Linkage (mechanical)

Coupling gears are gears which convert rotational movement into linear or oscillating motion, and vice versa. They are characterized by the coupling of at least two of the movable elements with a paddock.

Linkage are unevenly translated transmission.

The coupling is usually an engine part in the form of a connecting rod, a connecting rod, a coupling rod or a sliding block.

• 2.1 Kinematic chain
• 2.2 Simple four-bar
• 2.3 rocker arm
• 2.4 double crank
• 2.5 double rocker
• 2.6 crank
• 2.7 Scotch -Yoke crank mechanism ( also: cross slider crank, crank crank loop or loop )
• 2.8 Cross loop
• 2.9 wheels linkage

• 4.1 Initial Situation 4.1.1 Homologous documents

Groups

Four classes

The linkage sure most widely used is the four-membered linkage. This transmission is ( logically ) from four pivotally interconnected rods and has exactly one degree of freedom. In practice, such transmission see but often different, so most four-membered linkage are not recognized as such. Typically, the first gear member is the casing. The drive member is usually a lever or a disc, with the / is introduced, a rotary movement to the transmission. The output is either a rocker or also a rotationally shaped member which vibrates either or also rotates. In between there is a coupling element which transmits the movement from the driving to the driven member.

More than four limbs

There are also multi-unit linkage with 5, 6, 8 or more limbs. These transmissions are often divided with tools on multiple logical four-membered gear.

The six-membered gear are called Watt's or Stephenson'sche chain. A five-membered coupling gear usually has a degree of freedom of 2 That is, there must be two movements are initiated to create a defined behavior.

Therefore, 5 - and 6 -membered linkage also often used in cases where it matters, two moving units movably coupled together and to derive further behavior of the relative motion, such as the increase spring tension to a point where no technical spring can be mounted, as in the suspension of wheels of vehicles.

It is also common to tie a degree of freedom by a two- stroke.

Special designs

Locking gear

Locking gears are special forms of gearbox, wherein said output member carries some form of latching in continuous drive:

• Currently rest
• Rest
• Pilger

In the region of the coupling mechanism latching gear are often realized through related gear ( for example, by two-beat at a coupling point ) and on wheels linkage. They often are used when a discontinuous motion with high frequency is to be executed, which can cause extreme accelerations to destroy or at least to high energy consumption and high noise levels in primitive locking gears.

Special forms of planar linkage

Taking into account certain conditions it is possible in their entirety to bend flat Koppelgetrieb to surfaces. arise from the fact

• Cylindrical linkage
• Spherical linkage

In the analysis ( speed and acceleration ), and the synthesis of the curvature is irrelevant. However, it is important when considering the forces, the rigidity of the transmission elements, and other physical factors. These studies are, however, all outside the kinematic point of view. Therefore, a curvature planar mechanisms around a cylinder or a sphere need not be considered separately here.

Special dimensions

By special dimensions, meant are here: relations between the transmission parts, specific tasks can be solved, some of which require no special synthesis methods.

So you can as an example call forwarding Drehbwegungen with steam locomotives from one wheel to the other. Here had no special synthesis methods or scientific studies to perform, since the task and its solution were obvious. Transmission Technical ( ie from the perspective of coupled transmission) is in this ' rod connection ' to an extreme double crank, which also still has the particularity that it requires no auxiliary gearing, because the wheels equal to prevent by several factors that the double crank of at the turning points connecting rod ( the coupling ) by beat. The main reasons are:

Another typical gears with specific dimensions is a pantograph. The pantograph, in the sense of a device for scale-up or reduction of geometries realized a transfer task for which there is no general method of synthesis. Not least because the task is solvable by logical think, never was a need to synthesize a Panthographengetriebe.

There are a variety of coupled gears with special dimensions, which are also practical use. But pantograph and double cranks are probably the most basic forms of such transmission.

Spatial coupling gear

In spatial coupling transmissions are completely different analysis and synthesis method. They are in no way comparable with planar, cylindrical or spherical coupling gears, even if the layman can not distinguish them visually in most cases. The main external difference between spatial coupling gear on one side and the crooked planes coupled gears on the other hand, make that the axes of the joints in spatial transmissions neither on a line ( as in cylindrical ) yet at a point ( as in spherical gears ).

Spatial coupling transmission require by their nature, a new category. This is due not least to the fact that spatial transmission are needed only in very exceptional cases and use their synthesis is so extremely complex that hardly anyone can afford to develop spatial transmission.

All further discussed here are planar transmission gear, including cylindrical and spherical, but not spatial.

Four-Membered linkage

Kinematic chain

At the kinematic chain of the planar four-membered coupling gear with four rotary joints can be seen that such a transmission has exactly one degree of freedom. The circles in the corners of the square represent joints, the lines between the gear members. A transmission element is most often mounted in the real world to a reference system (for example, a housing or the earth itself ). In the illustrated kinematic chain can then be initiated exactly one rotation. The transmission then moves inevitably.

From a technical perspective, transmission is shown in the kinematic chain to a striking double crank. This fact should find no attention here but first. Special dimensions, as here, be treated under analysis and synthesis later. The presentation is intended only to indicate that in a four-membered linkage of each gear component can in principle take on any role. Therefore, all transmission elements are shown the same length.

Shape and shape change are particularly in the design of coupled gears successful strategies to solve complicated tasks elegant. From the kinematic chain, it is only a small step to the simple four-bar linkage.

Simple four-bar

To illustrate linkage of course, use the symbolism appearing in the picture. Here the transition from drawing the schematic kinematic chain is presented for four-bar mechanism in such a way that all elements from the representation of the kinematic chain are reproduced identically in the representation of the four-bar linkage.

The alterations are essentially two things: the first is the bottom line, that accounts for the lower gear member, and second, the bottom two hinge points are larger and partially filled. Pivot points which are shown here as the points A0 and B0 are to be regarded as fixed with the reference system. Put simply referred to these pivot points as a housing points.

Thus the housing is not shown connects the points A0 and B0 together so that a specific transmission element does not need to be drawn. This representation is similar in principle to the representation of potential connections ( eg ground) in electrical and electronic drawings, so it should be familiar and visually plausible therefore.

Crank-rocker

Double crank

Double cranks are characterized in that the drive and driven members are fully fit for circulation. This leads to the problem that double cranks have two special positions in which the movement can branch. If all transmission elements one above the other ( form a line), the direction of movement of the driven member can be reversed. If this happens accidentally, it can be used for terminals and thereby come to tear the transmission. Typically, prevents by an auxiliary gearing.

A coupling mechanism, which may have already seen in action most people, comes with old steam locomotives used and is attached there often on the outside. It transmits the driving force of the driven axle of the locomotive on the other axes. To this end, the wheels in question are eccentrically connected to a paddock.

Double rocker

For double swing is neither driving nor driven member is able to perform a complete revolution ( without tearing the transmission ). Input and output can only swing.

Find application such as a linear guide transmission or motion converter as in vending machines or drive machines in which a limited swinging movement or effecting service must be transformed or transferred. This can happen when a vibrating drive motion to produce a hard- coupled, synchronous output movement that will, for example, increase the distance between two transport workpieces.

Slider-crank

A slider-crank mechanism is used a rotary movement into a translational movement ( and vice versa) to reshape. The best known application of crank gears can be found at the piston engine.

Scotch -Yoke crank mechanism (also: cross slider crank, crank crank loop or loop )

In crank grinding transmission is, in which the crank is not connected as in the previously described gears, via a rotary joint with a coupling. Instead ( Antriebgsglied ) located at the end of the crank a thrust element which is in turn pivotally connected to the housing.

Scotch

In a scotch yoke drive and driven members are pushing members.

Typical applications: small compressors, film cameras

Wheels linkage

It is a combination of a gear transmission with a linkage. Such gears are used to convert rotary movements unkontinuierlichen continuous to intermittent rotational movements. This effect is achieved by the movement of a crank-rocker mechanism is added to the continuous rotary motion, which is transmitted by the gears.

One use of such gear is the drive of a paper in a paper drum turning device for printing machines. Here is a drum that rotates at high speed, perform a momentary rest after each rotation, so that the gripper, which is to turn the printed sheet, has the opportunity to access accurate and secure.

Analysis

Existing or specified in their dimensions linkage must be analyzed for their properties because linkage as opposed to gear trains have a complex behavior. Especially in connection with the synthesis of switching gears, the analysis is important because linkage can not be linear but only iteratively develop.

Investigate a number of properties, among others:

• Degree Running Analysis
• Coupler curves
• Translation
• Speeds
• Accelerations
• Angle-angle assignment
• Point -ply angle mapping
• Plane posi - angle mapping
• For circulation
• Special position / special sizes
• Quality of the intended movement
• Instantaneous centers

And many more.

Synthesis

The synthesis describes the creation and adaptation to the requirements of a coupling gear.

Initial situation

It is, except for special functions, not possible to synthesize coupling mechanism which implement a predetermined movement sequence is 100% accurate. Trajectories or plane layers can be specified is limited. The complexity of the synthesis process increases exponentially number of predetermined point or plane layers.

The synthesis of coupled gears is therefore in the best case an iterative process, in which the respective synthesis step using various analytical methods is examined for its suitability for the intended purpose. Will that be examined model does not meet the requirements, needs an additional synthesis step is performed, etc.

To compensate for the synthesis of planar linkage provides the opportunity to develop infinitely many different gearboxes that meet the given task ( point layers, layer positions ). In this case, inter alia, consideration of geometric and spatial possibilities and limits are taken.

In addition to the direct synthesis of gears, as indicated here, is for most gear the opportunity to develop so-called replacement gearbox or derive directly from the construction that are constructed geometrically and / or structurally different, but partially or completely, the identical behavior in terms of movement an interest element (usually the coupling ) have.

Homologous positions

As homologous positions different positions of the same element are called. The item ( crosspoint level ) has held that documents one at a time. The transmission to enable the desired movement to be connected to the element in question. So it 's not like that in a plane position synthesis, the coupling proceeds through the homologous positions. Rather, the coupling in the appropriate gear position with the moving plane is rigidly connected to. The same applies to the point of synthesis.

Typically one wishes in the synthesis a transmission that generates the homologous positions in the order named. However, the point and the plane position synthesis is not able to synthesize targeted gear that actually pace off the desired order. It is not even guaranteed that, the desired homologous layers reach to disassemble a non-rotating efficient transmission without (for example) and to mount the gear parts differently. This is another reason why an automated synthesis must be supported by an equally automated analysis.

Three position synthesis of crank swing

Given the 2 locating bearing of the crank swing gear ( A0 and B0) in the original plane and three homologous positions of the desired level, which is determined by the coupling for the synthesis. The homologous position was determined in each case by the position of any point of the plane and through the twisting angle of the coupling level to the original level, for example. Wanted is the location of the hinge points (A and B ) of the coupling in a certain position, because thereby the coupling gear is clearly described.

The clearest type of synthesis is carried out with a piece of tracing paper to represent the freely movable coupling plane. Any point and an arbitrary orientation are drawn on the transparency. On a paper underneath the fixed bearing ( A0 and B0) are recorded. The tracing paper is now placed in each one of the three desired positions and the fixed bearing by drawn. Thus, there are now 3 points for A0 and B0 for 3 points on the tracing paper. As point A and point A0 by the coupling have a fixed distance apart, it is evident that A must be located on a circle around A0. The same is true for B. Thus, only with the 3 points on the tracing paper a radius design to perform, it simply is the perpendicular bisector of 2 points in the intersection of these bisectors, the solution to A. The same is true for example, one has the understood process, so it is easy to implement this idea in a CAD system and therefore absolutely work exactly.

Two position synthesis of crank swing

If only two preferred locations are specified at a task instead of three, we obtain by the above procedure only a perpendicular bisector. In the simplest case, one can freely choose constructive desires a point on this line and securely attach a lever whose circulation may be limited ( for example by bill ).

But it is also possible to develop a slightly more complex construction, a complete four -membered linkage, wherein the housing of the transmission points do not lie on the mid-perpendicular.