Branding M Lock nut MS Washer, M3 X 3.
MS Split ring washer, M M Thermostat Electronics Enclosure Rear enclosure cover includes labels.. M Control board See Table on page Keps nut, M M Standoff, M3 8 x M Probe panel interface board M Power board M Split ring washer, M3 X 3. M Screw x. Refer section 6. Probe Panel Housing Probe panel housing top M Split ring washer M4 x 4. Jack ground plate Newer units display a label with a part number near the top of the elevating column.
Page Chapter 6: Illustrated Parts Base Assembly Bedded Models Only Note: It is important to select the correct version of elevating column as they are not forward or backward compatible. TABLE Rail Attachments Cover strip, plastic units without Split ring washer, M M Service Manual Bed Assembly - 2 Main axle Page Rear bed side panel assy. Page Replacement And Additional Parts 6.
M 6. Label Locations on Probe Panel Housing 6. Page Chapter 6: Illustrated Parts Labels 6. F7, F8 6. Control Board Service Manual The volunteers ranged in age from 18 to 50 years old, comprised men and women of varied skin pigmentation, and were selected from local population. This variation equals plus or minus, one standard deviation. Page A. This link in a practical machine usually takes the form of a stationary platform or base or a housing rigidly attached to such a base and is called the frame or base link.
The question of whether this reference frame is truly stationary in the sense of being an inertial reference frame is immaterial in the study of kinematics but becomes important in the investigation of kinetics, where forces are considered.
In either case, once a frame member is designated and other conditions are met , the kinematic chain becomes a mechanism and as the driver is moved through various positions, called phases, all other links have well-defined motions with respect to the chosen frame of reference. We use the term kinematic chain to specify a particular arrangement of links and joints when it is not clear which link is to be treated as the frame. When the frame link is specified, the kinematic chain is called a mechanism.
In order for a mechanism to be useful, the motions between links cannot be completely arbitrary; they too must be constrained to produce the proper relative motions, those chosen by the designer for the particular task to be performed. These desired relative motions are obtained by a proper choice of the number of links and the kinds of joints used to connect them.
Thus we are led to the concept that, in addition to the distances between successive joints, the nature of the joints themselves and the relative motions that they permit are es- sential in determining the kinematics of a mechanism.
For this reason it is important to look more closely at the nature of joints in general terms, and in particular at several of the more common types.
The controlling factor that determines the relative motions allowed by a given joint is the shapes of the mating surfaces or elements. Each type of joint has its own characteristic shapes for the elements, and each allows a given type of motion, which is determined by the possible ways in which these elemental surfaces can move with respect to each other.
For example, the pin joint in Fig. Thus a pinjoint allows the two connected links to experience relative rotation about the pin center. So, too, other joints each have their own characteristic element shapes and relative motions. These shapes restrict the totally arbitrary motion of two unconnected links to some prescribed type of relative motion and form the constraining conditions or constraints on the mechanism's motion.
It should be pointed out that the element shapes may often be subtly disguised and dif- ficult to recognize. For example, a pin joint might include a needle bearing, so that two mat- ing surfaces, as such, are not distinguishable.
Nevertheless, if the motions of the individual rollers are not of interest, the motions allowed by the joints are equivalent and the pairs are of the same generic type. Thus the criterion for distinguishing different pair types is the relative motions they permit and not necessarily the shapes of the elements, though these may provide vital clues.
The diameter of the pin used or other dimensional data is also of no more importance than the exact sizes and shapes of the connected links. In a similar way, the only kinematic function of a joint or pair is to con- trol the relative motion between the connected links.
All other features are determined for other reasons and are unimportant in the study of kinematics. When a kinematic problem is formulated, it is necessary to recognize the type of rela- tive motion permitted in each of the pairs and to assign to it some variable parameter s for measuring or calculating the motion.
There will be as many of these parameters as there are degrees of freedom of the joint in question, and they are referred to as the pair variables. Thus the pair variable of a pinned joint will be a single angle measured between reference lines fixed in the adjacent links, while a spheric pair will have three pair variables all angles to specify its three-dimensional rotation.
Kinematic pairs were divided by Reuleaux into higher pairs and lower pairs, with the latter category consisting of six prescribed types to be discussed next. He distinguished between the categories by noting that the lower pairs, such as the pin joint, have surface contact between the pair elements, while higher pairs, such as the connection between a earn and its follower, have line or point contact between the elemental surfaces.
However, as noted in the case of a needle bearing, this criterion may be misleading. We should rather look for distinguishing features in the relative motion s that the joint allows. The six lower pairs are illustrated in Fig. Table 1. This pair is often referred to as a pin joint. One such grouping divides mechanisms into planar, spherical, and spatiiI categories.
All three groups have many things in common; the criterion that distinguishes the groups, however, is to be found in the characteristics of the motions of the links. A planar mechanism is one in which all particles describe plane curves in space and all these curves lie in parallel planes; that is, the loci of all points are plane curves parallel to a single common plane.
This characteristic makes it possible to represent the locus of any chosen point of a planar mechanism in its true size and shape on a single drawing or figure. The motion transformation of any such mechanism is called coplanar. The plane four-bar linkage, the plate cam and follower, and the slider-crank mechanism are familiar examples of planar mechanisms. The vast majority of mechanisms in use today are planar.
Planar mechanisms utilizing only lower pairs are called planar linkages; they include only revolute and prismatic pairs. Although a planar pair might theoretically be included, this would impose no constraint and thus be equivalent to an opening in the kinematic chain. Planar motion also requires that all revolute axes be normal to the plane of motion and that all prismatic pair axes be parallel to the plane. The motions of all particles can therefore be completely described by their radial projections, or "shadows," on the surface of a sphere with a properly chosen center.
Hooke's universal joint is perhaps the most familiar example of a spherical mechanism. Spherical linkages are constituted entirely of revolute pairs.
A spheric pair would pro- duce no additional constraints and would thus be equivalent to an opening in the chain, while all other lower pairs have non spheric motion. In spheric linkages, the axes of all rev- olute pairs must intersect at a point. Spatial mechanisms, on the other hand, include no restrictions on the relative motions of the particles. The motion transformation is not necessarily coplanar, nor must it be concentric.
A spatial mechanism may have particles with loci of double curvature. Any linkage that contains a screw pair, for example, is a spatial mechanism, because the relative motion within a screw pair is helical. Thus, the overwhelmingly large category of planar mechanisms and the category of spherical mechanisms are only special cases, or subsets, of the all-inclusive category spa- tial mechanisms.
They occur as a consequence of special geometry in the particular orien- tations of their pair axes. If planar and spherical mechanisms are only special cases of spatial mechanisms, why is it desirable to identify them separately? Because of the particular geometric conditions that identify these types, many simplifications are possible in their design and analysis. As pointed out earlier, it is possible to observe the motions of all particles of a planar mecha- nism in true size and shape from a single direction.
In other words, all motions can be rep-. Thus, graphical techniques are well-suited to their solution. Because spatial mechanisms do not all have this fortunate geometry, visualization becomes more difficult and more powerful techniques must be developed for their analysis. Because the vast majority of mechanisms in use today are planar, one might question the need for the more complicated mathematical techniques used for spatial mechanisms.
There are a number of reasons why more powerful methods are of value even though tJ;1e simpler graphical techniques have been mastered: " I. They provide new, alternative methods that will solve the problems in a differeJllt way. Thus they provide a means of checking results. Certain problems, by their na- ture, may also be more amenable to one method than to another. Methods that are analytic in nature are better suited to solution by calculator or dig- ital computer than by graphic techniques.
Even though the majority of useful mechanisms are planar and well-suited to graphical solution, the few remaining must also be analyzed, and techniques should be known for analyzing them. One reason that planar linkages are so common is that good methods of analysis for the more general spatial linkages have not been available until relatively recently. Without methods for their analysis, their design and use has not been common, even though they may be inherently better suited in certain applications.
We will discover that spatial linkages are much more common in practice than their formal description indicates. Consider a four-bar linkage. It has four links connected by four pins whose axes are parallel.
This "parallelism" is a mathematical hypothesis; it is not a reality. The axes as pro- duced in a shop-in any shop, no matter how good-will be only approximately parallel. If they are far out of parallel, there will be binding in no uncertain terms, and the mecha- nism will move only because the "rigid" links flex and twist, producing loads in the bear- ings. If the axes are nearly parallel, the mechanism operates because of the looseness of the running fits of the bearings or flexibility of the links.
A common way of compensating for small nonparallelism is to connect the links with self-aligning bearings, which are actually spherical joints allowing three-dimensional rotation. Such a "planar" linkage is thus a low- grade spatial linkage. Ignoring for the moment certain excep- tions to be mentioned later, it is possible to determine the mobility of a mechanism directly from a count of the number of links and the number and types of joints that it includes.
To develop this relationship, consider that before they are connected together, each link of a planar mechanism has three degrees of freedom when moving relative to the fixed link. Not counting the fixed link, therefore, an n-link planar mechanism has 3 n - I degrees of freedom before any of the joints are connected. Connecting a joint that has one degree of freedom, such as a revolute pair, has the effect of providing two constraints be- tween the connected links. Movability includes the six degrees of freedom of the device as a whole, as though the ground link were not fixed, and thus applies to a kinematic chain.
Mobility neglects these and considers only the internal relative motions, thus applying to a mechanism. The English literature seldom recognizes this distinction, and the terms are used somewhat interchangeably. When the constraints for all joints are subtracted from the total freedoms of the unconnected links, we find the resulting mobility of the connected mechanism.
Its application is shown for several simple cases in Fig. Examples are shown in Fig. Note in these examples that when three links are joined by a single pin, two joints must be counted; such a connection is treated as two separate but concentric pairs.
Figure 1. Particular attention should be paid to the contact pair between the wheel and the fixed link in Fig. If this contact included gear teeth or if friction was high enough to pre- vent slipping, the joint would be counted as a one-degree-of-freedom pair, because only one relative motion would be possible between the links. Sometimes the Kutzbach criterion gives an incorrect result. Notice that Fig. However, if link 5 is arranged as in Fig.
The actual mobility of 1 results only if the parallelogram geometry is achieved. Because in the development of the Kutzbach cri- terion no consideration was given to the lengths of the links or other dimensional proper- ties, it is not surprising that exceptions to the criterion are found for particular cases with equal link lengths, parallel links, or other special geometric features. Even though the criterion has exceptions, it remains useful because it is so easily ap- plied.
To avoid exceptions, it would be necessary to include all the dimensional properties of the mechanism.
The resulting criterion would be very complex and would be useless at the early stages of design when dimensions may not be known. An earlier mobility criterion named after Griibler applies to mechanisms with only single-degree-of-freedom joints where the overall mobility of the mechanism is unity. This shows why the four-bar linkage Fig. Both the Kutzbach criterion, Eq. If similar criteria are developed for spatial mechanisms, we must recall that each unconnected link has six degrees of freedom; and each revolute pair, for example, provides five constraints.
Though historyS shows that many attempts have been made, none have been very successful in devising a completely satisfactory method. In view of the fact that the purpose of a mechanism is the transformation of motion, we shall follow Torfason's lead6 and classify mechanisms according to the type of motion transformation. Altogether, Torfason displays mechanisms, each of which is capable of variation in dimensions.
Linea r Actuators Linear actuators include: 1. Stationary screws with traveling nuts. Stationary nuts with traveling screws. Single- and double-acting hydraulic and pneumatic cylinders. Fine Adjustments Fine adjustments may be obtained with screws, including the dif- ferential screw of Fig.
Clamping Mechanisms Typical clamping mechanisms are the C-clamp, the wood- worker's screw clamp, cam- and lever-actuated clamps, vises, presses such as the toggle press of Fig. Locationa I Devices Torfason pictures 15 locational mechanisms.
These are usually self-centering and locate either axially or angularly using springs and detents. They have spe- cial geometric characteristics in that all revolute axes are parallel and perpendicular to the plane of motion and all prism axes lie in the plane of motion.
Ratchets and Escapements There are many different forms of ratchets and escape- ments, some quite clever. They are used in locks, jacks, clockwork, and other applications requiring some form of intermittent motion.
The ratchet in Fig. Pawl 3 is held against the wheel by gravity or a spring. A similar arrangement is used for lifting jacks, which then employ a toothed rack for rectilinear motion.
Graham's escapement of Fig. Anchor 3 drives a pendulum whose oscillating motion is caused by the two clicks engag- ing the escapement wheel 2. One is a push click, the other a pull click. The lifting and en- gaging of each click caused by oscillation of the pendulum results in a wheel motion which, at the same time, presses each respective click and adds a gentle force to the motion of the pendulum.
The escapement of Fig. Three or more slots up to 16 may be used in driver 2, and wheel 3 can be geared to the output to be indexed. High speeds and large inertias may cause problems with this indexer.
The toothless ratchet 5 in Fig. IOc is driven by the oscillating crank 2 of variable throw. Note the similarity of this to the ratchet of Fig. Torfason lists nine different indexing mechanisms, and many variations are possible.
Figure l. In Fig. This mechanism is described as a quick-return linkage because crank 2 rotates through a larger angle on the forward stroke of link 4 than on the return stroke. Figure I. I Ic is a four-har linkage called the crank-and-rocker mechanism. Crank 2 drives rocker 4 through coupler 3. Of course, link I is the frame. The characteristics of the rocking motion depend on the dimensions of the links and the placement of the frame points.
There are an endless variety of cam-and- follower mechanisms, many of which will be discussed in Chapter 5. In each case the cams can be formed to produce rocking motions with nearly any set of desired characteristics. Reciprocating Mechanisms Repeating straight-line motion is commonly obtained using pneumatic and hydraulic cylinders, a stationary screw and traveling nut, rectilinear drives using reversible motors or reversing gears, as well as cam-and-follower mecha- nisms.
A variety of typical linkages for obtaining reciprocating motion are shown in Figs. The offset slider-crank mechanism shown in Fig. If connecting rod 3 of an on-center slider-crank mechanism is large relative to the length of crank 2, then the resulting motion is nearly harmonic. Link 4 of the Scotch yoke mechanism shown in Fig. I 2h delivers exact harmonic motion. The six-bar linkage shown in Fig. Note that it is derived from Fig. I 2h by adding coupler 5 and slider 6.
The slider stroke has a quick-return characteristic. The linkage is shown in an upside-down configu- ration to show its similarity to Fig. In many applications, mechanisms are used to perform repetitive operations such as pushing parts along an assembly line, clamping parts together while they are welded, or folding cardboard boxes in an automated packaging machine. In such applications it is often desirable to use a constant-speed motor; this will lead us to a discussion of Grashof's law in Section 1.
In addition, however, we should also give some consideration to the power and timing requirements. In these repetitive operations there is usually a part of the cycle when the mechanism is under load, called the advance or working stroke, and a part of the cycle, called the return stroke, when the mechanism is not working but simply returning so that it may repeat the operation. In the offset slider-crank mechanism of Fig. In such situations, in order to keep the power requirements of the motor to a minimum and to avoid wasting valuable time, it is desirable to design the mechanism so that the piston will move much faster through the return stroke than it does during the working stroke-that is, to use a higher fraction of the cycle time for doing work than for returning.
A mechanism for which the value of Q is high is more desirable for such repetitive opera- tions than one in which Q is lower. Certainly, any such operations would use a mechanism for which Q is greater than unity. Because of this, mechanisms with Q greater than unity are called quick-return mechanisms. Assuming that the driving motor operates at constant speed, it is easy to find the time ratio.
Next, noticing the direction of rotation of the crank, we can measure the crank angle a traveled through dur- ing the advance stroke and the remaining crank angle f3 of the return stroke. Then, if the period of the motor is T, the time of the advance stroke is Notice that the time ratio of a quick-return mechanism does not depend on the amount of work being done or even on the speed of the driving motor.
It is a kinematic property of the mechanism itself and can be found strictly from the geometry of the device. We also notice, however, that there is a proper and an improper direction of rotation for such a device. If the motor were reversed in the example of Fig. Thus the motor must rotate counterclockwise for this mechanism to have the quick-return property. Many other mechanisms can be found with quick-return characteristics. Another example is the Whitworth mechanism, also called the crank-shaper mechanism, shown in Figs.
Although the determination of the angles a and f3 is different for each mechanism, Eq. Coupler point C should be located so as to produce the desired motion characteristic of slider 6. A crank-driven toggle mechanism is shown in Fig. With this mechanism, a high mechanic,al advantage is obtained at one end of the stroke of slider 6. Reversing Mechanisms When a mechanism is desired which is capable of delivering output rotation in either direction, some form of reversing mechanism is required.
Many such devices make use of a two-way clutch that connects the output shaft to either of two drive shafts turning in opposite directions. This method is used in both gear and belt drives and does not require that the drive be stopped to change direction. Gear-shift devices, as in automotive transmissions, are also in quite common use. Coupl ings and Con nectars Couplings and connectors are used to transmit motion between coaxial, parallel, intersecting, and skewed shafts.
Gears of one kind or another can be used for any of these situations. These will be discussed in Chapters 6 through 9. Flat belts can be used to transmit motion between parallel shafts. They can also be used between intersecting or skewed shafts if guide pulleys, as shown in Fig.
When parallel shafts are involved, the belts can be open or crossed, depending on the direction of rotation desired. Here crank 2 is the driver and link 4 is the output. For this reason, good prismatic pairs without backlash were not easy to make.
During that era, much thought was given to the problem of attaining a straight-line motion as a part of the coupler curve of a linkage having only revolute connections. Probably the best-known result of this search is the straight-line mechanism developed by Watt for guiding the piston of early steam engines. Although it does not gen- erate an exact straight line, a good approximation is achieved over a considerable distance of travel.
Another four-bar linkage in which the tracing point P generates an approximate straight-line coupler-curve segment is Roberts' mechanism Fig. The tracing point P of the Chebychev linkage in Fig. Yet another mechanism that generates a straight-line segment is the Peaucillier inver- sor shown in Fig. Under these conditions AC. Another interesting property is that if A D is not equal to CD, point P can be made to trace a true circular arc of very large radius. The pantagraph of Fig. If, for example, point P traces a map, then a pen at Q will draw the same map at a smaller scale.
Others will appear inisome of the chapters to follow. Until a frame link has been chosen, a connected set of links is called a kinematic chain. When dif- ferent links are chosen as the frame for a given kinematic chain, the relative motions between the various links are not altered, but their absolute motions those measured with respect to the frame link may be changed drastically. The process of choosing different links of a chain for the frame is known as kinematic inversion.
In an n-link kinematic chain, choosing each link in turn as the frame yields n distinct kinematic inversions of the chain, n different mechanisms. As an example, the four-link slider-crank chain of Fig. Link 4, the piston, is driven by the expanding gases and forms the input; link 2, the crank, is the driven output. The frame is the cylinder block, link 1. By reversing the roles of the input and output, this same mechanism can be used as a compressor. Link 1, formerly the frame, now rotates about the revolute at A.
This inversion of the slider-crank mechanism was used as the basis of the rotary engine found in early aircraft. Another inversion of the same slider-crank chain is shown in Fig. This mechanism was used to drive the wheels of early steam locomotives, link 2 being a wheel.
The fourth and final inversion of the slider-crank chain has the piston, link 4, station- ary. Mechanisms in which no link makes a complete revolution would not be useful in such applications. For the four-bar linkage, there is a very simple test of whether this is the case. Grashof's law states that for a planar four-bar linkage, the sum of the shortest and longest link lengths cannot be greater than the sum of the remaining two link lengths if there is to be continuous relative rotation between two members.
This is illustrated in Fig. We are free, therefore, to fix any of the four links. When we do so, we create the four inversions of the four-par linkage shown in Fig. All of these fit Grashof's law, and in each the link s makes a complete revolution relative to the other links. The different inversions are distinguished by the location of the link s relative to the fixed link. If the shortest link s is adjacent to the fixed link, as shown in Figs.
Link s is, of course, the crank because it is able to rotate continuously; and link p, which can only oscillate between limits, is the rocker. The drag-link mechanism, also called the double-crank linkage, is obtained by fixing the shortest link s as the frame. In this inversion, shown in Fig. Although this is a very common mechanism, you will find it an interesting challenge to devise a practical working model that can operate through the full cycle.
By fixing the link opposite to s we obtain the fourth inversion, the double-rocker mechanism of Fig. Note that although link s is able to make a complete revolution, neither link adjacent to the frame can do so; both must oscillate between limits and are therefore rockers.
In each of these inversions, the shortest link s is adjacent to the longest link I. How- ever, exactly the same types of linkage inversions will occur if the longest link I is opposite the shortest link s; you should demonstrate this to your own satisfaction. Reuleaux approaches the problem somewhat differently but, of course, obtains the same results.
In this approach, and using Fig. Consider the four-bar linkage shown in Fig. Since, according to Grashof's law, this particular linkage is of the crank-rocker variety, it is likely that link 2 is the driver and link 4 is the follower. Link I is the frame and link 3 is called the coupler because it couples the motions of the input and output cranks.
The mechanical advantage of a linkage is the ratio of the output torque exerted by the driven link to the necessary input torque required at the driver. In Section 3. Of course, both these angles, and therefore the mechanical advantage, are continuously changing as the linkage moves. When the sine of the angle fJ becomes zero, the mechanical advantage becomes infi- nite; thus, at such a position, only a small input torque is necessary to overcome a large output torque load.
This is the case when the driver A B of Fig. Note that these also define the extreme positions of travel of the rocker DC, and DC4. When the four-bar linkage is in either of these positions, the mechanical advan- tage is infinite and the linkage is said to be in a toggle position. The angle y between the coupler and the follower is called the transmission angle.
As this angle becomes small, the mechanical advantage decreases and even a small amount of friction will cause the mechanism to lock or jam. A common rule of thumb is that a four-. The extreme values of the transmission angle occur when the crank AB lies along the line of the frame AD. Because of the ease with which it can be visually inspected, the transmission angle has become a com- monly accepted measure of the quality of the design of a four-bar linkage. Note that the definitions of mechanical advantage, toggle, and transmission angle de- pend on the choice of the driver and driven links.
If, in the same figure, link 4 is used as the driver and link 2 as the follower, the roles of fJ and yare reversed. In this case the linkage has no toggle position, and its mechanical advantage becomes zero when link 2 is in posi- tion AB, or AB4, because the transmission angle is then zero.
These and other methods of rating the suitability of the four-bar or other linkages are discussed more thoroughly in Sec- tion 3. Novi Comment. The trans- lation is by A. Willis, Principles of Mechanism, 2nd ed. For additional reading see A. In a footnote Reuleaux gives 17 definitions, and his translator gives 7 more and discusses the whole problem in detail.
Richard S. For an excellent short history of the kinematics of mechanisms, see Hartenberg and Denavit, Kinematic Synthesis of Linkages, Chapter I. See L. Torfason, "A Thesaurus of Mechanisms," in J. Shigley and C. Mischke Eds. Alternately, see L. Hrones and G. They can be found in the workshop, in domestic appliances, on vehicles, on agricultural machines, and so on. Assemble the links in all possible combi- nations 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. 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. How many dis- wise, how far and in what direction will the cahiage tinct variations of this mechanism can you find? The rocker length is to mechanism of Fig.
Because motion can be thought of as a time series of displacements between successive positions, it is important to under- stand exactly the meaning of the term position; rules or conventions must be established to make the definition precise. Although many of the concepts in this chapter may appear intuitive and almost trivial, many subtleties are explained here which are required for an understanding of the next sev- eral chapters.
We are speaking of something that exists in nature and are posing the question of how to express this in words or symbols or numbers in such a way that the meaning is clear.
We soon discover that position cannot be defined on a truly absolute basis. We must define the position of a point in terms of some agreed- upon frame of reference, some reference coordinate system. In this very statement we see that three vitally important parts of the definition depend on the existence of the reference coordinate system: I.
The origin of coordinates 0 provides an agreed-upon location from which to measure the location of point P. When we use the word point, we have in mind something that has no dimensions-that is, something with zero length, zero width, and zero thickness.
When the word particle is used, we have in mind something whose dimensions are small and unimportant-that is, a tiny material body whose dimensions are negligible, a body small enough for its dimensions to have no effect on the analysis to be performed.
The successive positions of a moving point define a line or curve. This curve has no thickness because the point has no dimensions. However, the curve does have length be- cause the point occupies different positions as time changes.
This curve, representing the successive positions of the point, is called the path or locus of the moving point in the ref- erence coordinate system. If three coordinates are necessary to describe the path of a moving point, the point is said to have spatial motion.
If the path can be described by only two coordinates-that is, if the coordinate axes can be chosen such that one coordinate is always zero or constant- the path is contained in a single plane and the point is said to have planar motion. Some- times it happens that the path of a point can be described by a single coordinate. This means that two of its spatial position coordinates can be taken as zero or constant. In this case the point moves in a straight line and is said to have rectilinear motion.
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