Machine (mechanical)
Encyclopedia
The mechanical properties of a machine manage power to achieve desired forces and movement. Modern machines often include computers and sensors that monitor performance and plan movement, and are called mechanical system
s.
The meaning of the word "machine" is traced by the Oxford English Dictionary to an independently functioning structure and by Merriam-Webster Dictionary to something that has been constructed. This includes human design into the meaning of machine.
The adjective "mechanical" refers to skill in the practical application of an art or science, as well as relating to or caused by movement, physical forces, properties or agents such as is dealt with by mechanics
. Similarly Merriam-Webster Dictionary defines "mechanical" as relating to machinery or tools.
Power flow through a machine provides a way to understand the performance of devices ranging from levers and gear trains to automobiles and robotic systems. The German mechanician
Franz Reuleaux
wrote "a machine is a combination of resistant bodies so arranged that by their means the mechanical forces of nature can be compelled to do work accompanied by certain determinate motion." Notice that forces and motion combine to define power
.
More recently, Uicker et al. state that a machine is "a device for applying power or changing its direction." And McCarthy and Soh describe a machine as a system that "generally consists of a power source and a mechanism
for the controlled use of this power."
to define the lever
, pulley
and screw
as simple machines
. By the time of the Renaissance this list increased to include the wheel and axle
, wedge
and inclined plane
. The modern approach to characterizing machines focusses on the components that allow movement, known as joints.
Wedge (hand axe): Perhaps the first example of a device designed to manage power is the hand axe
, also see biface
and Olorgesailie
. A hand axe is made by chipping stone, generally flint, to form a bifacial edge, or wedge. A wedge is a simple machine that transforms lateral force and movement of the tool into a transverse splitting force and movement of the workpiece. The available power is limited by the effort of the person using the tool, but because power is the product of force and movement, the wedge amplifies the force by reducing the movement. This amplification, or mechanical advantage
is the ratio of the input speed to output speed. For a wedge this is given by 1/tanα, where α is the tip angle. The faces of a wedge are modeled as straight lines to form a sliding or prismatic joint
.
Lever: The lever
is another important and simple device for managing power. This is a body that pivots on a fulcrum. Because the velocity of a point farther from the pivot is greater than the velocity of a point near the pivot, forces applied far from the pivot are amplified near the pivot by the associated decrease in speed. If a is the distance from the pivot to the point where the input force is applied and b is the distance to the point where the output force is applied, then a/b is the mechanical advantage
of the lever. The fulcrum of a lever is modeled as a hinged or revolute joint
.
Wheel: The wheel
is clearly an important early machine, such as the chariot
. A wheel uses the law of the lever to reduce the force needed to overcome friction
when pulling a load. To see this notice that the friction associated with pulling a load on the ground is approximately the same as the friction in a simple bearing that supports the load on the axle of a wheel. However, the wheel forms a lever that magnifies the pulling force so that it overcomes the frictional resistance in the bearing.
s that generate the output forces and movement, and an interface to the user. Electric motor
s, hydraulic
and pneumatic
actuators provide the input forces and movement. This input is shaped by mechanisms consisting of gears and gear trains, belt and chain drives, cam and follower mechanisms, and linkages as well as friction devices such as brakes and clutches. Structural components consist of the frame, fasteners, bearings, springs, lubricants and seals, as well as a variety of specialized machine element
s such as splines, pins and keys. The user interface ranges from switches and buttons to programmable logic controllers and includes the covers that provide texture, color and styling
.
The transmission of rotation between contacting toothed wheels can be traced back to the Antikythera mechanism
of Greece and the South Pointing Chariot
of China. Illustrations by the renaissance scientist Georgius Agricola show gear trains with cylindrical teeth. The implementation of the involute tooth
yielded a standard gear design that provides a constant speed ratio. Some important features of gears and gear trains are:
and follower
is formed by the direct contact of two specially shaped links. The driving link is called the cam (also see cam shaft
) and the link that is driven through the direct contact of their surfaces is called the follower. The shape of the contacting surfaces of the cam
and follower
determines the movement of the mechanism.
is a collection of links connected by joints. Generally, the links are the structural elements and the joints allow movement. Perhaps the single most useful example is the planar four-bar linkage. However, there are many more special linkages:
treatise on Mechanics focussed on the study of lifting heavy weights. Today mechanics
refers to the mathematical analysis of the forces and movement of a mechanical system, and consists of the study of the kinematics
and dynamics
of these systems.
applies geometry to the analysis of movement in a mechanical system. The rotation and sliding movement central to mechanical systems are modeled mathematically as Euclidean, or rigid, transformations
. The set of rigid transformations in three dimensional space forms a Lie group
, denoted as SE(3).
Planar mechanisms: While all mechanisms in a mechanical system are three dimensional, they can be analyzed using plane geometry
, if the movement of the individual components are constrained so all point trajectories are parallel to a plane. In this case the system is called a planar mechanism. The kinematic analysis of planar mechanisms uses the subset of SE(3) consisting of planar rotations and translations, denote SE(2).
The group SE(2) is three dimensional, which means that every position of a body in the plane is defined by three parameters. The parameters are often the x and y coordinates of the origin of a coordinate frame in M measured from the origin of a coordinate frame in F, and the angle measured from the x-axis in F to the x-axis in M. This is often described saying a body in the plane has three degrees-of-freedom.
The pure rotation of a hinge and the linear translation of a slider can be identified with subgroups of SE(2), and define the two joints one degree-of-freedom joints of planar mechanisms. The cam joint formed by two surfaces in sliding and rotating contact is a two degree-of-freedom joint.
Select this link to see Theo Jansen's Strandbeest walking machine with legs constructed from planar eight-bar linkages
Spherical mechanisms: It is possible to construct a mechanism such that the point trajectories in all components lie in concentric spherical shells around a fixed point. An example is the gimbal
ed gyroscope
. These devices are called spherical mechanisms. Spherical mechanisms are constructed by connecting links with hinged joints such that the axes of each hinge passes through the same point. This point becomes center of the concentric spherical shells. The movement of these mechanisms is characterized by the group SO(3) of rotations in three dimensional space. Other examples of spherical mechanisms are the automotive differential and the robotic wrist.
Select this link for an animation of a Spherical deployable mechanism.
The rotation group SO(3)
is three dimensional. An example of the three parameters that specify a spatial rotation are the roll, pitch and yaw angles
used to define the orientation of an aircraft.
Spatial mechanisms: A mechanism in which a body moves through a general spatial movement is called a spatial mechanism. An example is the RSSR linkage, which can be viewed as a four-bar linkage in which the hinged joints of the coupler link are replaced by rod ends
, also called spherical joints or ball joint
s. The rod ends allow the input and output cranks of the RSSR linkage to be misaligned to the point that they lie in different planes, which causes the coupler link to move in a general spatial movement. Robot arms
, Stewart platform
s, and humanoid robotic systems
are also examples of spatial mechanisms.
Select this link for an animation of Bennett's linkage, which is a spatial mechanism constructed from four hinged joints.
The group SE(3)
is six dimensional, which means the position of a body in space is defined by six parameters. Three of the parameters define the origin of the moving reference frame relative to the fixed frame. Three other parameters define the orientation of the moving frame relative to the fixed frame.
Mechanical system
A mechanical system manages power to accomplish a task that involves forces and movement. Mechanical is derived from the Latin word machina, which in turn derives from the Doric Greek μαχανά , Ionic Greek μηχανή "contrivance, machine, engine" and that from μῆχος , "means, expedient, remedy".The...
s.
The meaning of the word "machine" is traced by the Oxford English Dictionary to an independently functioning structure and by Merriam-Webster Dictionary to something that has been constructed. This includes human design into the meaning of machine.
The adjective "mechanical" refers to skill in the practical application of an art or science, as well as relating to or caused by movement, physical forces, properties or agents such as is dealt with by mechanics
Mechanics
Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....
. Similarly Merriam-Webster Dictionary defines "mechanical" as relating to machinery or tools.
Power flow through a machine provides a way to understand the performance of devices ranging from levers and gear trains to automobiles and robotic systems. The German mechanician
Mechanician
A mechanician is an engineer or a scientist working in the field of mechanics, or in a related or sub-field: engineering or computational mechanics, applied mechanics, geomechanics, biomechanics, and mechanics of materials...
Franz Reuleaux
Franz Reuleaux
Franz Reuleaux , was a mechanical engineer and a lecturer of the Berlin Royal Technical Academy, later appointed as the President of the Academy. He was often called the father of kinematics...
wrote "a machine is a combination of resistant bodies so arranged that by their means the mechanical forces of nature can be compelled to do work accompanied by certain determinate motion." Notice that forces and motion combine to define power
Power (physics)
In physics, power is the rate at which energy is transferred, used, or transformed. For example, the rate at which a light bulb transforms electrical energy into heat and light is measured in watts—the more wattage, the more power, or equivalently the more electrical energy is used per unit...
.
More recently, Uicker et al. state that a machine is "a device for applying power or changing its direction." And McCarthy and Soh describe a machine as a system that "generally consists of a power source and a mechanism
Mechanism (engineering)
A mechanism is a device designed to transform input forces and movement into a desired set of output forces and movement. Mechanisms generally consist of moving components such as gears and gear trains, belt and chain drives, cam and follower mechanisms, and linkages as well as friction devices...
for the controlled use of this power."
Simple machines
The idea that a machine can be decomposed into simple movable elements led ArchimedesArchimedes
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...
to define the lever
Lever
In physics, a lever is a rigid object that is used with an appropriate fulcrum or pivot point to either multiply the mechanical force that can be applied to another object or resistance force , or multiply the distance and speed at which the opposite end of the rigid object travels.This leverage...
, pulley
Pulley
A pulley, also called a sheave or a drum, is a mechanism composed of a wheel on an axle or shaft that may have a groove between two flanges around its circumference. A rope, cable, belt, or chain usually runs over the wheel and inside the groove, if present...
and screw
Screw
A screw, or bolt, is a type of fastener characterized by a helical ridge, known as an external thread or just thread, wrapped around a cylinder. Some screw threads are designed to mate with a complementary thread, known as an internal thread, often in the form of a nut or an object that has the...
as simple machines
Simple Machines
Simple Machines was a record label that operated out of Arlington, Virginia. The label was masterminded by Jenny Toomey and Kristin Thomson and, at its peak, had four paid workers- Toomey, Thomson, Pat Graham and Mickey Menard...
. By the time of the Renaissance this list increased to include the wheel and axle
Wheel and axle
The wheel and axle is one of six simple machines developed in ancient times and is in the category of a second- or third-class lever. In its simplest form it consists of a rod attached to a wheel so that their movements are coupled when one of the parts is turned...
, wedge
Wedge
Wedge may refer to:Mathematics:* Triangular prism, a parallel triangle wedge* Wedge , a polyhedral solid defined by two triangles and three trapezoid faces* Wedge product, a mathematical term, named for the ∧ operator symbol used...
and inclined plane
Inclined plane
The inclined plane is one of the original six simple machines; as the name suggests, it is a flat surface whose endpoints are at different heights. By moving an object up an inclined plane rather than completely vertical, the amount of force required is reduced, at the expense of increasing the...
. The modern approach to characterizing machines focusses on the components that allow movement, known as joints.
Wedge (hand axe): Perhaps the first example of a device designed to manage power is the hand axe
Hand axe
A hand axe is a bifacial Stone tool typical of the lower and middle Palaeolithic , and is the longest-used tool of human history.-Distribution:...
, also see biface
Biface
In archaeology, a biface is a two-sided stone tool and is used as a multi purposes knife, manufactured through a process of lithic reduction, that displays flake scars on both sides. A profile view of the final product tends to exhibit a lenticular shape...
and Olorgesailie
Olorgesailie
Olorgesailie is a geological formation in East Africa containing a group of Lower Paleolithic archaeological sites. It is on the floor of the Eastern Rift Valley in southern Kenya, southwest of Nairobi along the road to Lake Magadi. Olorgesailie is noted for the large number of Acheulean hand...
. A hand axe is made by chipping stone, generally flint, to form a bifacial edge, or wedge. A wedge is a simple machine that transforms lateral force and movement of the tool into a transverse splitting force and movement of the workpiece. The available power is limited by the effort of the person using the tool, but because power is the product of force and movement, the wedge amplifies the force by reducing the movement. This amplification, or mechanical advantage
Mechanical advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...
is the ratio of the input speed to output speed. For a wedge this is given by 1/tanα, where α is the tip angle. The faces of a wedge are modeled as straight lines to form a sliding or prismatic joint
Prismatic joint
A prismatic joint provides a linear sliding movement between two bodies, and is often called a slider, as in the slider-crank linkage. A prismatic joint is formed with a polygonal cross-section to resist rotation...
.
Lever: The lever
Lever
In physics, a lever is a rigid object that is used with an appropriate fulcrum or pivot point to either multiply the mechanical force that can be applied to another object or resistance force , or multiply the distance and speed at which the opposite end of the rigid object travels.This leverage...
is another important and simple device for managing power. This is a body that pivots on a fulcrum. Because the velocity of a point farther from the pivot is greater than the velocity of a point near the pivot, forces applied far from the pivot are amplified near the pivot by the associated decrease in speed. If a is the distance from the pivot to the point where the input force is applied and b is the distance to the point where the output force is applied, then a/b is the mechanical advantage
Mechanical advantage
Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...
of the lever. The fulcrum of a lever is modeled as a hinged or revolute joint
Revolute joint
A revolute joint is a one degree of freedom kinematic pair used in mechanisms. Revolute joints provide single-axis rotation function used in many places such as door hinges, folding mechanisms, and other uni-axial rotation devices. -See also:* Cylindrical joint* Kinematics* Degrees of freedom *...
.
Wheel: The wheel
Wheel
A wheel is a device that allows heavy objects to be moved easily through rotating on an axle through its center, facilitating movement or transportation while supporting a load, or performing labor in machines. Common examples found in transport applications. A wheel, together with an axle,...
is clearly an important early machine, such as the chariot
Chariot
The chariot is a type of horse carriage used in both peace and war as the chief vehicle of many ancient peoples. Ox carts, proto-chariots, were built by the Proto-Indo-Europeans and also built in Mesopotamia as early as 3000 BC. The original horse chariot was a fast, light, open, two wheeled...
. A wheel uses the law of the lever to reduce the force needed to overcome friction
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...
when pulling a load. To see this notice that the friction associated with pulling a load on the ground is approximately the same as the friction in a simple bearing that supports the load on the axle of a wheel. However, the wheel forms a lever that magnifies the pulling force so that it overcomes the frictional resistance in the bearing.
Mechanisms
A machine consists of an actuator input, a system of mechanismMechanism (engineering)
A mechanism is a device designed to transform input forces and movement into a desired set of output forces and movement. Mechanisms generally consist of moving components such as gears and gear trains, belt and chain drives, cam and follower mechanisms, and linkages as well as friction devices...
s that generate the output forces and movement, and an interface to the user. Electric motor
Electric motor
An electric motor converts electrical energy into mechanical energy.Most electric motors operate through the interaction of magnetic fields and current-carrying conductors to generate force...
s, hydraulic
Hydraulic cylinder
A Hydraulic cylinder is a mechanical actuator that is used to give a unidirectional force through a unidirectional stroke. It has many applications, notably in engineering vehicles.- Operation :...
and pneumatic
Pneumatic cylinder
Pneumatic cylinders are mechanical devices which utilize the power of compressed gas to produce a force in a reciprocating linear motion....
actuators provide the input forces and movement. This input is shaped by mechanisms consisting of gears and gear trains, belt and chain drives, cam and follower mechanisms, and linkages as well as friction devices such as brakes and clutches. Structural components consist of the frame, fasteners, bearings, springs, lubricants and seals, as well as a variety of specialized machine element
Machine element
Machine elements are basic mechanical parts used as the building blocks of most machines. Most are standardized to common sizes, but customs are also common for specialized applications.-Types:*Shafts**Couplings*Keys*Splines*Bearings**Roller bearings...
s such as splines, pins and keys. The user interface ranges from switches and buttons to programmable logic controllers and includes the covers that provide texture, color and styling
Industrial design
Industrial design is the use of a combination of applied art and applied science to improve the aesthetics, ergonomics, and usability of a product, but it may also be used to improve the product's marketability and production...
.
Gears and gear trains
Antikythera mechanism
The Antikythera mechanism is an ancient mechanical computer designed to calculate astronomical positions. It was recovered in 1900–1901 from the Antikythera wreck. Its significance and complexity were not understood until decades later. Its time of construction is now estimated between 150 and 100...
of Greece and the South Pointing Chariot
South Pointing Chariot
The south-pointing chariot was an ancient Chinese two-wheeled vehicle that carried a movable pointer to indicate the south, no matter how the chariot turned. Usually, the pointer took the form of a doll or figure with an outstretched arm...
of China. Illustrations by the renaissance scientist Georgius Agricola show gear trains with cylindrical teeth. The implementation of the involute tooth
Involute gear
The involute gear profile is the most commonly used system for gearing today. In an involute gear, the profiles of the teeth are involutes of a circle. In involute gear design contact between a pair of gear teeth occurs...
yielded a standard gear design that provides a constant speed ratio. Some important features of gears and gear trains are:
- The ratio of the pitch circles of mating gears defines the speed ratioGear ratioThe gear ratio of a gear train is the ratio of the angular velocity of the input gear to the angular velocity of the output gear, also known as the speed ratio of the gear train. The gear ratio can be computed directly from the numbers of teeth of the various gears that engage to form the gear...
and the mechanical advantageMechanical advantageMechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...
of the gear set. - A planetary gear trainEpicyclic gearingEpicyclic gearing or planetary gearing is a gear system consisting of one or more outer gears, or planet gears, revolving about a central, or sun gear. Typically, the planet gears are mounted on a movable arm or carrier which itself may rotate relative to the sun gear...
provides high gear reduction in a compact package. - It is possible to design gear teeth for gears that are non-circularNon-circular gearA non-circular gear is a special gear design with special characteristics and purpose. While a regular gear is optimized to transmit torque to another engaged member with minimum noise and wear and with maximum efficiency, a non-circular gear's main objective might be ratio variations, axle...
, yet still transmit torque smoothly. - The speed ratios of chainChain driveChain drive is a way of transmitting mechanical power from one place to another. It is often used to convey power to the wheels of a vehicle, particularly bicycles and motorcycles...
and belt drivesBelt (mechanical)A belt is a loop of flexible material used to link two or more rotating shafts mechanically. Belts may be used as a source of motion, to transmit power efficiently, or to track relative movement. Belts are looped over pulleys. In a two pulley system, the belt can either drive the pulleys in the...
are computed in the same way as gear ratios. See bicycle gearingBicycle gearingA bicycle gear or gear ratio refers to the rate at which the rider's legs turn compared to the rate at which the wheels turn. Bicycle gearing refers to how the gear ratio is set or changed. On some bicycles, there is only one gear so the ratio is fixed. Most modern bicycles have multiple gears,...
.
Cam and follower mechanisms
A camCam
A cam is a rotating or sliding piece in a mechanical linkage used especially in transforming rotary motion into linear motion or vice-versa. It is often a part of a rotating wheel or shaft that strikes a lever at one or more points on its circular path...
and follower
Cam follower
A cam follower, also known as a track follower, is a specialized type of roller or needle bearing designed to follow cams. Cam followers come in a vast array of different configurations, however the most defining characteristic is how the cam follower mounts to its mating part; stud style cam...
is formed by the direct contact of two specially shaped links. The driving link is called the cam (also see cam shaft
Camshaft
A camshaft is a shaft to which a cam is fastened or of which a cam forms an integral part.-History:An early cam was built into Hellenistic water-driven automata from the 3rd century BC. The camshaft was later described in Iraq by Al-Jazari in 1206. He employed it as part of his automata,...
) and the link that is driven through the direct contact of their surfaces is called the follower. The shape of the contacting surfaces of the cam
Cam
A cam is a rotating or sliding piece in a mechanical linkage used especially in transforming rotary motion into linear motion or vice-versa. It is often a part of a rotating wheel or shaft that strikes a lever at one or more points on its circular path...
and follower
Cam follower
A cam follower, also known as a track follower, is a specialized type of roller or needle bearing designed to follow cams. Cam followers come in a vast array of different configurations, however the most defining characteristic is how the cam follower mounts to its mating part; stud style cam...
determines the movement of the mechanism.
Linkages
A linkageLinkage (mechanical)
A mechanical linkage is an assembly of bodies connected together to manage forces and movement. The movement of a body, or link, is studied using geometry so the link is considered to be rigid. The connections between links are modeled as providing ideal movement, pure rotation or sliding for...
is a collection of links connected by joints. Generally, the links are the structural elements and the joints allow movement. Perhaps the single most useful example is the planar four-bar linkage. However, there are many more special linkages:
- Watt's linkageWatt's linkageWatt's linkage is a type of mechanical linkage invented by James Watt in which the central moving point of the linkage is constrained to travel on an approximation to a straight line...
is a four-bar linkage that generates an approximate straight line. It was critical to the operation of his design for the steam engine. This linkage also appears in vehicle suspensions to prevent side-to-side movement of the body relative to the wheels. Also see the article Parallel motionParallel motionThe parallel motion is a mechanical linkage invented by the Scottish engineer James Watt in 1784 for his double-acting steam engine.In previous engines built by Newcomen and Watt, the piston pulled one end of the walking beam downwards during the power stroke using a chain, and the weight of the...
. - The success of Watt's linkage lead to the design of similar approximate straight-line linkages, such as Hoeken's linkage and Chebyshev's linkageChebyshev linkageThe Hoekens linkage is a four-bar mechanism that converts rotational motion to approximate straight-line motion. The Hoekens linkage is a cognate linkage of the Chebyshev linkage.-See also:*Straight line mechanism*Peaucellier–Lipkin linkage...
. - The Peaucellier linkagePeaucellier-Lipkin linkageThe Peaucellier–Lipkin linkage , invented in 1864, was the first planar linkage capable of transforming rotary motion into perfect straight-line motion, and vice versa...
generates a true straight-line output from a rotary input. - The Sarrus linkageSarrus linkageThe Sarrus linkage, invented in 1853 by Pierre Frédéric Sarrus, is a mechanical linkage to convert a limited circular motion to a linear motion without reference guideways. The linkage uses two perpendicular hinged rectangular plates positioned parallel over each other...
is a spatial linkage that generates straight-line movement from a rotary input. Select this link for an animation of the Sarrus linkage - The Klann linkageKlann LinkageThe Klann linkage is a planar mechanism designed to simulate the gait of legged animal and function as a wheel replacement. The linkage consists of the frame, a crank, two grounded rockers, and two couplers all connected by pivot joints....
and the Jansen linkageTheo JansenTheo Jansen is a Dutch artist and kinetic sculptor. He builds large works which resemble skeletons of animals, that are able to walk using wind power on the beaches of the Netherlands...
are recent inventions that provide interesting walking movements. They are respectively a six-bar and an eight-bar linkage.
Flexure mechanisms
A flexure mechanism consisted of a series of rigid bodies connected by compliant elements (also known as flexure joints) that is designed to produce a geometrically well-defined motion upon application of a force.Structural components
A number of machine elements provide important structural functions such as the frame, bearings, splines, spring and seals.- The recognition that the frame of a mechanism is an important machine element changed the name three-bar linkage into four-bar linkage. Frames are generally assembled from trussTrussIn architecture and structural engineering, a truss is a structure comprising one or more triangular units constructed with straight members whose ends are connected at joints referred to as nodes. External forces and reactions to those forces are considered to act only at the nodes and result in...
or beamBeam (structure)A beam is a horizontal structural element that is capable of withstanding load primarily by resisting bending. The bending force induced into the material of the beam as a result of the external loads, own weight, span and external reactions to these loads is called a bending moment.- Overview...
elements. - BearingsBearing (mechanical)A bearing is a device to allow constrained relative motion between two or more parts, typically rotation or linear movement. Bearings may be classified broadly according to the motions they allow and according to their principle of operation as well as by the directions of applied loads they can...
are components designed to manage the interface between moving elements and are the source of frictionFrictionFriction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...
in machines. In general, bearings are designed for pure rotation or straight line movement. - Splines and keys are two ways to reliably mount an axleAxleAn axle is a central shaft for a rotating wheel or gear. On wheeled vehicles, the axle may be fixed to the wheels, rotating with them, or fixed to its surroundings, with the wheels rotating around the axle. In the former case, bearings or bushings are provided at the mounting points where the axle...
to a wheel, pulley or gear so that torque can be transferred through the connection. - SpringSpring (device)A spring is an elastic object used to store mechanical energy. Springs are usually made out of spring steel. Small springs can be wound from pre-hardened stock, while larger ones are made from annealed steel and hardened after fabrication...
s provides forces that can either hold components of a machine in place or acts as a suspensionSuspension (vehicle)Suspension is the term given to the system of springs, shock absorbers and linkages that connects a vehicle to its wheels. Suspension systems serve a dual purpose — contributing to the car's roadholding/handling and braking for good active safety and driving pleasure, and keeping vehicle occupants...
to support part of a machine. - SealsSeal (mechanical)A mechanical seal is a device which helps join systems or mechanisms together by preventing leakage , containing pressure, or excluding contamination...
are used between mating parts of a machine to ensure fluids, such as water, hot gases, or lubricant do not leak between the mating surfaces. - FastenerFastenerA fastener is a hardware device that mechanically joins or affixes two or more objects together.Fasteners can also be used to close a container such as a bag, a box, or an envelope; or they may involve keeping together the sides of an opening of flexible material, attaching a lid to a container,...
s such as screwScrewA screw, or bolt, is a type of fastener characterized by a helical ridge, known as an external thread or just thread, wrapped around a cylinder. Some screw threads are designed to mate with a complementary thread, known as an internal thread, often in the form of a nut or an object that has the...
s, bolts, spring clips, and rivetRivetA rivet is a permanent mechanical fastener. Before being installed a rivet consists of a smooth cylindrical shaft with a head on one end. The end opposite the head is called the buck-tail. On installation the rivet is placed in a punched or pre-drilled hole, and the tail is upset, or bucked A rivet...
s are critical to the assembly of components of a machine. Fasteners are generally considered to be removable. In contrast, joining methods, such as weldingWeldingWelding is a fabrication or sculptural process that joins materials, usually metals or thermoplastics, by causing coalescence. This is often done by melting the workpieces and adding a filler material to form a pool of molten material that cools to become a strong joint, with pressure sometimes...
, solderingSolderingSoldering is a process in which two or more metal items are joined together by melting and flowing a filler metal into the joint, the filler metal having a lower melting point than the workpiece...
, crimpingCrimp (joining)Crimping is joining two pieces of metal or other malleable material by deforming one or both of them to hold the other. The bend or deformity is called the crimp.- Uses :...
and the application of adhesiveAdhesiveAn adhesive, or glue, is a mixture in a liquid or semi-liquid state that adheres or bonds items together. Adhesives may come from either natural or synthetic sources. The types of materials that can be bonded are vast but they are especially useful for bonding thin materials...
s, usually require cutting the parts to disassemble the components
Mechanics
Usher reports that Hero of Alexandria'sHero of Alexandria
Hero of Alexandria was an ancient Greek mathematician and engineerEnc. Britannica 2007, "Heron of Alexandria" who was active in his native city of Alexandria, Roman Egypt...
treatise on Mechanics focussed on the study of lifting heavy weights. Today mechanics
Mechanics
Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....
refers to the mathematical analysis of the forces and movement of a mechanical system, and consists of the study of the kinematics
Kinematics
Kinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
and dynamics
Analytical dynamics
In classical mechanics, analytical dynamics, or more briefly dynamics, is concerned about the relationship between motion of bodies and its causes, namely the forces acting on the bodies and the properties of the bodies...
of these systems.
Kinematics of Mechanisms
KinematicsKinematics
Kinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
applies geometry to the analysis of movement in a mechanical system. The rotation and sliding movement central to mechanical systems are modeled mathematically as Euclidean, or rigid, transformations
Rigid transformation
In mathematics, a rigid transformation or a Euclidean transformation is a transformation from a Euclidean space to itself that preserves distances between every pair of points...
. The set of rigid transformations in three dimensional space forms a Lie group
Lie group
In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
, denoted as SE(3).
Planar mechanisms: While all mechanisms in a mechanical system are three dimensional, they can be analyzed using plane geometry
Plane geometry
In mathematics, plane geometry may refer to:*Euclidean plane geometry, the geometry of plane figures,*geometry of a plane,or sometimes:*geometry of a projective plane, most commonly the real projective plane but possibly the complex projective plane, Fano plane or others;*geometry of the hyperbolic...
, if the movement of the individual components are constrained so all point trajectories are parallel to a plane. In this case the system is called a planar mechanism. The kinematic analysis of planar mechanisms uses the subset of SE(3) consisting of planar rotations and translations, denote SE(2).
The group SE(2) is three dimensional, which means that every position of a body in the plane is defined by three parameters. The parameters are often the x and y coordinates of the origin of a coordinate frame in M measured from the origin of a coordinate frame in F, and the angle measured from the x-axis in F to the x-axis in M. This is often described saying a body in the plane has three degrees-of-freedom.
The pure rotation of a hinge and the linear translation of a slider can be identified with subgroups of SE(2), and define the two joints one degree-of-freedom joints of planar mechanisms. The cam joint formed by two surfaces in sliding and rotating contact is a two degree-of-freedom joint.
Select this link to see Theo Jansen's Strandbeest walking machine with legs constructed from planar eight-bar linkages
Spherical mechanisms: It is possible to construct a mechanism such that the point trajectories in all components lie in concentric spherical shells around a fixed point. An example is the gimbal
Gimbal
A gimbal is a pivoted support that allows the rotation of an object about a single axis. A set of two gimbals, one mounted on the other with pivot axes orthogonal, may be used to allow an object mounted on the innermost gimbal to remain immobile regardless of the motion of its support...
ed gyroscope
Gyroscope
A gyroscope is a device for measuring or maintaining orientation, based on the principles of angular momentum. In essence, a mechanical gyroscope is a spinning wheel or disk whose axle is free to take any orientation...
. These devices are called spherical mechanisms. Spherical mechanisms are constructed by connecting links with hinged joints such that the axes of each hinge passes through the same point. This point becomes center of the concentric spherical shells. The movement of these mechanisms is characterized by the group SO(3) of rotations in three dimensional space. Other examples of spherical mechanisms are the automotive differential and the robotic wrist.
Select this link for an animation of a Spherical deployable mechanism.
The rotation group SO(3)
Rotation group
In mechanics and geometry, the rotation group is the group of all rotations about the origin of three-dimensional Euclidean space R3 under the operation of composition. By definition, a rotation about the origin is a linear transformation that preserves length of vectors and preserves orientation ...
is three dimensional. An example of the three parameters that specify a spatial rotation are the roll, pitch and yaw angles
Euler angles
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body. To describe such an orientation in 3-dimensional Euclidean space three parameters are required...
used to define the orientation of an aircraft.
Spatial mechanisms: A mechanism in which a body moves through a general spatial movement is called a spatial mechanism. An example is the RSSR linkage, which can be viewed as a four-bar linkage in which the hinged joints of the coupler link are replaced by rod ends
Rod end bearing
A rod end bearing, also known as a heim joint or rose joint , is a mechanical articulating joint. Such joints are used on the ends of control rods, steering links, tie rods, or anywhere a precision articulating joint is required...
, also called spherical joints or ball joint
Ball joint
In an automobile, ball joints are spherical bearings that connect the control arms to the steering knuckles.More specifically, a ball joint is a steel bearing stud and socket enclosed in a steel casing. The bearing stud is tapered and threaded. It fits into a tapered hole in the steering knuckle. A...
s. The rod ends allow the input and output cranks of the RSSR linkage to be misaligned to the point that they lie in different planes, which causes the coupler link to move in a general spatial movement. Robot arms
Robotic arm
A mechanical arm is a robotic, usually programmable, with similar functions to a human arm. The links of such a manipulator are connected by joints allowing either rotational motion or translational displacement. The links of the manipulator can be considered to form a kinematic chain...
, Stewart platform
Stewart platform
A Stewart platform is a type of parallel robot that incorporates six prismatic actuators, commonly hydraulic jacks. These actuators are mounted in pairs to the mechanism's base, crossing over to three mounting points on a top plate. Devices placed on the top plate can be moved in the six degrees...
s, and humanoid robotic systems
Humanoid robot
A humanoid robot or an anthropomorphic robot is a robot with its overall appearance, based on that of the human body, allowing interaction with made-for-human tools or environments. In general humanoid robots have a torso with a head, two arms and two legs, although some forms of humanoid robots...
are also examples of spatial mechanisms.
Select this link for an animation of Bennett's linkage, which is a spatial mechanism constructed from four hinged joints.
The group SE(3)
Euclidean group
In mathematics, the Euclidean group E, sometimes called ISO or similar, is the symmetry group of n-dimensional Euclidean space...
is six dimensional, which means the position of a body in space is defined by six parameters. Three of the parameters define the origin of the moving reference frame relative to the fixed frame. Three other parameters define the orientation of the moving frame relative to the fixed frame.