Linkages are primarily used as machine components and tools. Typical examples are automotive suspensions and bolt cutters. The internal combustion engine's piston/rod/crank is a classic four-bar linkage with one degree of freedom. Linkages are often the simplest, least expensive and most efficient mechanism to perform complicated motions.
One highly visible application is the windshield wiper: a four bar linkage changes the motor's rotary motion to oscillation. Some wipers also have a second set of four bar linkages to keep the wiper blades oriented correctly as they sweep. Another visible application is heavy equipment which makes extensive use of four and six bar linkages.
Spatial linkages are becoming more common due to computer aided design.
"The 4-Bar Linkage" is an adapted mechanical linkage used on bicycles. With a normal full-suspension bike the back wheel moves in a very tight arc shape. This means that more power is lost when going uphill. With a bike fitted with a 4-Bar Linkage, the wheel moves in such a large arc that it is moving almost vertically. This way the power loss is reduced by up to 30%.
Tuesday, April 29, 2008
history of linkage
Mechanical linkages are a fundamental part of machine design, and yet many simple linkages were not well understood nor invented until the 19th century. Consider a stick: it has six degrees of freedom, three of which are the coordinates of its centre in space, the other three describing its rotation. Once nudged between a boulder and fulcrum it is constrained to a particular motion, to act as a lever to move the boulder. When more links are added and joined in various ways their collective motion can be further defined. Very complicated and precise motions can be designed into a linkage with only a few parts.
The Industrial Revolution was the golden age of mechanical linkages. Mathematical, engineering and manufacturing advances provided both the need and the ability to create new mechanisms. Many simple mechanisms that seem obvious today required some of the greatest minds of the era to create. Leonhard Euler was one of the first mathematicians to study linkage synthesis, and James Watt worked very hard to invent the Watt linkage to support his steam engine's piston. Chebyshev worked on mechanical linkage design for over thirty years, which led to his work on polynomials2. New linkage inventions, designed by need, were instrumental in cloth making, power conversion and speed regulation. Even the ability of a mechanism to produce accurate linear motion, without a reference guide way, took years to solve.
Scientists, mostly German, Russian and English, have researched this domain over the last 200 years, so that today most traditional analysis or synthesis problems (e.g. planar movement) have been solved (see online libraries under External links). Recently, compliant structures have come to the fore.
Electronic technology has replaced many linkage applications taken for granted today, such as mechanical computation, typewriting and machining. However, modern linkage design continues to advance, and designs that used to occupy an engineer for days are now optimized with a computer in seconds.
Even though servomechanisms with digital control are common, and at first glance easy to use, some motion problems (especially for quick and accurate movements) are still only soluble using linkages and cams.
The Industrial Revolution was the golden age of mechanical linkages. Mathematical, engineering and manufacturing advances provided both the need and the ability to create new mechanisms. Many simple mechanisms that seem obvious today required some of the greatest minds of the era to create. Leonhard Euler was one of the first mathematicians to study linkage synthesis, and James Watt worked very hard to invent the Watt linkage to support his steam engine's piston. Chebyshev worked on mechanical linkage design for over thirty years, which led to his work on polynomials2. New linkage inventions, designed by need, were instrumental in cloth making, power conversion and speed regulation. Even the ability of a mechanism to produce accurate linear motion, without a reference guide way, took years to solve.
Scientists, mostly German, Russian and English, have researched this domain over the last 200 years, so that today most traditional analysis or synthesis problems (e.g. planar movement) have been solved (see online libraries under External links). Recently, compliant structures have come to the fore.
Electronic technology has replaced many linkage applications taken for granted today, such as mechanical computation, typewriting and machining. However, modern linkage design continues to advance, and designs that used to occupy an engineer for days are now optimized with a computer in seconds.
Even though servomechanisms with digital control are common, and at first glance easy to use, some motion problems (especially for quick and accurate movements) are still only soluble using linkages and cams.
gears
Spur gears
Spur gears are the simplest, and probably most common, type of gear. Their general form is a cylinder or disk. The teeth project radially, and with these "straight-cut gears", the leading edges of the teeth are aligned parallel to the axis of rotation. These gears can only mesh correctly if they are fitted to parallel axles.[3]
Helical gears
Helical gears from a Meccano construction set.
Helical gears offer a refinement over spur gears. The leading edges of the teeth are not parallel to the axis of rotation, but are set at an angle. Since the gear is curved, this angling causes the tooth shape to be a segment of a helix. The angled teeth engage more gradually than do spur gear teeth. This causes helical gears to run more smoothly and quietly than spur gears. Helical gears also offer the possibility of using non-parallel shafts. A pair of helical gears can be meshed in two ways: with shafts oriented at either the sum or the difference of the helix angles of the gears. These configurations are referred to as parallel or crossed, respectively. The parallel configuration is the more mechanically sound. In it, the helices of a pair of meshing teeth meet at a common tangent, and the contact between the tooth surfaces will, generally, be a curve extending some distance across their face widths. In the crossed configuration, the helices do not meet tangentially, and only point contact is achieved between tooth surfaces. Because of the small area of contact, crossed helical gears can only be used with light loads.
Quite commonly, helical gears come in pairs where the helix angle of one is the negative of the helix angle of the other; such a pair might also be referred to as having a right handed helix and a left handed helix of equal angles. If such a pair is meshed in the 'parallel' mode, the two equal but opposite angles add to zero: the angle between shafts is zero -- that is, the shafts are parallel. If the pair is meshed in the 'crossed' mode, the angle between shafts will be twice the absolute value of either helix angle.
Note that 'parallel' helical gears need not have parallel shafts -- this only occurs if their helix angles are equal but opposite. The 'parallel' in 'parallel helical gears' must refer, if anything, to the (quasi) parallelism of the teeth, not to the shaft orientation.
As mentioned at the start of this section, helical gears operate more smoothly than do spur gears. With parallel helical gears, each pair of teeth first make contact at a single point at one side of the gear wheel; a moving curve of contact then grows gradually across the tooth face. It may span the entire width of the tooth for a time. Finally, it recedes until the teeth break contact at a single point on the opposite side of the wheel. Thus force is taken up and released gradually. With spur gears, the situation is quite different. When a pair of teeth meet, they immediately make line contact across their entire width. This causes impact stress and noise. Spur gears make a characteristic whine at high speeds and can not take as much torque as helical gears because their teeth are receiving impact blows. Whereas spur gears are used for low speed applications and those situations where noise control is not a problem, the use of helical gears is indicated when the application involves high speeds, large power transmission, or where noise abatement is important. The speed is considered to be high when the pitch line velocity (that is, the circumferential velocity) exceeds 5000 ft/min.[4] A disadvantage of helical gears is a resultant thrust along the axis of the gear, which needs to be accommodated by appropriate thrust bearings, and a greater degree of sliding friction between the meshing teeth, often addressed with specific additives in the lubricant.
Double helical gears
Double helical gears, invented by André Citroën and also known as herringbone gears, overcome the problem of axial thrust presented by 'single' helical gears by having teeth that set in a 'V' shape. Each gear in a double helical gear can be thought of as two standard, but mirror image, helical gears stacked. This cancels out the thrust since each half of the gear thrusts in the opposite direction. They can be directly interchanged with spur gears without any need for different bearings.
Where the oppositely angled teeth meet in the middle of a herringbone gear, the alignment may be such that tooth tip meets tooth tip, or the alignment may be staggered, so that tooth tip meets tooth trough. The latter type of alignment results in what is known as a Wuest type herringbone gear.
With the older method of fabrication, herringbone gears had a central channel separating the two oppositely-angled courses of teeth. This was necessary to permit the shaving tool to run out of the groove. The development of the Sykes gear shaper now makes it possible to have continuous teeth, with no central gap.
The Citroën Motor Company logo of the double chevron comes from the shape of the double helical gear.
Bevel gears
If the gear in a worm-and-gear set is an ordinary helical gear only point contact between teeth will be achieved.[10] If medium to high power transmission is desired, the tooth shape of the gear is modified to achieve more intimate contact with the worm thread. A noticeable feature of most such gears is that the tooth tops are concave, so that the gear partly envelopes the worm. A further development is to make the worm concave (viewed from the side, perpendicular to its axis) so that it partly envelopes the gear as well; this is called a cone-drive or Hindley worm.[11]
A right hand helical gear or right hand worm is one in which the teeth twist clockwise as they recede from an observer looking along the axis. The designations, right hand and left hand, are the same as in the long established practice for screw threads, both external and internal. Two external helical gears operating on parallel axes must be of opposite hand. An internal helical gear and its pinion must be of the same hand.
A left hand helical gear or left hand worm is one in which the teeth twist counterclockwise as they recede from an observer looking along the axis.[2]Crown gear
A crown gear
A crown gear or contrate gear is a particular form of bevel gear whose teeth project at right angles to the plane of the wheel; in their orientation the teeth resemble the points on a crown. A crown gear can only mesh accurately with another bevel gear, although crown gears are sometimes seen meshing with spur gears. A crown gear is also sometimes meshed with an escapement such as found in mechanical clocks.
Hypoid gears
Main article: Hypoid
Hypoid gears resemble spiral bevel gears, except that the shaft axes are offset, not intersecting. The pitch surfaces appear conical but, to compensate for the offset shaft, are in fact hyperboloids of revolution.[citation needed] Hypoid gears are almost always designed to operate with shafts at 90 degrees. Depending on which side the shaft is offset to, relative to the angling of the teeth, contact between hypoid gear teeth may be even smoother and more gradual than with spiral bevel gear teeth. Also, the pinion can be designed with fewer teeth than a spiral bevel pinion, with the result that gear ratios of 60:1 and higher are "entirely feasible" using a single set of hypoid gears.[6]
Worm gear
Rack and pinion animation
Main article: Rack and pinion
A rack is a toothed bar or rod that can be thought of as a sector gear with an infinitely large radius of curvature. Torque can be converted to linear force by meshing a rack with a pinion: the pinion turns; the rack moves in a straight line. Such a mechanism is used in automobiles to convert the rotation of the steering wheel into the left-to-right motion of the tie rod(s). Racks also feature in the theory of gear geometry, where, for instance, the tooth shape of an interchangeable set of gears may be specified for the rack (infinite radius), and the tooth shapes for gears of particular actual radii then derived from that. The rack and pinion gear type is employed in a rack railway.
Spur gears are the simplest, and probably most common, type of gear. Their general form is a cylinder or disk. The teeth project radially, and with these "straight-cut gears", the leading edges of the teeth are aligned parallel to the axis of rotation. These gears can only mesh correctly if they are fitted to parallel axles.[3]
Helical gears
Helical gears from a Meccano construction set.
Helical gears offer a refinement over spur gears. The leading edges of the teeth are not parallel to the axis of rotation, but are set at an angle. Since the gear is curved, this angling causes the tooth shape to be a segment of a helix. The angled teeth engage more gradually than do spur gear teeth. This causes helical gears to run more smoothly and quietly than spur gears. Helical gears also offer the possibility of using non-parallel shafts. A pair of helical gears can be meshed in two ways: with shafts oriented at either the sum or the difference of the helix angles of the gears. These configurations are referred to as parallel or crossed, respectively. The parallel configuration is the more mechanically sound. In it, the helices of a pair of meshing teeth meet at a common tangent, and the contact between the tooth surfaces will, generally, be a curve extending some distance across their face widths. In the crossed configuration, the helices do not meet tangentially, and only point contact is achieved between tooth surfaces. Because of the small area of contact, crossed helical gears can only be used with light loads.
Quite commonly, helical gears come in pairs where the helix angle of one is the negative of the helix angle of the other; such a pair might also be referred to as having a right handed helix and a left handed helix of equal angles. If such a pair is meshed in the 'parallel' mode, the two equal but opposite angles add to zero: the angle between shafts is zero -- that is, the shafts are parallel. If the pair is meshed in the 'crossed' mode, the angle between shafts will be twice the absolute value of either helix angle.
Note that 'parallel' helical gears need not have parallel shafts -- this only occurs if their helix angles are equal but opposite. The 'parallel' in 'parallel helical gears' must refer, if anything, to the (quasi) parallelism of the teeth, not to the shaft orientation.
As mentioned at the start of this section, helical gears operate more smoothly than do spur gears. With parallel helical gears, each pair of teeth first make contact at a single point at one side of the gear wheel; a moving curve of contact then grows gradually across the tooth face. It may span the entire width of the tooth for a time. Finally, it recedes until the teeth break contact at a single point on the opposite side of the wheel. Thus force is taken up and released gradually. With spur gears, the situation is quite different. When a pair of teeth meet, they immediately make line contact across their entire width. This causes impact stress and noise. Spur gears make a characteristic whine at high speeds and can not take as much torque as helical gears because their teeth are receiving impact blows. Whereas spur gears are used for low speed applications and those situations where noise control is not a problem, the use of helical gears is indicated when the application involves high speeds, large power transmission, or where noise abatement is important. The speed is considered to be high when the pitch line velocity (that is, the circumferential velocity) exceeds 5000 ft/min.[4] A disadvantage of helical gears is a resultant thrust along the axis of the gear, which needs to be accommodated by appropriate thrust bearings, and a greater degree of sliding friction between the meshing teeth, often addressed with specific additives in the lubricant.
Double helical gears
Double helical gears, invented by André Citroën and also known as herringbone gears, overcome the problem of axial thrust presented by 'single' helical gears by having teeth that set in a 'V' shape. Each gear in a double helical gear can be thought of as two standard, but mirror image, helical gears stacked. This cancels out the thrust since each half of the gear thrusts in the opposite direction. They can be directly interchanged with spur gears without any need for different bearings.
Where the oppositely angled teeth meet in the middle of a herringbone gear, the alignment may be such that tooth tip meets tooth tip, or the alignment may be staggered, so that tooth tip meets tooth trough. The latter type of alignment results in what is known as a Wuest type herringbone gear.
With the older method of fabrication, herringbone gears had a central channel separating the two oppositely-angled courses of teeth. This was necessary to permit the shaving tool to run out of the groove. The development of the Sykes gear shaper now makes it possible to have continuous teeth, with no central gap.
The Citroën Motor Company logo of the double chevron comes from the shape of the double helical gear.
Bevel gears
If the gear in a worm-and-gear set is an ordinary helical gear only point contact between teeth will be achieved.[10] If medium to high power transmission is desired, the tooth shape of the gear is modified to achieve more intimate contact with the worm thread. A noticeable feature of most such gears is that the tooth tops are concave, so that the gear partly envelopes the worm. A further development is to make the worm concave (viewed from the side, perpendicular to its axis) so that it partly envelopes the gear as well; this is called a cone-drive or Hindley worm.[11]
A right hand helical gear or right hand worm is one in which the teeth twist clockwise as they recede from an observer looking along the axis. The designations, right hand and left hand, are the same as in the long established practice for screw threads, both external and internal. Two external helical gears operating on parallel axes must be of opposite hand. An internal helical gear and its pinion must be of the same hand.
A left hand helical gear or left hand worm is one in which the teeth twist counterclockwise as they recede from an observer looking along the axis.[2]Crown gear
A crown gear
A crown gear or contrate gear is a particular form of bevel gear whose teeth project at right angles to the plane of the wheel; in their orientation the teeth resemble the points on a crown. A crown gear can only mesh accurately with another bevel gear, although crown gears are sometimes seen meshing with spur gears. A crown gear is also sometimes meshed with an escapement such as found in mechanical clocks.
Hypoid gears
Main article: Hypoid
Hypoid gears resemble spiral bevel gears, except that the shaft axes are offset, not intersecting. The pitch surfaces appear conical but, to compensate for the offset shaft, are in fact hyperboloids of revolution.[citation needed] Hypoid gears are almost always designed to operate with shafts at 90 degrees. Depending on which side the shaft is offset to, relative to the angling of the teeth, contact between hypoid gear teeth may be even smoother and more gradual than with spiral bevel gear teeth. Also, the pinion can be designed with fewer teeth than a spiral bevel pinion, with the result that gear ratios of 60:1 and higher are "entirely feasible" using a single set of hypoid gears.[6]
Worm gear
Rack and pinion animation
Main article: Rack and pinion
A rack is a toothed bar or rod that can be thought of as a sector gear with an infinitely large radius of curvature. Torque can be converted to linear force by meshing a rack with a pinion: the pinion turns; the rack moves in a straight line. Such a mechanism is used in automobiles to convert the rotation of the steering wheel into the left-to-right motion of the tie rod(s). Racks also feature in the theory of gear geometry, where, for instance, the tooth shape of an interchangeable set of gears may be specified for the rack (infinite radius), and the tooth shapes for gears of particular actual radii then derived from that. The rack and pinion gear type is employed in a rack railway.
gears
The interlocking of the teeth in a pair of meshing gears means that their circumferences necessarily move at the same rate of linear motion (eg., metres per second, or feet per minute). Since rotational speed (eg. measured in revolutions per second, revolutions per minute, or radians per second) is proportional to a wheel's circumferential speed divided by its radius, we see that the larger the radius of a gear, the slower will be its rotational speed, when meshed with a gear of given size and speed. The same conclusion can also be reached by a different analytical process: counting teeth. Since the teeth of two meshing gears are locked in a one to one correspondence, when all of the teeth of the smaller gear have passed the point where the gears meet -- ie., when the smaller gear has made one revolution -- not all of the teeth of the larger gear will have passed that point -- the larger gear will have made less than one revolution. The smaller gear makes more revolutions in a given period of time; it turns faster. The speed ratio is simply the reciprocal ratio of the numbers of teeth on the two gears.
(Speed A * Number of teeth A) = (Speed B * Number of teeth B)
This ratio is known as the gear ratio.
The torque ratio can be determined by considering the force that a tooth of one gear exerts on a tooth of the other gear. Consider two teeth in contact at a point on the line joining the shaft axes of the two gears. In general, the force will have both a radial and a circumferential component. The radial component can be ignored: it merely causes a sideways push on the shaft and does not contribute to turning. The circumferential component causes turning. The torque is equal to the circumferential component of the force times radius. Thus we see that the larger gear experiences greater torque; the smaller gear less. The torque ratio is equal to the ratio of the radii. This is exactly the inverse of the case with the velocity ratio. Higher torque implies lower velocity and vice versa. The fact that the torque ratio is the inverse of the velocity ratio could also be inferred from the law of conservation of energy. Here we have been neglecting the effect of friction on the torque ratio. The velocity ratio is truly given by the tooth or size ratio, but friction will cause the torque ratio to be actually somewhat less than the inverse of the velocity ratio.
In the above discussion we have made mention of the gear "radius". Since a gear is not a proper circle but a roughened circle, it does not have a radius. However, in a pair of meshing gears, each may be considered to have an effective radius, called the pitch radius, the pitch radii being such that smooth wheels of those radii would produce the same velocity ratio that the gears actually produce. The pitch radius can be considered sort of an "average" radius of the gear, somewhere between the outside radius of the gear and the radius at the base of the teeth.
The issue of pitch radius brings up the fact that the point on a gear tooth where it makes contact with a tooth on the mating gear varies during the time the pair of teeth are engaged; also the direction of force may vary. As a result, the velocity ratio (and torque ratio) is not, actually, in general, constant, if one considers the situation in detail, over the course of the period of engagement of a single pair of teeth. The velocity and torque ratios given at the beginning of this section are valid only "in bulk" -- as long-term averages; the values at some particular position of the teeth may be different.
It is in fact possible to choose tooth shapes that will result in the velocity ratio also being absolutely constant -- in the short term as well as the long term. In good quality gears this is usually done, since velocity ratio fluctuations cause undue vibration, and put additional stress on the teeth, which can cause tooth breakage under heavy loads at high speed. Constant velocity ratio may also be desirable for precision in instrumentation gearing, clocks and watches. The involute tooth shape is one that results in a constant velocity ratio, and is the most commonly used of such shapes today.
(Speed A * Number of teeth A) = (Speed B * Number of teeth B)
This ratio is known as the gear ratio.
The torque ratio can be determined by considering the force that a tooth of one gear exerts on a tooth of the other gear. Consider two teeth in contact at a point on the line joining the shaft axes of the two gears. In general, the force will have both a radial and a circumferential component. The radial component can be ignored: it merely causes a sideways push on the shaft and does not contribute to turning. The circumferential component causes turning. The torque is equal to the circumferential component of the force times radius. Thus we see that the larger gear experiences greater torque; the smaller gear less. The torque ratio is equal to the ratio of the radii. This is exactly the inverse of the case with the velocity ratio. Higher torque implies lower velocity and vice versa. The fact that the torque ratio is the inverse of the velocity ratio could also be inferred from the law of conservation of energy. Here we have been neglecting the effect of friction on the torque ratio. The velocity ratio is truly given by the tooth or size ratio, but friction will cause the torque ratio to be actually somewhat less than the inverse of the velocity ratio.
In the above discussion we have made mention of the gear "radius". Since a gear is not a proper circle but a roughened circle, it does not have a radius. However, in a pair of meshing gears, each may be considered to have an effective radius, called the pitch radius, the pitch radii being such that smooth wheels of those radii would produce the same velocity ratio that the gears actually produce. The pitch radius can be considered sort of an "average" radius of the gear, somewhere between the outside radius of the gear and the radius at the base of the teeth.
The issue of pitch radius brings up the fact that the point on a gear tooth where it makes contact with a tooth on the mating gear varies during the time the pair of teeth are engaged; also the direction of force may vary. As a result, the velocity ratio (and torque ratio) is not, actually, in general, constant, if one considers the situation in detail, over the course of the period of engagement of a single pair of teeth. The velocity and torque ratios given at the beginning of this section are valid only "in bulk" -- as long-term averages; the values at some particular position of the teeth may be different.
It is in fact possible to choose tooth shapes that will result in the velocity ratio also being absolutely constant -- in the short term as well as the long term. In good quality gears this is usually done, since velocity ratio fluctuations cause undue vibration, and put additional stress on the teeth, which can cause tooth breakage under heavy loads at high speed. Constant velocity ratio may also be desirable for precision in instrumentation gearing, clocks and watches. The involute tooth shape is one that results in a constant velocity ratio, and is the most commonly used of such shapes today.
gear
A gear is a component within a transmission device that transmits rotational force to another gear or device. A gear is different from a pulley in that a gear is a round wheel which has linkages ("teeth" or "cogs") that mesh with other gear teeth, allowing force to be fully transferred without slippage. Depending on their construction and arrangement, geared devices can transmit forces at different speeds, torques, or in a different direction, from the power source. Gears are a very useful simple machine. The most common situation is for a gear to mesh with another gear, but a gear can mesh with any device having compatible teeth, such as linear moving racks. A gear's most important feature is that gears of unequal sizes (diameters) can be combined to produce a mechanical advantage, so that the rotational speed and torque of the second gear are different from that of the first. In the context of a particular machine, the term "gear" also refers to one particular arrangement of gears among other arrangements (such as "first gear"). Such arrangements are often given as a ratio, using the number of teeth or gear diameter as units. The term "gear" is also used in non-geared devices which perform equivalent tasks:
Tuesday, March 4, 2008
The new project
I am being asked to make a mechanical toy for my new project.There are a lot of things i need to do like make the design journal to keep track of my work,design of toy,design specification,mind map and a lot more.I so far only done the journal but not the toy.I now need to make measurement for the toy and then construct it.
Wednesday, January 30, 2008
project i am working on
My class were being ask to make a machanical toys for our own reasons. We were also asked to make a joounal,which our teacher called it 'book of rubbish' since its all the design that we are going to take from later, on the things we are doing to do the project. We were being taught about the tools and safety in the workshop. There were 28 tools we were being told. Thats all for now till then.Bye!
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