In mechanical engineering, an eccentric is a circular disk solidly fixed to a rotating axle with its centre offset from that of the axle. It is used most in steam engines, used to convert rotary into linear reciprocating motion to drive a sliding valve or pump ram. To do so, an eccentric has a groove at its circumference fitted a circular collar. An attached eccentric rod is suspended in such a way that its other end can impart the required reciprocating motion. A return crank fulfills the same function except that it can only work at the end of an axle or on the outside of a wheel whereas an eccentric can be fitted to the body of the axle between the wheels. Unlike a cam, which converts rotary into linear motion at any rate of acceleration and deceleration, an eccentric or return crank can only impart simple harmonic motion; the term is used to refer to the device used on tandem bicycles with timing chains, single-speed bicycles with a rear disc brake or an internal-geared hub, or any bicycle with vertical dropouts and no derailleur, to allow slight repositioning and aft, of a bottom bracket to properly tension the chain.
They may be held in place by a built-in wedge, set screws threaded into the bottom bracket shell, or pinch bolts that tighten a split bottom bracket shell. As a standard sized bottom bracket threads into the eccentric, an oversized bottom bracket shell is required to accommodate the eccentric. Balance shaft Cam Crank Concentric Crankshaft Linkage
A motorcycle transmission is a transmission created for motorcycle applications. They may be found in use on other light vehicles such as motor tricycles and quadbikes, go-karts offroad buggies, auto rickshaws and other utility vehicles and some superlight racing cars. Most manual transmission two-wheelers use a sequential gearbox. Most modern motorcycles change gears by foot lever. On a typical motorcycle either first or second gear can be directly selected from neutral, but higher gears may only be accessed in order – it is not possible to shift from second gear to fourth gear without shifting through third gear. A five-speed of this configuration would be known as "one down, four up" because of the placement of the gears with relation to neutral, though some motorcycle gearboxes and/or shift mechanisms can be reversed so that a "one up, four down" shifting pattern can be used. Neutral is to be found "half a click" away from first and second gears, so shifting directly between the two gears can be made in a single movement.
Automatic transmissions are less common on motorcycles than manual, are found only on scooters and some custom cruisers and exotic sports bikes. Types include continuously variable transmission, semi-automatic transmission and dual clutch transmission; the weight of the largest touring motorcycles is sometimes such that they cannot be pushed backwards by a seated rider, they are fitted with a reverse gear as standard. In some cases, including the Honda Gold Wing and BMW K1200LT, this is not a reverse gear, but a feature of the starter motor which when reversed, performs the same function. To avoid accidental operation, reverse is engaged using an separate control switch - e.g. a pull-toggle at the head of the fuel tank - when the main gearshift is in neutral. In earlier times, hand-operated gear changes were common, with a lever provided to the side of the fuel tank. British and many other motorcycles after World War II used a lever on the right, but today gear-changing is standardised on a foot-operated lever to the left.
Traditional scooters still have manual gear-changing by a twist grip on the left hand side of the handlebar, with a co-rotated clutch lever. Modern scooters were fitted with a throttle-controlled continuously variable transmission, thus earning the term twist-and-go. Underbone and miniature motorcycles have a three to five-speed foot change, but the clutch is automatic; the clutch in a manual-shift motorcycle transmission is an arrangement of plates stacked in alternating fashion, one geared on the inside to the engine and the next geared on the outside to the transmission input shaft. Whether wet or dry, the plates are squeezed together by a spring, causing friction build up between the plates until they rotate as a single unit, driving the transmission directly. A lever on the handlebar exploits mechanical advantage through a cable or hydraulic arrangement to release the clutch spring, allowing the engine to freewheel with respect to the transmission. Automatic and semi-automatics use a centrifugal clutch which operates in a different fashion.
At idle, the engine is disconnected from the gearbox input shaft, allowing both it and the bike to freewheel. As the throttle is opened and engine speed rises, counterweights attached to movable inner friction surfaces within the clutch assembly are thrown further outwards, until they start to make contact with the inside of the outer housing and transmit an increasing amount of engine power; the effective "bite point" is found automatically by equilibrium where the power being transmitted through the clutch is equal to what the engine can provide. This allows fast full-throttle takeoffs without the engine slowing or bogging down, as well as more relaxed starts and low-speed maneuvers at lower throttle settings and rpms. Above a certain engine speed - when the bike is properly in motion, so the gearbox input shaft is rotating and so allowing the engine to accelerate further by way of clutch slip - the outward pressure of the weighted friction plates is sufficient that the clutch will enter full lock-up, the same as a conventional plate-clutch with a released lever or pedal.
After this, there is no clutch slip, the engine is locked to and providing all of its available power to the transmission. In a typical CVT, the gear ratio will be chosen so the engine can reach and maintain its maximum-power speed as soon as possible, but in a semi-auto the rider is responsible for this choice, they can ride around all day in top gear if they so prefer; when the engine is turning fast enough to lock the clutch, it will stay engaged until the RPMs fall below that critical point again if the throttle is released. Below the lock-up point or releasing the throttle can lead to the RPM falling off thanks to the feedback loop of lower engine speed meaning less friction pressure; this toggle-like mode of operation can lead to certain characteristic cen
The radial engine is a reciprocating type internal combustion engine configuration in which the cylinders "radiate" outward from a central crankcase like the spokes of a wheel. It resembles a stylized star when viewed from the front, is called a "star engine" in some languages; the radial configuration was used for aircraft engines before gas turbine engines became predominant. Since the axes of the cylinders are coplanar, the connecting rods cannot all be directly attached to the crankshaft unless mechanically complex forked connecting rods are used, none of which have been successful. Instead, the pistons are connected to the crankshaft with a master-and-articulating-rod assembly. One piston, the uppermost one in the animation, has a master rod with a direct attachment to the crankshaft; the remaining pistons pin their connecting rods' attachments to rings around the edge of the master rod. Extra "rows" of radial cylinders can be added in order to increase the capacity of the engine without adding to its diameter.
Four-stroke radials have an odd number of cylinders per row, so that a consistent every-other-piston firing order can be maintained, providing smooth operation. For example, on a five-cylinder engine the firing order is 1, 3, 5, 2, 4, back to cylinder 1. Moreover, this always leaves a one-piston gap between the piston on its combustion stroke and the piston on compression; the active stroke directly helps compress the next cylinder to fire. If an number of cylinders were used, an timed firing cycle would not be feasible; the prototype radial Zoche aero-diesels have an number of cylinders, either four or eight. The radial engine uses fewer cam lobes than other types; as with most four-strokes, the crankshaft takes two revolutions to complete the four strokes of each piston. The camshaft ring is geared to spin slower and in the opposite direction to the crankshaft; the cam lobes exhaust. For example, four cam lobes serve all five cylinders, whereas 10 would be required for a typical inline engine with the same number of cylinders and valves.
Most radial engines use overhead poppet valves driven by pushrods and lifters on a cam plate, concentric with the crankshaft, with a few smaller radials, like the Kinner B-5 and Russian Shvetsov M-11, using individual camshafts within the crankcase for each cylinder. A few engines use sleeve valves such as the 14-cylinder Bristol Hercules and the 18-cylinder Bristol Centaurus, which are quieter and smoother running but require much tighter manufacturing tolerances. C. M. Manly constructed a water-cooled five-cylinder radial engine in 1901, a conversion of one of Stephen Balzer's rotary engines, for Langley's Aerodrome aircraft. Manly's engine produced 52 hp at 950 rpm. In 1903–1904 Jacob Ellehammer used his experience constructing motorcycles to build the world's first air-cooled radial engine, a three-cylinder engine which he used as the basis for a more powerful five-cylinder model in 1907; this was made a number of short free-flight hops. Another early radial engine was the three-cylinder Anzani built as a W3 "fan" configuration, one of which powered Louis Blériot's Blériot XI across the English Channel.
Before 1914, Alessandro Anzani had developed radial engines ranging from 3 cylinders — early enough to have been used on a few French-built examples of the famous Blériot XI from the original Blériot factory — to a massive 20-cylinder engine of 200 hp, with its cylinders arranged in four rows of five cylinders apiece. Most radial engines are air-cooled, but one of the most successful of the early radial engines was the Salmson 9Z series of nine-cylinder water-cooled radial engines that were produced in large numbers during the First World War. Georges Canton and Pierre Unné patented the original engine design in 1909, offering it to the Salmson company. From 1909 to 1919 the radial engine was overshadowed by its close relative, the rotary engine, which differed from the so-called "stationary" radial in that the crankcase and cylinders revolved with the propeller, it was similar in concept to the radial, the main difference being that the propeller was bolted to the engine, the crankshaft to the airframe.
The problem of the cooling of the cylinders, a major factor with the early "stationary" radials, was alleviated by the engine generating its own cooling airflow. In World War I many French and other Allied aircraft flew with Gnome, Le Rhône, Bentley rotary engines, the ultimate examples of which reached 250 hp although none of those over 160 hp were successful. By 1917 rotary engine development was lagging behind new inline and V-type engines, which by 1918 were producing as much as 400 hp, were powering all of the new French and British combat aircraft. Most German aircraft of the time used water-cooled inline 6-cylinder engines. Motorenfabrik Oberursel made licensed copies of the Gnome and Le Rhône rotary powerplants, Siemens-Halske built their own designs, including the Siemens-Halske Sh. III eleven-cylinder rotary engine, unusual for the period in being geared through a bevel geartrain in the rear end of the crankcase without the crankshaft being mounted to the aircraft's airframe, so that the engine's internal working components (fully in
The Bourke engine was an attempt by Russell Bourke, in the 1920s, to improve the two-stroke engine. Despite finishing his design and building several working engines, the onset of World War II, lack of test results, the poor health of his wife compounded to prevent his engine from coming to market; the main claimed virtues of the design are that it has only two moving parts, is lightweight, has two power pulses per revolution, does not need oil mixed into the fuel. The Bourke engine is a two-stroke design, with one horizontally opposed piston assembly using two pistons that move in the same direction at the same time, so that their operations are 180 degrees out of phase; the pistons are connected to a Scotch Yoke mechanism in place of the more usual crankshaft mechanism, thus the piston acceleration is sinusoidal. This causes the pistons to spend more time at top dead center than conventional engines; the incoming charge is compressed in a chamber under the pistons, as in a conventional crankcase-charged two-stroke engine.
The connecting-rod seal prevents the fuel from contaminating the bottom-end lubricating oil. The operating cycle is similar to that of a current production spark ignition two-stroke with crankcase compression, with two modifications: The fuel is injected directly into the air as it moves through the transfer port; the engine is designed to run without using spark ignition. This is known as auto-ignition or dieseling, the air/fuel mixture starts to burn due to the high temperature of the compressed gas, and/or the presence of hot metal in the combustion chamber; the following design features have been identified: Scotch yoke instead of connecting rods to translate linear motion to rotary motion Fewer moving parts and the opposed cylinders are combinable to make 2, 4, 6, 8, 10, 12 or any number of cylinders The piston is connected to the Scotch yoke through a slipper bearing Mechanical fuel injection. Ports rather than valves. Easy maintenance with simple tools; the Scotch yoke does not create lateral forces on the piston, reducing piston wear.
O-rings are used to seal joints rather than gaskets. The Scotch Yoke makes the pistons dwell slightly longer at top dead center, so the fuel burns more in a smaller volume. Low exhaust temperature so metal exhaust components are not required, plastic ones can be used if strength is not required from exhaust system 15:1 to 24:1 compression ratio for high efficiency and it can be changed as required by different fuels and operation requirements. Fuel is vaporised when it is injected into the transfer ports, the turbulence in the intake manifolds and the piston shape above the rings stratifies the fuel air mixture into the combustion chamber. Lean burn for reduced emissions; this design uses oil seals to prevent the pollution from the combustion chamber from polluting the crankcase oil, extending the life of the oil as it is used for keeping the rings full of oil to hold and use to lubricate. Oil was shown to be used by the dropfull as needed, but checking the quantity and cleanness of it was still recommended by Russell Bourke, its creator.
The lubricating oil in the base is protected from combustion chamber pollution by an oil seal over the connecting rod. The piston rings are supplied with oil from a small supply hole in the cylinder wall at bottom dead center. Efficiency 0.25 /hp is claimed - about the same as the best diesel engine, or twice as efficient as the best two strokes. This is equivalent to a thermodynamic efficiency of 55.4%, an exceedingly high figure for a small internal combustion engine. In a test witnessed by a third party, the actual fuel consumption was 1.1 hp/, or 0.9 /hp, equivalent to a thermodynamic efficiency of about 12.5%, typical of a 1920s steam engine. A test of a 30 cubic inch Vaux engine, built by a close associate of Bourke, gave a fuel consumption of 1.48 lb/, or 0.7 /hp at maximum power. Power to weight The Silver Eagle was claimed to produce 25 hp from 45 lb, or a power to weight ratio of 0.55 hp/lb. The larger 140 cubic inch engine was good for 120 hp from 125 lb, or 1 hp/lb; the Model H was claimed to produce 60 hp with a weight of 95 lb, hence giving a power to weight ratio of 0.63 hp/lb.
The 30 cu in twin was reported to produce 114 hp at 15000rpm while weighing only 38 lb, an incredible 3 hp/lb However a 30 cu in replica from Vaux Engines produced just 8.8 hp at 4000 rpm after substantial reworking. Other sources claim 0.9 to 2.5 hp/lb, although no independently witnessed test to support these high figures has been documented. The upper range of this is twice as good as the best four-stroke production engine shown here, or 0.1 hp/lb better than a Graupner G58 two-stroke. The lower claim is unremarkable exceeded by production four-stroke engines, never mind two strokes. Emissions Achieved no hydrocarbons or carbon monoxide in published test results, however no power output was given for these results, NOx was not measured. Low Emissions The engine is claimed to be able to operate on hydrogen or any hydro-carbon fuel without any modifications, producing only water vapor and carbon dioxide as emissions; the Bourke Engine has some interesting features, but the extravagant claims for its performance are unlikely to be borne out by real tests.
Many of the claims are contradictory. Seal friction from the seal between the air compressor chamber and the crankcase, agai
Pin tumbler lock
The pin tumbler lock is a lock mechanism that uses pins of varying lengths to prevent the lock from opening without the correct key. Pin tumblers are most employed in cylinder locks, but may be found in tubular pin tumbler locks; the first tumbler lock was found in the ruins of the Palace of Khorsabad in Iraq. Basic principles of the pin tumbler lock may date as far back as 2000 BC in Egypt; the bolt had vertical openings. These could be lifted, using a key, to a sufficient height to allow the bolt to move and unlock the door; this wooden lock was one of Egypt's major developments in domestic architecture during classical times. Such a lock, may be defeated by lifting the pins uniformly beyond the unlatching point. In 1805, the earliest patent for a double-acting pin tumbler lock — one where lifting the pins too much or too little prevented opening — was granted to American physician Abraham O. Stansbury in England, it was based on Joseph Bramah's tubular pin tumbler lock. Two years Stansbury was granted a patent in the United States for his lock.
In 1848, Linus Yale, Sr. invented the modern pin-tumbler lock. In 1861, Linus Yale, Jr. inspired by the original 1840s pin-tumbler lock designed by his father and patented a smaller flat key with serrated edges as well as pins of varying lengths within the lock itself, the same design of the pin-tumbler lock in use today. The pin tumbler is used in cylinder locks. In this type of lock, an outer casing has a cylindrical hole. To open the lock, the plug must rotate; the plug has a straight-shaped slot known as the keyway at one end to allow the key to enter the plug. The keyway has protruding ledges that serve to prevent the key pins from falling into the plug, to make the lock more resistant to picking. A series of holes five or six of them, are drilled vertically into the plug; these holes contain key pins of various lengths, which are rounded to permit the key to slide over them easily. Above each key pin is a corresponding set of driver pins. Simpler locks have only one driver pin for each key pin, but locks requiring multi-keyed entry, such as a group of locks having a master key, may have extra driver pins known as spacer pins.
The outer casing has several vertical shafts. When the plug and outer casing are assembled, the pins are pushed down into the plug by the springs; the point where the plug and cylinder meet is called the shear point. With a key properly cut and inserted into the groove on the end of the plug, the pins will rise causing them to align at the shear point; this allows the plug to rotate, thus opening the lock. When the key is not in the lock, the pins straddle the shear point, preventing the plug from rotating. Pin tumbler locks are found in a cylinder that can be unscrewed by a locksmith to facilitate rekeying; the first main advantage to a cylinder lock known as a profile cylinder lock or euro, is that the cylinder can be changed without altering the boltwork hardware. Removing the cylinder requires only loosening a set screw sliding the cylinder from the boltwork; the second is that it is possible to obtain, from various lock manufacturers, cylinders in different formats that can all be used with the same type of key.
This allows the user to have keyed-alike, master-keyed systems that incorporate a wide variety of different types of lock, such as nightlatches and roller door locks. Commercial padlocks can be included, although these have removable cylinders. Standardised types of cylinder include: Rim mounted Euro cylinders Key-in-knobset cylinders Ingersoll format cylinders American, Scandinavian round mortise cylinders Scandinavian oval cylindersThere are standardised cross-sectional profiles for lock cylinders that may vary in length - for example to suit different door thicknesses; these profiles include the europrofile, the British oval profile and the Swiss profile A tubular pin tumbler lock is a pin-tumbler lock with a round keyway. A dimple lock is a pin tumbler lock where the bitting is located on the side of the key, rather than the top. A master keyed lock is a variation of the pin tumbler lock that allows the lock to be opened with two different keys; this type is used for doorlocks in commercial buildings with multiple tenants, such as office buildings, student accommodation and storage facilities.
Each tenant is given a key that only unlocks their own door, called the change key, but the second key is the master key, which unlocks all the doors, is kept by the building manager, so they can enter any room in the building. In a master keyed lock, some or all of the shaft hole in the lock have three pins in them instead of two. Between the driver pin and the key pin is a third pin called the spacer pin, thus each pin line has two shear points, one where the driver and spacer pins meet, one where the spacer and key pins meet. So the lock will open with two keys; the locks are manufactured so one set of shear points is unique to each lock, while the second set is identical in all the locks. A more secure type of mechanism has two separate tumblers, each opened by one key. More complicated master-key lock systems are made, with two or more levels of master keyin
In its primitive form, a wheel is a circular block of a hard and durable material at whose center has been bored a circular hole through, placed an axle bearing about which the wheel rotates when a moment is applied by gravity or torque to the wheel about its axis, thereby making together one of the six simple machines. When placed vertically under a load-bearing platform or case, the wheel turning on the horizontal axle makes it possible to transport heavy loads; the English word wheel comes from the Old English word hweol, from Proto-Germanic *hwehwlan, *hwegwlan, from Proto-Indo-European *kwekwlo-, an extended form of the root *kwel- "to revolve, move around". Cognates within Indo-European include Icelandic hjól "wheel, tyre", Greek κύκλος kúklos, Sanskrit chakra, the latter two both meaning "circle" or "wheel"; the invention of the wheel falls into the late Neolithic, may be seen in conjunction with other technological advances that gave rise to the early Bronze Age. This implies the passage of several wheel-less millennia after the invention of agriculture and of pottery, during the Aceramic Neolithic.
4500–3300 BCE: Copper Age, invention of the potter's wheel. Precursors of wheels, known as "tournettes" or "slow wheels", were known in the Middle East by the 5th millennium BCE; these were made of stone or clay and secured to the ground with a peg in the center, but required significant effort to turn. True potter's wheels were in use in Mesopotamia by 3500 BCE and as early as 4000 BCE, the oldest surviving example, found in Ur, dates to 3100 BCE; the first evidence of wheeled vehicles appears in the second half of the 4th millennium BCE, near-simultaneously in Mesopotamia, the Northern and South Caucasus, Eastern Europe, so the question of which culture invented the wheeled vehicle is still unresolved. The earliest well-dated depiction of a wheeled vehicle is on the 3500–3350 BCE Bronocice clay pot excavated in a Funnelbeaker culture settlement in southern Poland. In nearby Olszanica 5000 BCE 2.2 m wide door were constructed for wagon entry. This barn was 40 m long with 3 doors; the oldest securely dated real wheel-axle combination, that from Stare Gmajne near Ljubljana in Slovenia is now dated within two standard deviations to 3340–3030 BCE, the axle to 3360–3045 BCE.
Two types of early Neolithic European wheel and axle are known. They both are dated to c. 3200–3000 BCE. In China, the wheel was present with the adoption of the chariot in c. 1200 BCE, although Barbieri-Low argues for earlier Chinese wheeled vehicles, c. 2000 BCE. In Britain, a large wooden wheel, measuring about 1 m in diameter, was uncovered at the Must Farm site in East Anglia in 2016; the specimen, dating from 1,100–800 BCE, represents the most complete and earliest of its type found in Britain. The wheel's hub is present. A horse's spine found; the wheel was found in a settlement built on stilts over wetland, indicating that the settlement had some sort of link to dry land. Although large-scale use of wheels did not occur in the Americas prior to European contact, numerous small wheeled artifacts, identified as children's toys, have been found in Mexican archeological sites, some dating to about 1500 BCE, it is thought that the primary obstacle to large-scale development of the wheel in the Americas was the absence of domesticated large animals which could be used to pull wheeled carriages.
The closest relative of cattle present in Americas in pre-Columbian times, the American Bison, is difficult to domesticate and was never domesticated by Native Americans. The only large animal, domesticated in the Western hemisphere, the llama, a pack animal but not physically suited to use as a draft animal to pull wheeled vehicles, did not spread far beyond the Andes by the time of the arrival of Columbus. Nubians from after about 400 BCE used wheels as water wheels, it is thought. It is known that Nubians used horse-drawn chariots imported from Egypt; the wheel was used, with the exception of the Horn of Africa, in Sub-Saharan Africa well into the 19th century but this changed with the arrival of the Europeans. Early wheels were simple wooden disks with a hole for the axle; some of the earliest wheels were made from horizontal slices of tree trunks
A mechanical linkage is an assembly of bodies connected to manage forces and movement. The movement of a body, or link, is studied using geometry; the connections between links are modeled as providing ideal movement, pure rotation or sliding for example, are called joints. A linkage modeled as a network of ideal joints is called a kinematic chain. Linkages may be constructed from open chains, closed chains, or a combination of open and closed chains; each link in a chain is connected by a joint to one or more other links. Thus, a kinematic chain can be modeled as a graph in which the links are paths and the joints are vertices, called a linkage graph; the movement of an ideal joint is associated with a subgroup of the group of Euclidean displacements. The number of parameters in the subgroup is called the degrees of freedom of the joint. Mechanical linkages are designed to transform a given input force and movement into a desired output force and movement; the ratio of the output force to the input force is known as the mechanical advantage of the linkage, while the ratio of the input speed to the output speed is known as the speed ratio.
The speed ratio and mechanical advantage are defined so they yield the same number in an ideal linkage. A kinematic chain, in which one link is fixed or stationary, is called a mechanism, a linkage designed to be stationary is called a structure; the simplest linkage is the lever, a link that pivots around a fulcrum attached to ground, or a fixed point. As a force rotates the lever, points far from the fulcrum have a greater velocity than points near the fulcrum; because power into the lever equals the power out, a small force applied at a point far from the fulcrum equals a larger force applied at a point near the fulcrum. The amount the force is amplified is called mechanical advantage; this is the law of the lever. Two levers connected by a rod so that a force applied to one is transmitted to the second is known as a four-bar linkage; the levers are called cranks, the fulcrums are called pivots. The connecting rod is called the coupler; the fourth bar in this assembly is the frame, on which the cranks are mounted.
Linkages are important components of tools. Examples range from the four-bar linkage used to amplify force in a bolt cutter or to provide independent suspension in an automobile, to complex linkage systems in robotic arms and walking machines; the internal combustion engine uses a slider-crank four-bar linkage formed from its piston, connecting rod, crankshaft to transform power from expanding burning gases into rotary power. Simple linkages are used to perform complicated tasks. Interesting examples of linkages include the windshield wiper, the bicycle suspension, hydraulic actuators for heavy equipment. In these examples the components in the linkage move in parallel planes and are called planar linkages. A linkage with at least one link; the skeletons of robotic systems are examples of spatial linkages. The geometric design of these systems relies on modern computer aided design software. Archimedes applied geometry to the study of the lever. Into the 1500s the work of Archimedes and Hero of Alexandria were the primary sources of machine theory.
It was Leonardo da Vinci. In the mid-1700s the steam engine was of growing importance, James Watt realized that efficiency could be increased by using different cylinders for expansion and condensation of the steam; this drove his search for a linkage that could transform rotation of a crank into a linear slide, resulted in his discovery of what is called Watt's linkage. This led to the study of linkages that could generate straight lines if only approximately; the work of Sylvester inspired A. B. Kempe, who showed that linkages for addition and multiplication could be assembled into a system that traced a given algebraic curve. Kempe's design procedure has inspired research at the intersection of computer science. In the late 1800s F. Reuleaux, A. B. W. Kennedy, L. Burmester formalized the analysis and synthesis of linkage systems using descriptive geometry, P. L. Chebyshev introduced analytical techniques for the study and invention of linkages. In the mid-1900s F. Freudenstein and G. N. Sandor used the newly developed digital computer to solve the loop equations of a linkage and determine its dimensions for a desired function, initiating the computer-aided design of linkages.
Within two decades these computer techniques were integral to the analysis of complex machine systems and the control of robot manipulators. R. E. Kaufman combined the computer's ability to compute the roots of polynomial equations with a graphical user interface to unite Freudenstein's techniques with the geometrical methods of Reuleaux and Burmester and form KINSYN, an interactive computer graphics system for linkage design The modern study of linkages includes the analysis and design of articulated systems that appear in robots, machine tools, cable driven and tensegrity systems; these techniques are being applied to biological systems and the study of proteins. The configuration of a system of rigid links connected by ideal joints is defined by a set of configuration parameters, such as the angles around a revolute joint and the slides along prismatic joints measured between adjacent links; the geometric constraints of the linkage allow calculation of all