Learn about Simple machines

The idea that a machine can be decomposed into simple movable elements led Archimedes 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.

Flint hand axe found in Winchester
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.

Know anout Machine mechanical

Machines employ power to achieve desired forces and movement (motion). A machine has a power source and actuators that generate forces and movement, and a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement. Modern machines often include computers and sensors that monitor performance and plan movement, and are called mechanical systems.

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. stated 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.

Linkage (mechanical)

Perhaps the simplest linkage is the lever, which is 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 (with greater velocity) equals a larger force applied at a point near the fulcrum (with less velocity). 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, and the fulcrums are called pivots. The connecting rod is also called the coupler. The fourth bar in this assembly is the ground, or frame, on which the cranks are mounted.

Linkages are important components of machines and 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, and crankshaft to transform power from expanding burning gases into rotary power. Relatively simple linkages are often used to perform complicated tasks.

Interesting examples of linkages include the windshield wiper, the bicycle suspension, and 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 that moves in three-dimensional space is called a "spatial linkage." The skeletons of robotic systems are examples of spatial linkages. The geometric design of these systems relies on modern computer aided design software.


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.[clarification needed] 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%.

A linkage 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 linkage 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 motion.
The success of Watt's linkage lead to the design of similar approximate straight-line linkages, such as Hoeken's linkage and Chebyshev's linkage.
The Peaucellier linkage generates a true straight-line output from a rotary input.
The Sarrus linkage is a spatial linkage that generates straight-line movement from a rotary input.
The Klann linkage and the Jansen linkage are recent inventions that provide interesting walking movements. They are respectively a six-bar and an eight-bar linkage.

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 so the link is considered to be rigid. The connections between links are modeled as providing ideal movement, pure rotation or sliding for example, and are called joints. A linkage modeled as a network of rigid links and 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, which is called a linkage graph.

The deployable mirror linkage is constructed from a series of rhombus or scissor linkages.

An extended scissor lift

The movement of an ideal joint is generally 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 usually 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, and a linkage designed to be stationary is called a structure.

What is Planar Mechanism

A planar mechanism is a mechanical system that is constrained so the trajectories of points in all the bodies of the system lie on planes parallel to a ground plane. The rotational axes of hinged joints that connect the bodies in the system are perpendicular to this ground plane.

Spherical mechanism
A spherical mechanism is a mechanical system in which the bodies move in a way that the trajectories of points in the system lie on concentric spheres. The rotational axes of hinged joints that connect the bodies in the system pass through the center of these spheres.

Spatial mechanism
A spatial mechanism is a mechanical system that has at least one body that moves in a way that its point trajectories are general space curves. The rotational axes of hinged joints that connect the bodies in the system form lines in space that do not intersect and have distinct common normals.


From the time of Archimedes through the Renaissance, mechanisms were considered to be constructed from simple machines, such as the lever, pulley, screw, wheel and axle, wedge and inclined plane. It was Reuleaux who focussed on bodies, called links, and the connections between these bodies called kinematic pairs, or joints.

In order to use geometry to study the movement of a mechanism, its links are modeled as rigid bodies. This means distances between points in a link are assumed to be unchanged as the mechanism moves, that is the link does not flex. Thus, the relative movement between points in two connected links is considered to result from the kinematic pair that joins them.

Kinematic pairs, or joints, are considered to provide ideal constraints between two links, such as the constraint of a single point for pure rotation, or the constraint of a line for pure sliding, as well as pure rolling without slipping and point contact with slipping. A mechanism is modeled as an assembly of rigid links and kinematic pairs.

What is Kinematic pairs

Kinematics is the branch of classical mechanics which describes the motion of points, bodies and systems of bodies without consideration of the causes of motion. Kinematics as a field of study is often referred to as the geometry of motion. For further detail, see Analytical dynamics.

Hartenberg & Denavit presents the definition of a kinematic pair:

In the matter of connections between rigid bodies, Reuleaux recognized two kinds; he called them higher and lower pairs (of elements). With higher pairs, the two elements are in contact at a point or along a line, as in a ball bearing or disk cam and follower; the relative motions of coincident points are dissimilar. Lower pairs are those for which area contact may be visualized, as in pin connections, crossheads, ball-and socket joints and some others; the relative motion of coincident points of the elements, and hence of their links, are similar, and an exchange of elements from one link to the other does not alter the relative motion of the parts as it would with higher pairs.

A kinematic pair is a connection between two bodies that imposes constraints on their relative movement. Franz Reuleaux introduced the kinematic pair as a new approach to the study of machines that provided an advance over the motion of elements consisting of simple machines

A lower pair is an ideal joint that constrains contact between a surface in the moving body to a corresponding surface in the fixed body. A lower pair is one in which there occurs a surface or area contact between two members, e.g. nut and screw, universal joint used to connect two propeller shafts. Cases of lower joints:

A revolute pair, or hinged joint, requires a line in the moving body to remain co-linear with a line in the fixed body, and a plane perpendicular to this line in the moving body maintain contact with a similar perpendicular plane in the fixed body. This imposes five constraints on the relative movement of the links, which therefore has one degree of freedom.
A prismatic joint, or slider, requires that a line in the moving body remain co-linear with a line in the fixed body, and a plane parallel to this line in the moving body maintain contact with a similar parallel plane in the fixed body. This imposes five constraints on the relative movement of the links, which therefore has one degree of freedom.
A screw pair requires cut threads in two links,so that there is a turning as well as sliding motion between them.This joint has one degree of freedom.
A cylindrical joint requires that a line in the moving body remain co-linear with a line in the fixed body. It is a combination of a revolute joint and a sliding joint. This joint has two degrees of freedom.
A ball or spherical joint requires that a point in the moving body maintain contact with a point in the fixed body. This joint has three degrees of freedom.
A planar joint requires that a plane in the moving body maintain contact with a plane in fixed body. This joint has three degrees of freedom.

Know about types of mechanism

From the time of Archimedes through the Renaissance, mechanisms were considered to be constructed from simple machines, such as the lever, pulley, screw, wheel and axle, wedge and inclined plane. It was Reuleaux who focussed on bodies, called links, and the connections between these bodies called kinematic pairs, or joints.

In order to use geometry to study the movement of a mechanism, its links are modeled as rigid bodies. This means distances between points in a link are assumed to be unchanged as the mechanism moves, that is the link does not flex. Thus, the relative movement between points in two connected links is considered to result from the kinematic pair that joins them.

Kinematic pairs, or joints, are considered to provide ideal constraints between two links, such as the constraint of a single point for pure rotation, or the constraint of a line for pure sliding, as well as pure rolling without slipping and point contact with slipping. A mechanism is modeled as an assembly of rigid links and kinematic pairs.

Kinematic pairs:

1.Lower pair
2.Higher pairs

Planar mechanism:
A planar mechanism is a mechanical system that is constrained so the trajectories of points in all the bodies of the system lie on planes parallel to a ground plane. The rotational axes of hinged joints that connect the bodies in the system are perpendicular to this ground plane.

1.Spherical mechanism
2.Spatial mechanism

Getting through Mechanism

An assembly of moving parts performing a complete functional motion, often being part of a large machine; linkage.

From the time of Archimedes through the Renaissance, mechanisms were considered to be constructed from simple machines, such as the lever, pulley, screw, wheel and axle, wedge and inclined plane. It was Reuleaux who focussed on bodies, called links, and the connections between these bodies called kinematic pairs, or joints.

In order to use geometry to study the movement of a mechanism, its links are modeled as rigid bodies. This means distances between points in a link are assumed to be unchanged as the mechanism moves, that is the link does not flex. Thus, the relative movement between points in two connected links is considered to result from the kinematic pair that joins them.

Kinematic pairs, or joints, are considered to provide ideal constraints between two links, such as the constraint of a single point for pure rotation, or the constraint of a line for pure sliding, as well as pure rolling without slipping and point contact with slipping. A mechanism is modeled as an assembly of rigid links and kinematic pairs.

Kinematic pairs:
Reuleaux called the ideal connections between links kinematic pairs. He distinguished between higher pairs which were said to have line contact between the two links and lower pairs that have area contact between the links. J. Phillips shows that there are many ways to construct pairs that do not fit this simple.

Lower pair: A lower pair is an ideal joint that has surface contact between the pair of elements. We have the following cases:

A revolute pair, or hinged joint, requires a line in the moving body to remain co-linear with a line in the fixed body, and a plane perpendicular to this line in the moving body maintain contact with a similar perpendicular plane in the fixed body. This imposes five constraints on the relative movement of the links, which therefore has one degree of freedom.
A prismatic joint, or slider, requires that a line in the moving body remain co-linear with a line in the fixed body, and a plane parallel to this line in the moving body maintain contact with a similar parallel plan in the fixed body. This imposes five constraints on the relative movement of the links, which therefore has one degree of freedom.
A cylindrical joint requires that a line in the moving body remain co-linear with a line in the fixed body. It is a combination of a revolute joint and a sliding joint. This joint has two degrees of freedom.
A spherical joint, or ball joint, requires that a point in the moving body maintain contact with a point in the fixed body. This joint has three degrees of freedom.
A planar joint requires that a plane in the moving body maintain contact with a plane in fixed body. This joint has three degrees of freedom.
A screw joint, or helical joint, has only one degree of freedom because the sliding and rotational motions are related by the helix angle of the thread. Higher pairs: Generally, a higher pair is a constraint that requires a line or point contact between the elemental surfaces. For example, the contact between a cam and its follower is a higher pair called a cam joint. Similarly, the contact between the involute curves that form the meshing teeth of two gears are cam joints.

Planar mechanism
A planar mechanism is a mechanical system that is constrained so the trajectories of points in all the bodies of the system lie on planes parallel to a ground plane. The rotational axes of hinged joints that connect the bodies in the system are perpendicular to this ground plane.

Spherical mechanism
A spherical mechanism is a mechanical system in which the bodies move in a way that the trajectories of points in the system lie on concentric spheres. The rotational axes of hinged joints that connect the bodies in the system pass through the center of these spheres.

Spatial mechanism
A spatial mechanism is a mechanical system that has at least one body that moves in a way that its point trajectories are general space curves. The rotational axes of hinged joints that connect the bodies in the system form lines in space that do not intersect and have distinct common normals.

Gears and gear trains
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:

The ratio of the pitch circles of mating gears defines the speed ratio and the mechanical advantage of the gear set.
A planetary gear train provides high gear reduction in a compact package.
It is possible to design gear teeth for gears that are non-circular, yet still transmit torque smoothly.
The speed ratios of chain and belt drives are computed in the same way as gear ratios. See bicycle gearing.

Cam and follower mechanisms

Cam follower Mechanism- Force is Applied From Follower To Cam
A cam 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. In general a cam follower mechanism's energy is transferred from cam to follower. The cam shaft is rotated and, according to the cam profile, the follower moves up and down. Now slightly different types of eccentric cam followers are also available in which energy is transferred from the follower to the cam. The main benefit of this type of cam follower mechanism is that the follower moves a little bit and helps to rotate the cam 6 times more circumference length with 70% force.