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mallet-and-hammer-what-is-the-difference-graph View all. What is the difference between a hammer and a mallet? What’s the difference between hammers and mallets? Hammers have a smaller metal head that is meant to output blunt force. That is probably a 'mallet'.An actual hammer may have a metal handle and/or head, but a mallet always has a non-metallic head which is, historically, wooden. Difference between a framing hammer and a regular hammer? A framing hammer has a heavier head and a longer shaft than a regular hammer. What is a synonym for wooden mallet?  Here are some www.- doctor hit my knee with a little rubber mallet and made it www.- tapped the board into place with a wooden www.- used a mallet and chisel to carve the stone into the shape of a bird. What did you use the mallet for when building a pyramid? I found out it helped the Egyptians hammer the blocks into place. What are the examples of driving tools?. What’s the difference between hammers and mallets? Hammers have a smaller metal head that is meant to output blunt force. Mallets, on the other hand, have a larger round head that is made of wood, rubber, or another softer material. Aside from their differences in Mallet And Hammer What Is The Difference Free shape, hammers are used for applying force to objects, while mallets are meant for a softer impact on the surface in question.  While hammers and mallets are both in the same family of tools, and can be mistaken for one another often times, they are actually very different. Both fundamentally and physically, hammers and mallets have plenty of differences. Hammers: Heavy metal head. Calculating the slabs. These dynamic forces are proportional to acceleration, which brings us back to kinematics, the foundation of mechanical design. Petrocelli Books. Real design problems more often take the form of "What we need digference a framus to stuff this widget into that hole within the time allocated to the transfer of this other gizmo. Norton earned undergraduate degrees in both mechanical engineering and in- dustrial technology at Northeastern Mallet and hammer what is the difference graph and an MS in engineering design at Tufts University. He counted five ways of obtaining rel- Machines, Montreal, p. Note that these specifications constrain the design without overly restricting the engineer's design freedom.

The Rand P pairs are the basic building blocks of all other pairs which are combinations of those two as shown in Table A more useful means to classify joints pairs is by the number of degrees of free- dom that they allow between the two elements joined.

Figure also shows examples of both one- and two-freedom joints commonly found in planar mechanisms. Figure b shows two forms of a planar, one-freedom joint or pair , namely, a rotating pin joint R and a translating slider joint P. These are also referred to as full joints i.

These are both contained within and each is a limiting case of another common, one-freedom joint, the screw and nut Figure a. Motion of either the nut or the screw with respect to the other results in helical motion.

If the helix angle is made zero, the nut rotates without advancing and it becomes the pin joint. If the helix angle is made 90 degrees, the nut will translate along the axis of the screw, and it becomes the slider joint. Figure c shows examples of two-freedom joints h1gherpairs which simultaneously allow two independent, relative motions, namely translation and rotation, between the joined links.

Paradoxically, this two-freedom joint is sometimes referred to as a "half joint," with its two freedoms placed in the denominator. The half joint is also called a roll-slide joint because it allows both rolling and sliding.

A spherical, or ball-and-socket joint Figure a , is an example of a three-freedom joint, which allows three independent angular motions be- tween the two links joined. This ball joint would typically be used in a three-dimensional mechanism, one example being the ball joints in an automotive suspension system.

A joint with more than one freedom may also be a higher pair as shown in Figure c. Note that if you do not allow the two links in Hgore c connected by a roll-slide joint to slide, perhaps by providing a high friction coefficient between them, you can "lock out" the translating At freedom and make it behave as a full joint.

This is then called a pure rolling joint and has rotational freedom AD only. A cornmon example of this type of joint is your automobile tire rolling against die road, as shown in Figure e. In normal use there is pure rolling and no sliding at Ibis joint, unless, of course, you encounter an icy road or become too enthusiastic about accelerating or cornering. If you lock your brakes on ice, this joint converts to a pure sliding one like the slider block in Figure b.

Friction determines the actual number of freedoms at this kind of joint. It can be pure roll, pure slide, or roll-slide. To visualize the degree of freedom of a joint in a mechanism, it is helpful to "men- tally disconnect" the two links which create the joint from the rest of the mechanism. You can then more easily see how many freedoms the two joined links have with respect to one another. Figure c also shows examples of both form-closed and force-closed joints.

A form-closed joint is kept together or closed by its geometry. A pin in a hole or a slider in a two-sided slot are form closed. In contrast, a force-closed joint, such as a pin in a half-bearing or a slider on a surface, requires some external force to keep it together or closed.

This force could be supplied by gravity, a spring, or any external means. There can be substantial differences in the behavior of a mechanism due to the choice of force or form closure, as we shall see.

The choice should be carefully considered. In linkag- es, form closure is usually preferred, and it is easy to accomplish. But for cam-follower systems, force closure is often preferred. This topic will be explored further in later chap- ters. Figure d shows examples of joints of various orders, where order is defined as the number of links joined minus one. It takes two links to make a single joint; thus the simplest joint combination of two links has order one.

As additional links are placed on the same joint, the order is increased on a one for one basis. Joint order has significance in the proper determination of overall degree of freedom for the assembly. We gave def- initions for a mechanism and a machine in Chapter 1. With the kinematic elements of links and joints now defined, we can define those devices more carefully based on Reu- leaux's classifications of the kinematic chain, mechanism, and machine.

A mechanism is defined as: A kinematic chain in which at least one link has been "grounded," or attached, to the frame of reference which itself may be in motion.

A machine is defined as: A combination of resistant bodies arranged to compel the mechanical forces of nature to do work accompanied by determinate motions. By Reuleaux's definition [1] a machine is a collection of mechanisms arranged to transmit forces and do work.

He viewed all energy or force transmitting devices as ma- chines which utilize mechanisms as their building blocks to provide the necessary mo- tion constraints. We will now define a crank as a link which makes a complete revolution and is piv- oted to ground, a rocker as a link which has oscillatory back andforth rotation and is pivoted to ground, and a coupler or connecting rod which has complex motion and is not pivoted to ground.

Ground is defined as any link or links that are fixed nonmov- ing with respect to the reference frame. Note that the reference frame may in fact itself be in motion.

We need to be able to quickly determine the DOF of any collection of links and joints which may be suggested as a solution to a problem. Degree of free- dom also called the mobility M of a system can be defined as: Degree of Freedom the number of inputs which need to be provided in order to create a predictable output; also: the number of independent coordinates required to define its position.

At the outset of the design process, some general definition of the desired output motion is usually available.

The number of inputs needed to obtain that output mayor may not be specified. Cost is the principal constraint here. Each required input will need some type of actuator, either a human operator or a "slave" in the fonn of a motor, sole- noid, air cylinder, or other energy conversion device.

These devices are discussed in Section 2. These multiple input devices will have to have their actions coordinated by a "controller," which must have some intelligence.

This control is now often provid- ed by a computer but can also be mechanically programmed into the mechanism design. There is no requirement that a mechanism have only one DOF, although that is often desirable for simplicity. Some machines have many DOF. For example, picture the num- ber of control levers or actuating cylinders on a bulldozer or crane.

See Figure I-lb p. Kinematic chains or mechanisms may be either open or closed. Figure shows both open and closed mechanisms.

A closed mechanism will have no open attachment points or nodes and may have one or more degrees of freedom. An open mechanism of more than one link will always have more than one degree of freedom, thus requiring as many actuators motors as it has DOF. A common example of an open mechanism is an industrial robot.

An open kinematic chain of two binary links and one joint is called a dyad. The sets of links shown in Figure a and b are dyads. Reuleaux limited his definitions to closed kinematic chains and to mechanisms hav- ing only one DOF, which he called constrained. A multi-DOF mechanism, such as a robot, will be constrained in its motions as long as the necessary number of inputs are supplied to control all its DOF.

Degree of Freedom in Planar Mechanisms To determine the overall DOF of any mechanism, we must account for the number of links and joints, and for the interactions among them. The DOF of any assembly of links can be predicted from an investigation of the Gruebler condition.

In Figure c the half joint removes only one DOF from the system because a half joint has two DOF , leaving the system of two links connected by a half joint with a total of five DOF. In addition, when any link is grounded or attached to the reference frame, all three of its DOF will be removed. Multiple joints count as one less than the number oflinks joined at that joint and add to the "full" 11 category.

The DOF of any proposed mechanism can be quickly ascertained from this expression before investing any time in more detailed design. It is interesting to note that this equation has no information in it about link sizes or shapes, only their quantity.

Figure a shows a mechanism with one DOF and only full joints in it. Figure b shows a structure with zero DOF and which contains both half and mul- tiple joints. Note the schematic notation used to show the ground link.

The ground link need not be drawn in outline as long as all the grounded joints are identified. Note also the joints labeled "multiple" and "half' in Figure a and b. As an exercise, compute the DOF of these examples with Kutzbach's equation. Degree of Freedom in Spatial Mechanisms The approach used to determine the mobility of a planar mechanism can be easily ex- tended to three dimensions.

Each unconnected link in three-space has 6 DOF, and any one of the six lower pairs can be used to connect them, as can higher pairs with more freedom. Grounding a link removes 6 DOF. This leads to the Kutzbach mobility equation for spa- tiallinkages: where the subscript refers to the number of freedoms of the joint.

We will limit our study to 2-D mechanisms in this text. There are only three possibilities. If the DOF is positive, it will be a mechanism, and the links will have relative motion. If the DOF is exactly zero, then it will be a structure, and no motion is possible.

If the DOF is negative, then it is a preloaded structure, which means that no motion is possible and some stresses may also be present at the time of assembly.

Figure shows examples of these three cases. One link is grounded in each case. Figure a shows four links joined by four full joints which, from the Gruebler equation, gives one DOF.

It will move, and only one input is needed to give predictable results. Figure b shows three links joined by three full joints. It has zero DOF and is thus a structure. Figure c shows two links joined by two full joints.

It has a DOF of minus one, making it a preloaded structure. In order to insert the two pins without straining the links, the center distances of the holes in both links must be exactly the same.

Practical- ly speaking, it is impossible to make two parts exactly the same. There will always be some manufacturing error, even if very small. Thus you may have to force the second pin into place, creating some stress in the links. The structure will then be preloaded. You have probably met a similar situation in a course in applied mechanics in the form of an indeterminate beam, one in which there were too many supports or constraints for the equations available.

Both structures and preloaded structures are commonly encountered in engineering. In fact the true structure of zero DOF is rare in engineering practice. Even simple structures like the chair you are sitting in then their interconnection are often preloaded.

Since our concern here is with mechanisms, we will concentrate on is impossible. Order in this context refers to the number of nodes perlink, i. The value of number synthesis is to allow the exhaustive determination of all possible combinations of links which will yield any chosen DOF. This then equips the designer with a definitive catalog of potential linkages to solve a variety of motion control prob- lems.

As an example we will now derive all the possible link combinations for one DOF, including sets of up to eight links, and link orders up to and including hexagonal links. For simplicity we will assume that the links will be connected with only full rotating joints. We can later introduce half joints, multiple joints, and sliding joints through link- age transformation. First let's look at some interesting attributes of linkages as defined by the above assumption regarding full joints.

Hypothesis: If all joints are full joints, an odd number of DOFrequires an even number of links and vice versa. Proof: Given: All even integers can be denoted by 2m or by 2n, and all odd integers can be denoted by 2m - I or by 2n - 1, where n and m are any positive integers.

The number of joints must be a positive integer. There are other examples of paradoxes which disobey the Gruebler criterion due to their unique geometry. The designer needs to be alert to these possible inconsistencies. Isomers in chemis- try are compounds that have the same number and type of atoms but which are intercon- nected differently and thus have different physical properties.

Figure a shows two hydrocarbon isomers, n-butane and isobutane. Note that each has the same number of carbon and hydrogen atoms C4HlO , but they are differently interconnected and have different properties. Linkage isomers are analogous to these chemical compounds in that the links like atoms have various nodes electrons available to connect to other links' nodes. The assembled linkage is analogous to the chemical compound.

Depending on the particular connections of available links, the assembly will have different motion properties. The number of isomers possible from a given collection of links as in any row of Table is far from obvious.

In fact the problem of mathematically predicting the number of iso- mers of all link combinations has been a long-unsolved problem. Many researchers have spent much effort on this problem with some recent success. See references [3] through [7] for more information. Dhararipragada [6] presents a good historical summary of iso- mer research to Table shows the number of valid isomers found for one-DOF mechanisms with revolute pairs, up to 12 links.

Figure b shows all the isomers for the simple cases of one DOF with 4 and 6 links. Note that there is only one isomer for the case of 4 links. An isomer is only unique if the interconnections between its types of links are different. That is, all binary links are considered equal, just as all hydrogen atoms are equal in the chemical analog. Link lengths and shapes do not figure into the Gruebler criterion or the condition of isomer- ism.

The 6-link case of 4 binaries and 2 ternaries has only two valid isomers. These are known as the Watt's chain and the Stephenson's chain after their discoverers.

Note the different interconnections of the ternaries to the binaries in these two examples. The Watt's chain has the two ternaries directly connected, but the Stephenson's chain does not.

There is also a third potential isomer for this case of six links, as shown in Figure c, but it fails the test of distribution of degree of freedom, which requires that the overall DOF here 1 be uniformly distributed throughout the linkage and not concentrat- ed in a subchain.

This creates a truss, or delta triplet. Thus this arrange- ment has been reduced to the simpler case of the fourbar linkage despite its six bars. This is an invalid isomer and is rejected. It is left as an exercise for the reader to find the 16 valid isomers of the eight bar, one-DOF cases. If we now relax the arbitrary constraint which restricted us to only revolute joints, we can transform these basic linkages to a wider variety of mech- Mallet And Hammer What Is The Difference Videos anisms with even greater usefulness.

There are several transformation techniques or rules that we can apply to planar kinematic chains. This will create a multiple joint but will not change the DOF of the mechanism. A multiple joint will be created, and the DOF will be reduced. Figure 2-lOa shows a fourbar crank-rocker linkage transformed into the fourbar slider-crank by the application of rule 1.

It is still a fourbar linkage. Link 4 has be- come a sliding block. The Gruebler's equation is unchanged at one DOF because the slid- er block provides a full joint against link 1, as did the pin joint it replaces. Note that this transformation from a rocking output link to a slider output link is equivalent to increas- ing the length radius of rocker link 4 until its arc motion at the joint between links 3 and 4 becomes a straight line.

Thus the slider block is equivalent to an infinitely long rocker link 4, which is pivoted at infinity along a line perpendicular to the slider axis as shown in Figure 2-lOa. The first version shown retains the same motion of fourbar linkage are the slider as the original linkage by use of a curved slot in link 4.

The effective coupler replaced by prismatic. Also, pler. The second version shown has the slot made straight and perpendicular to the slid- if three revolutes in a four- er axis. The effective coupler now is "pivoted" at infinity. This is called a Scotch yoke bar loop are replaced with and gives exact simple harmonic motion of the slider in response to a constant speed in- prismatic joints, the one put to the crank.

Link 3 has been removed and a half joint substituted for a full pinned links together as joint between links 2 and 4. This still has one DOF, and the cam-follower is in fact a one.

This effectively fourbar linkage in another disguise, in which the coupler link 3 has become an effec- reduces the assembly to a tive link of variable length. We will investigate the fourbar linkage and these variants of threebar linkage which should have zero DOF. But, a delta triplet with Figure 2-lla shows the Stephenson's sixbar chain from Figure b p. It is one DOF-another Gruebler's paradox.

The two triangular subchains are obvious. Just as the fourbar chain is the basic building block of one-DOF mechanisms, this threebar triangle delta triplet is the basic building block of zero-DOF structures trusses. A dwell is a period in which the output link remains stationary while the input link continues to move.

There are many applications in machinery which require intermittent motion. The earn-follower varia- tion on the fourbar linkage as shown in Figure 2-lOc p. The design of that device for both intermittent and continuous output will be ad- dressed in detail in Chapter 8. Other pure linkage dwell mechanisms are discussed in the next chapter.

This is also a transformed fourbar linkage in which the coupler has been replaced by a half joint. The input crank link 2 is typically motor driven at a constant speed. The Geneva wheel is fitted with at least three equis- paced, radial slots. The crank has a pin that enters a radial slot and causes the Geneva wheel to turn through a portion of a revolution.

When the pin leaves that slot, the Gene- va wheel remains stationary until the pin enters the next slot. The result is intermittent rotation of the Geneva wheel. The crank is also fitted with an arc segment, which engages a matching cutout on the periphery of the Geneva wheel when the pin is out of the slot. This keeps the Gene- va wheel stationary and in the proper location for the next entry of the pin.

A Geneva wheel needs a minimum of three stops to work. The maximum number of stops is limited only by the size of the wheel. The arm pivots about the center of the toothed ratchet wheel and is moved back and forth to index the wheel. The driving pawl rotates the ratchet wheel or ratchet in the counter- clockwise direction and does no work on the return clockwise trip. The locking pawl prevents the ratchet from reversing direction while the driving pawl returns.

Both pawls are usually spring-loaded against the ratchet. This mechanism is widely used in devices such as "ratchet" wrenches, winches, etc. This mechanism is anal- ogous to an open Scotch yoke device with multiple yokes. It can be used as an intermit- tent conveyor drive with the slots arranged along the conveyor chain or belt. It al 'r;an be used with a reversing motor to get linear, reversing oscillation of a single slotte, put slider.

Even with the limitations imposed in the number synthesis example one DOF, eight links, up to hexagonal order , there are eight linkage combinations shown in Table p. In addition, we can introduce another factor, namely mechanism inversion. An inversion is created by grounding a different link in the kinematic chain. Thus there are as many inversions of a given linkage as it has links.

The motions resulting from each inversion can be quite different, but some inver- sions of a linkage may yield motions similar to other inversions of the same linkage.

In these cases only some of the inversions may have distinctly different motions. We will denote the inversions which have distinctly different motions as distinct inversions. Figure previous page shows the four inversions of the fourbar slider-crank linkage, all of which have distinct motions. Inversion 1, with link 1 as ground and its slider block in pure translation, is the most commonly seen and is used for piston en- gines and piston pumps.

Inversion 2 is obtained by grounding link 2 and gives the Whitworth or crank-shaper quick-return mechanism, in which the slider block has complex motion. Quick-return mechanisms will be investigated further in the next chapter. Inversion 3 is obtained by grounding link 3 and gives the slider block pure rotation. Inversion 4 is obtained by grounding the slider link 4 and is used in hand op- erated, well pump mechanisms, in which the handle is link 2 extended and link 1 pass- es down the well pipe to mount a piston on its bottom.

It is upside down in the figure. The Watt's sixbar chain has two distinct inversions, and the Stephenson's sixbar has three distinct inversions, as shown in Figure The pin-jointed fourbar has four distinct inversions: the crank-rocker, double-crank, double-rocker, and triple-rocker which are shown in Figures and It also appears in various disguis- es such as the slider-crank and the earn-follower.

It is in fact the most common and ubiquitous device used in machinery. It is also extremely versatile in terms of the types of motion which it can generate. Simplicity is one mark of good design. The fewest parts that can do the job will usu- ally give the least expensive and most reliable solution. Thus the fourbar linkage should be among the first solutions to motion control problems to be investigated.

The Grashof condition [8] is a very simple relationship which predicts the rotation behavior or rotat- ability of a fourbar linkage's inversions based only on the link lengths. This is called a Class I kinematic chain. If the inequality is not true, then the linkage is non-Grashof and no link will be capable of a complete rev- olution relative to any other link. This is a Class II kinematic chain.

Note that the above statements apply regardless of the order of assembly of the links. That is, the determination of the Grashof condition can be made on a set of unassembled links. The motions possible from a fourbar linkage will depend on both the Grashof con- dition and the inversion chosen.

The inversions will be defined with respect to the short- est link. Ground the shortest link and you will get a double-crank, in which both links piv- oted to ground make complete revolutions as does the coupler. Ground the link opposite the shortest and you will get a Grashof double-rocker, in which both links pivoted to ground oscillate and only the coupler makes a full revolu- tion.

At these change points the output behavior will become indeterminate. The linkage behavior is then unpredictable as it may assume either of two configurations. Its motion must be lim- ited to avoid reaching the change points or an additional, out-of-phase link provided to guarantee a "carry through" of the change points.

See Figure c. Figure p. The two crank-rockers give similar motions and so are not distinct from one another. Figure a and b shows the parallelogram and antiparallelogram configurations of the special-case Grashof linkage. The parallelogram linkage is quite useful as it ex- actly duplicates the rotary motion of the driver crank at the driven crank.

One common use is to couple the two windshield wiper output rockers across the width of the wind- shield on an automobile. The coupler of the parallelogram linkage is in curvilinear trans- lation, remaining at the same angle while all points on it describe identical circular paths.

It is often used for this parallel motion, as in truck tailgate lifts and industrial robots. The antiparallelogram linkage is also a double-crank, but the output crank has an angular velocity different from the input crank.

Note that the change points allow the linkage to switch unpredictably between the parallelogram and anti parallelogram forms every degrees unless some additional links are provided to carry it through those positions. This can be achieved by adding an out-of-phase companion linkage coupled to the same crank, as shown in Figure c. A common application of this double par- allelogram linkage was on steam locomotives, used to connect the drive wheels togeth- er.

The change points were handled by providing the duplicate linkage, 90 degrees out of phase, on the other side of the locomotive's axle shaft. When one side was at a change point, the other side would drive it through. The double-parallelogram arrangement shown in Figure c is quite useful as it gives a translating coupler which remains horizontal in all positions.

Figure d shows the deltoid or kite configuration which is a crank-rocker. There is nothing either bad or good about the Grashof condition. Linkages of all three persuasions are equally useful in their place. If, for example, your need is for a motor driven windshield wiper linkage, you may want a non-special-case Grashof crank- rocker linkage in order to have a rotating link for the motor's input, plus a special-case parallelogram stage to couple the two sides together as described above.

If your need is to control the wheel motions of a car over bumps, you may want a non-Grashof triple- rocker linkage for short stroke oscillatory motion. If you want to exactly duplicate some input motion at a remote location, you may want a special-case Grashof parallelogram linkage, as used in a drafting machine. In any case, this simply determined condition tells volumes about the behavior to be expected from a proposed fourbar linkage design prior 10 any construction of models or prototypes.

See Figure 2-lOa p. Barker also defines a "solution space" whose axes are the link ratios Ai, A3, "-4 as shown in Figure These ratios' values theoretically extend to infinity, but for any practical linkages the ratios can be limited to a reasonable value. Applying this criterion in terms of the three link ratios defines four planes of zero mobility which provide limits to the solution space. It is an ex- tremely versatile and useful device.

Many quite complex motion control problems can be solved with just four links and four pins. Thus in the interest of simplicity, designers should always first try to solve their problems with a fourbar linkage.

However, there will be cases when a more complicated solution is necessary. Adding one link and one joint to form a fivebar Figure a will increase the DOF by one, to two. By adding a pair of gears to tie two links together with a new half joint, the DOF is reduced again to one, and the geared fivebar mechanism GFBM of Figure b is created. The geared fivebar mechanism provides more complex motions than the fourbar mechanism at the expense of the added link and gearset as can be seen in Appendix E.

The reader may also observe the dynamic behavior of the linkage shown in Figure b by running the program FIVEBARprovided with this text and opening the data file Fb.

See Appendix A for instructions in running the program. Accept all the default values, and animate the linkage. Sixbar Linkages We already met the Watt's and Stephenson's sixbar mechanisms. See Figure p. The Watt's sixbar can be thought of as two fourbar linkages connected in series and sharing two links in common.

The Stephenson's sixbar can be thought of as two four- bar linkages connected in parallel and sharing two links in common. Many linkages can be designed by the technique of combining multiple fourbar chains as basic building blocks into more complex assemblages.

Many real design problems will require solu- tions consisting of more than four bars. You may run that program to observe these linkages dynamically. Select any example from the menu, accept all default responses, and animate the linkages.

Revolvability refers to a specific link in a chain and indicates that it is one of the links that can rotate. Additional theorems and corollaries regarding limits on link motions can be found in references [12] and [13]. Space does not permit their complete exposition here. Note that the rules regarding the behavior of geared fivebar linkages and fourbar linkages the Grashoflaw stated above are consistent with, and contained within, these general rotat- ability theorems.

In many mechanisms and machines, it is necessary to counterbalance the static loads applied to the device. Unless you have the cheap mod- el with the strut that you place in a hole to hold up the hood, it will probably have either a fourbar or sixbar linkage connecting the hood to the body on each side. The hood may be the coupler of a non-Grashof linkage whose two rockers are pivoted to the body.

A spring is fitted between two of the links to provide a force to hold the hood in the open position. The spring in this case is an additional link of variable length. As long as it can provide the right amount of force, it acts to reduce the DOF of the mechanism to zero, and holds the system in static equilibrium. However, you can force it to again be a one- DOF system by overcoming the spring force when you pull the hood shut.

Another example, which may now be right next to you, is the ubiquitous adjustable arm desk lamp, shown in Figure This device has two springs that counterbalance the weight of the links and lamp head. If well designed and made, it will remain stable over a fairly wide range of positions despite variation in the overturning moment due to the lamp head's changing moment arm.

This is accomplished by careful design of the geometry of the spring-link relationships so that, as the spring force changes with in- creasing length, its moment arm also changes in a way that continually balances the changing moment of the lamp head. Doubling its deflection will double the force. Most coil springs of the type used in these examples are linear.

The design of spring-loaded link- ages will be addressed in a later chapter. Not all of them are contained within the applicable theories. A great deal of art based on ex- perience is involved in design as well. This section attempts to describe a few such prac- tical considerations in machine design.

Such an interface is called a bearing. Assuming the proper materials have been chosen, the choice of joint type can have a sig- nificant effect on the ability to provide good, clean lubrication over the lifetime of the machine. It is relatively easy and inexpensive to design and build a good quality pin joint. In its pure form-a so-called sleeve or journal bearing- the geometry of pin-in-hole traps a lubricant film within its annular interface by capil- lary action and promotes a condition called hydrodynamic lubrication in which the parts are separated by a thin film of lubricant as shown in Figure Seals can easily be provided at the ends of the hole, wrapped around the pin, to prevent loss of the lubricant.

Replacement lubricant can be introduced through radial holes into the bearing interface, either continuously or periodically, without disassembly. A convenient form of bearing for linkage pivots is the commercially available spherical rod end shown in Figure This has a spherical, sleeve-type bearing which self-aligns to a shaft that may be out of parallel. Its body threads onto the link, allowing links to be conveniently made from round stock with threaded ends that allow adjustment of link length.

Relatively inexpensive ball and roller bearings are commercially available in a large variety of sizes for revolute joints as shown in Figure Some of these bear- ings principally ball type can be obtained prelubricated and with end seals.

Their roll- ing elements provide low-friction operation and good dimensional control. Note that rolling-element bearings actually contain higher-joint interfaces half joints at each ball or roller, which is potentially a problem as noted below.

However, the ability to trap lubricant within the roll cage by end seals combined with the relatively high rolling speed of the balls or rollers promotes hydrodynamic lubrication and long life. For more detailed information on bearings and lubrication, see reference [15]. For revolute joints pivoted to ground, several commercially available bearing types make the packaging easier.

Pillow blocks and flange-mount bearings Figure are available fitted with either rolling-element ball, roller bearings or sleeve-type journal bearings. The pillow block allows convenient mounting to a surface parallel to the pin axis, and flange mounts fasten to surfaces perpendicular to the pin axis. The bearings often must be custom made, though linear ball bearings Figure are commercially available but must be run over hardened and ground shafts.

Lubrication is difficult to maintain in any sliding joint. The lubricant is not geo- metrically captured, and it must be resupplied either by running the joint in an oil bath or by periodic manual regreasing.

An open slot or shaft tends to accumulate airborne dirt particles which can act as a grinding compound when trapped in the lubricant. This will accelerate wear. This type of joint needs to be run in an oil bath for long life. This requires that the assembly be housed in an expen- sive, oil-tight box with seals on all protruding shafts. These joint types are all used extensively in machinery with great success. As long as the proper attention to engineering detail is paid, the design can be successful.

Some common examples of all three joint types can be found in an automobile. The windshield wiper mechanism is a pure pin-jointed linkage. The pistons in the engine cylinders are true sliders and are bathed in engine oil.

The valves in the engine are opened and closed by earn-follower halt joints which are drowned in engine oil. You probably change your engine oil fairly frequently. When was the last time you lubricated your windshield wiper linkage?

Has this linkage not the motor ever failed? Cantilever or Straddle Mount? Any joint must be supported against the joint loads. Two basic approaches are possible as shown in Figure A cantilevered joint has the pin Goumal supported only, as a cantilever beam.

A professional garden designer can design your patio based on your ideas, or you can design it yourself. If you intend using a garden designer, use their skills to incorporate landscaping and plant choice as well. These figure s represent a basic design but can be higher, depending on the complexity o f the ideas. To excavate the patio require s a hired excavator , or someone with a shovel and wheelbarrow, depending on the excavated volume.

Most modern houses in the UK only have a small path around the side of the building. S o it might be challenging to move soil from the back garden to the waste skip on the driveway.

Waste removal. The size of your patio determines the cost. Quality of slabs. Remember , you get what you pay for.

E ither because the materials are difficult to work with , or because you need someone with better skills. You also have to choose which type of slab you want. Cheap concrete slabs contain lots of air bubbles, which soak up water and crack when f r ozen. Eventually , the slabs break, needing replacements. Generally, high — quality slabs contain fewer air bubbles which subsequently last longer.

Labour costs. But, they also vary depending on whether you choose a specialist company, building company, handyman or landscape gardene r. Generally, sole traders charge the lowest rates and often produce a better quality product.

Base material. Usually, patios need a sub-base to give firm and stable foundations. If the subsoil is firm and well — drained, you might not need to use compacted hardcore. You can either use coarse hardcore such as broken brick or concrete , or use MOT Type 1 broken rock.

Both these materials require compacting before going any further. However, b roken rubble is difficult to compact and needs blind ing with sharp sand to fill all the cavities and smooth off the surface before compaction. In contrast, quarry stone compacts better and when blinded give s a good firm base ready for laying slabs.

Sometimes, allowing the rainwater to run off the patio onto the lawn might not be enough, especially if you have a large patio.

In this case, you should incorporate a drainage channel at the edges, diverting the runoff to a soakaway or surface water drain. Weed suppressant. If you want to prevent weeds from growing through the Mallet And Hammer What Is The Difference Test patio foundations, consider using a weed — suppress ing fabric. First, ensure you have removed all roots and weeds from the ground, before laying the weed membrane.

Prices vary depending on the effectiveness and quality. If your patio dimensions are wider than the roll width, you must overlap the fabric by at least mm. You can trim it later on. Bed the slabs or blocks onto a mixture of 4 parts sharp sand to 1 part Portland cement. Some professionals prefer to use a dry mix similar to floor screed and allow the moisture from the surroundings to activate the cement.

In contrast, others like to lay slabs onto a wet mix, similar to laying bricks in a wall. Both methods have their pros and cons, and you should leave the choice to the tradesperson. However, a dry mix is firmer, and you can use the patio almost immediately. Grouting joints. Use a dry mix of 1 part sand to 1 part cement and push the mix into the joints with a hand brush and jointing tool. Afterwards , brush the surface with a stiff broom to remove any excess.

If you want to use coloured grout, mix in a mortar dye. Calculating the slabs. When you know the area of the patio, you can calculate how many slabs to buy. To make things easier , design your patio with dimensions of a multiple of slab sizes. For example, if you choose mm x mm slabs, make sure the patio dimensions are mm, mm, mm, mm, and so on.

The method of laying a patio is pretty straightforward, so if you follow the instructions to the letter, anyone who enjoys DIY can do it.

Prepare the area. They should be a minimum of mm below the surface, but you never know. Mark out the perimeter of the patio area with pegs and string. Measure diagonals. Lay the pavers out on the grass, so you can see what goes where. Draw the pattern on paper and then remove the pavers to somewhere safe. Remove the turf and store in case you need any to patch up the edges.

Dig down about mm to the highest point. This depth accommodate s all the sub-base layers and the pavers. Mark out a series of wooden stakes with the depths of the various layers and hammer them into the ground about 1m apart.

These give you a level guide when compacting. Fill sub-base. Pour and compact each layer into the excavation, using the pegs as guides, before moving on to the next task.

Laying pavers. Start in one corner preferably the highest corner. Lay eno u gh mortar or dry mix on top of the sub-base to bed one paver. Wet the reverse side of the paver to help with adhesion and to give a lubricant when adjusting. Place this first slab onto its bed and tap level using a rubber mallet. Fill gaps underneath the edges with mortar using a trowel. Place a bed for the next slab.

Then , wet the slab and place it on the bed. Continue with each paving slab , in turn, keeping the gradi en t level in one direction and sloped in the other.

Between each paver place small pieces of wood to act as spacers. When finished, allow the mortar to dry before grouting the joints. Grouting the joints. Sprinkle the mix onto the gap and brush in using a small hand brush.

Finally, compress the joints using a jointing tool and continue adding more grout until the gap becomes full. The type of patio and its finish depends on your preference and your budget.

However, each type has its pros and cons. Patios can look rigid and formal, and might not look good in certain types of garden. If you want an alternative to a patio in your garden, consider using one or a combination of the following.

You can buy chipped bark in small bags from garden c entres or in large quantities from wholesalers or sawmills. Prepare t he area to contain the bark in the same way as for a patio. Th erefore , you should have a weed suppressant layer, compacted hardcore and sand to provide a firm base, and a low retaining wall. A disadvantage is that it is easily blown around if you r garden suffer s from high winds.

Resin — bound gravel. Use gravel of your choice embedded into a resin. Unfortunately , it needs a firm surface such as tarmac or concrete, to support the resin. So , it might be suitable as a top layer if your existing patio looks in poor condition.

The material is difficult for an amateur to work with , so use a specialist company unless you know what you are doing. An advantage is that the natural gaps between the gravel allow easy drainage. Prices vary with geographical location and quality of the material. People commonly use gravel as an alternative. Prepare the sub-base , in the same way as for a patio. But , allow for between 50mm and 75mm of gravel as a top layer.

Less than this wear s away over time, while more than 75mm is difficult to walk on. Over time, gravel eventually finds its way scattered across the garden. Prices vary depending on the type of gravel you choose. Ongoing Maintenance. No matter which type of patio surface you decide upon, there are standard maintenance tasks you should do. There are no Planning Permission restrictions on building a patio in your back garden.

However, you might need to apply for permission if the patio requires a large amount of banking or terracing on sloped ground. Furthermore, if you live in a listed building , you might have to apply for permission.

You should also check with your local planning department whether there is a pre-existing planning condition or covenant prohibiting developments of this type. Similarly, no parts of a patio come under the Building Regulations. However, you must ensure that none of the alterations associated with the patio make s access to your home more difficult.

It includes, the number of passes, type of stresses i. As stated in this research , the compaction and the average relative breakage of the soil mixture has a non-liner relation with increase of compaction effort.

However, the compaction effort does not have any significant effect on the value of optimum moisture content. The one-liner of the test is, that soil is mixed with increased moisture content and with the help of proctor apparatus the weight of soil and thus density, in standard cylinder of known volume, is determined.

The standard compaction mold used is a metal cylinder with detachable base plate and a collar of 2 inches thickness. The height of mold is 4. Two sizes of molds are used either of 4 inches internal diameter or 6 inches. Standard compacting rammer of 5. Repeat the above calculation to determine the dry density for number of moisture contents at least 3 to 4 times so that the graph can be plotted.

Take moisture content on abscissa and dry density on ordinate, plot the points on a graph as a curvilinear relationship. Match the plotting points with a free hand curve and determine the optimum moisture content corresponding with that of the maximum dry density. Volume of Mold. Weight of Hammer. Dia of Cone. Weight of Tin. Dry Density. Yes Dear, Its not yet over. Because I have made a ready to use excel sheet for you to just put in values of standard proctor test and it will automatically calculate the optimum moisture content and the maximum dry density along with plotting of graph.

You can download this excel file for standard proctor test by clicking the button below. Download the Excel Spread sheet.

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