Mechanism (engineering)

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Schematic of the actuator mechanism for an aircraft landing gear Landing gear schematic.svg
Schematic of the actuator mechanism for an aircraft landing gear

In engineering, a mechanism is a device that transforms input forces and movement into a desired set of output forces and movement. Mechanisms generally consist of moving components which may include:

Contents

The German scientist Franz Reuleaux defines machine as "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". In this context, his use of machine is generally interpreted to mean mechanism.

The combination of force and movement defines power, and a mechanism manages power to achieve a desired set of forces and movement.

A mechanism is usually a piece of a larger process, known as a mechanical system or machine. Sometimes an entire machine may be referred to as a mechanism; examples are the steering mechanism in a car, or the winding mechanism of a wristwatch. However, typically, a set of multiple mechanisms is called a machine.

Kinematic pairs

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

To use geometry to study the movement of a mechanism, its links are modelled as rigid bodies. This means that distances between points in a link are assumed to not change 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 modelled as an assembly of rigid links and kinematic pairs.

Revolute pair cutaway view Revolute Pin Joint.png
Revolute pair cutaway view

Reuleaux called the ideal connections between links kinematic pairs. He distinguished between higher pairs, with line contact between the two links, and lower pairs, with area contact between the links. J. Phillips[ clarification needed ] shows that there are many ways to construct pairs that do not fit this simple model.

Lower pair: A lower pair is an ideal joint that has surface contact between the pair of elements, as in the following cases:

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.

Kinematic diagram

Dimensioned drawing of a slider-crank (left) and its kinematic diagram (right) Piston bielle vilebrequin coupe et schema cinematique.svg
Dimensioned drawing of a slider-crank (left) and its kinematic diagram (right)

A kinematic diagram reduces machine components to a skeleton diagram that emphasises the joints and reduces the links to simple geometric elements. This diagram can also be formulated as a graph by representing the links of the mechanism as edges and the joints as vertices of the graph. This version of the kinematic diagram has proven effective in enumerating kinematic structures in the process of machine design. [1]

An important consideration in this design process is the degree of freedom of the system of links and joints, which is determined using the Chebychev–Grübler–Kutzbach criterion.

Planar mechanisms

Theo Jansen's Strandbeest, a group of planar walking mechanisms Strandbeest-Animation-rgb-100ms.gif
Theo Jansen's Strandbeest, a group of planar walking mechanisms

While all mechanisms in a mechanical system are three-dimensional, they can be analysed using plane geometry if the movement of the individual components is constrained so that all point trajectories are parallel or in a series connection to a plane. In this case the system is called a planar mechanism. The kinematic analysis of planar mechanisms uses the subset of Special Euclidean group SE, consisting of planar rotations and translations, denoted by SE.

The group SE 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, and define the two joints one degree-of-freedom joints of planar mechanisms.[ incomprehensible ] The cam joint formed by two surfaces in sliding and rotating contact is a two degree-of-freedom joint.

Spherical mechanisms

An example of a spherical deployable mechanism Spherical Deployable Mechanism.gif
An example of a spherical deployable mechanism

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 gimbaled gyroscope. These devices are called spherical mechanisms. [2] Spherical mechanisms are constructed by connecting links with hinged joints such that the axes of each hinge pass through the same point. This point becomes centre of the concentric spherical shells. The movement of these mechanisms is characterised by the group SO(3) of rotations in three-dimensional space. Other examples of spherical mechanisms are the automotive differential and the robotic wrist.

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

An example of a Stewart Platform, a spatial mechanism Hexapod general Anim.gif
An example of a Stewart Platform, a spatial mechanism

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 joints. The rod ends let the input and output cranks of the RSSR linkage 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 platforms, and humanoid robotic systems are also examples of spatial mechanisms.

Bennett's linkage is an example of a spatial overconstrained mechanism, which is 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.

Linkages

Theo Jansen's kinetic sculpture Strandbeest, a wind-driven walking machine Jansen-Strandbeest crop.jpg
Theo Jansen's kinetic sculpture Strandbeest, a wind-driven walking machine

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. There are, however, many more special linkages:

Compliant mechanisms

A compliant mechanism is a series of rigid bodies connected by compliant elements. These mechanisms have many advantages, including reduced part-count, reduced "slop" between joints (no parasitic motion because of gaps between parts [3] ), energy storage, low maintenance (they don't require lubrication and there is low mechanical wear), and ease of manufacture. [4]

Flexure bearings (also known as flexure joints) are a subset of compliant mechanisms that produce a geometrically well-defined motion (rotation) on application of a force.

Cam and follower mechanisms

Cam and follower mechanism: force is applied from the follower to the cam Clean Energy Cheaper Than Coal Cam Follower Mechanism-Gif.gif
Cam and follower mechanism: force is applied from the follower to the cam

A cam and follower mechanism is formed by the direct contact of two specially shaped links. The driving link is called the cam 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 and follower mechanism's energy is transferred from cam to follower. The camshaft is rotated and, according to the cam profile, the follower moves up and down. Nowadays, 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 and follower mechanism is that the follower moves slightly and helps to rotate the cam six times more circumference length with 70% of the force.

Gears and gear trains

Gears, a type of mechanism Gears animation.gif
Gears, a type of mechanism

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:

Mechanism synthesis

The design of mechanisms to achieve a particular movement and force transmission is known as the kinematic synthesis of mechanisms. [5] This is a set of geometric techniques which yield the dimensions of linkages, cam and follower mechanisms, and gears and gear trains to perform a required mechanical movement and power transmission. [6]

See also

Related Research Articles

<span class="mw-page-title-main">Simple machine</span> Mechanical device that changes the direction or magnitude of a force

A simple machine is a mechanical device that changes the direction or magnitude of a force. In general, they can be defined as the simplest mechanisms that use mechanical advantage to multiply force. Usually the term refers to the six classical simple machines that were defined by Renaissance scientists:

<span class="mw-page-title-main">Machine</span> Powered mechanical device

A machine is a physical system that uses power to apply forces and control movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natural biological macromolecules, such as molecular machines. Machines can be driven by animals and people, by natural forces such as wind and water, and by chemical, thermal, or electrical power, and include a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement. They can also include computers and sensors that monitor performance and plan movement, often called mechanical systems.

Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. The study of how forces act on bodies falls within kinetics, not kinematics. For further details, see analytical dynamics.

<span class="mw-page-title-main">Four-bar linkage</span> Mechanical linkage consisting of four links connected by joints in a loop

In the study of mechanisms, a four-bar linkage, also called a four-bar, is the simplest closed-chain movable linkage. It consists of four bodies, called bars or links, connected in a loop by four joints. Generally, the joints are configured so the links move in parallel planes, and the assembly is called a planar four-bar linkage. Spherical and spatial four-bar linkages also exist and are used in practice.

<span class="mw-page-title-main">Linkage (mechanical)</span> Assembly of systems connected to manage forces and movement

A mechanical linkage is an assembly of systems 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.

In physics, the degrees of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration or state. It is important in the analysis of systems of bodies in mechanical engineering, structural engineering, aerospace engineering, robotics, and other fields.

<span class="mw-page-title-main">Overconstrained mechanism</span> Moveable linkage with zero mobility

In mechanical engineering, an overconstrained mechanism is a linkage that has more degrees of freedom than is predicted by the mobility formula. The mobility formula evaluates the degree of freedom of a system of rigid bodies that results when constraints are imposed in the form of joints between the links.

The following outline is provided as an overview of and topical guide to machines:

Multibody system is the study of the dynamic behavior of interconnected rigid or flexible bodies, each of which may undergo large translational and rotational displacements.

In classical mechanics, a kinematic pair is a connection between two physical objects that imposes constraints on their relative movement (kinematics). German engineer 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.

<span class="mw-page-title-main">Kinematic chain</span> Mathematical model for a mechanical system

In mechanical engineering, a kinematic chain is an assembly of rigid bodies connected by joints to provide constrained motion that is the mathematical model for a mechanical system. As the word chain suggests, the rigid bodies, or links, are constrained by their connections to other links. An example is the simple open chain formed by links connected in series, like the usual chain, which is the kinematic model for a typical robot manipulator.

<span class="mw-page-title-main">Straight-line mechanism</span> Mechanisms generating real or approximate straight line motion

A straight-line mechanism is a mechanism that converts any type of rotary or angular motion to perfect or near-perfect straight-line motion, or vice versa. Straight-line motion is linear motion of definite length or "stroke", every forward stroke being followed by a return stroke, giving reciprocating motion. The first such mechanism, patented in 1784 by James Watt, produced approximate straight-line motion, referred to by Watt as parallel motion.

<span class="mw-page-title-main">Sarrus linkage</span> Six-bar straight-line mechanism

The Sarrus linkage, invented in 1853 by Pierre Frédéric Sarrus, is a mechanical linkage to convert a limited circular motion to a linear motion or vice versa without reference guideways. It is a spatial six-bar linkage (6R) with two groups of three parallel adjacent joint-axes.

<span class="mw-page-title-main">Cognate linkage</span> Linkages of different dimensions with the same output motion

In kinematics, cognate linkages are linkages that ensure the same coupler curve geometry or input-output relationship, while being dimensionally dissimilar. In case of four-bar linkage coupler cognates, the Roberts–Chebyshev Theorem, after Samuel Roberts and Pafnuty Chebyshev, states that each coupler curve can be generated by three different four-bar linkages. These four-bar linkages can be constructed using similar triangles and parallelograms, and the Cayley diagram.

The Chebychev–Grübler–Kutzbach criterion determines the number of degrees of freedom of a kinematic chain, that is, a coupling of rigid bodies by means of mechanical constraints. These devices are also called linkages.

<span class="mw-page-title-main">Instant centre of rotation</span> Point fixed to a body undergoing planar movement

The instant center of rotation of a body undergoing planar movement is a point that has zero velocity at a particular instant of time. At this instant, the velocity vectors of the other points in the body generate a circular field around this center of rotation which is identical to what is generated by a pure rotation.

<span class="mw-page-title-main">Revolute joint</span> Kinematic pair which constrains bodies to pure rotation about a common axis

A revolute joint is a one-degree-of-freedom kinematic pair used frequently in mechanisms and machines. The joint constrains the motion of two bodies to pure rotation along a common axis. The joint does not allow translation, or sliding linear motion, a constraint not shown in the diagram. Almost all assemblies of multiple moving bodies include revolute joints in their designs. Revolute joints are used in numerous applications such as door hinges, mechanisms, and other uni-axial rotation devices.

In kinematics, Burmester theory comprises geometric techniques for synthesis of linkages. It was introduced in the late 19th century by Ludwig Burmester (1840–1927). His approach was to compute the geometric constraints of the linkage directly from the inventor's desired movement for a floating link. From this point of view a four-bar linkage is a floating link that has two points constrained to lie on two circles.

<span class="mw-page-title-main">Slider-crank linkage</span> Mechanism for conveting rotary motion into linear motion

A slider-crank linkage is a four-link mechanism with three revolute joints and one prismatic, or sliding, joint. The rotation of the crank drives the linear movement of the slider, or the expansion of gases against a sliding piston in a cylinder can drive the rotation of the crank.

In mechanical engineering, kinematic synthesis determines the size and configuration of mechanisms that shape the flow of power through a mechanical system, or machine, to achieve a desired performance. The word synthesis refers to combining parts to form a whole. Hartenberg and Denavit describe kinematic synthesis as

...it is design, the creation of something new. Kinematically, it is the conversion of a motion idea into hardware.

References

  1. Lung-Wen Tsai, 2001, Mechanism design: enumeration of kinematic structures according to function, CRC Press
  2. J. M. McCarthy and G. S. Soh, Geometric Design of Linkages, 2nd Edition, Springer 2010
  3. Nigatu, Hassen; Yihun, Yimesker (2020), Larochelle, Pierre; McCarthy, J. Michael (eds.), "Algebraic Insight on the Concomitant Motion of 3RPS and 3PRS PKMs" (PDF), Proceedings of the 2020 USCToMM Symposium on Mechanical Systems and Robotics, Cham: Springer International Publishing, vol. 83, pp. 242–252, doi:10.1007/978-3-030-43929-3_22, ISBN   978-3-030-43928-6, S2CID   218789290 , retrieved 2020-12-14
  4. "Compliant Mechanisms | About Compliant Mechanisms". compliantmechanisms. Retrieved 2019-02-08.
  5. Hartenberg, R.S. and J. Denavit (1964) Kinematic synthesis of linkages, New York: McGraw-Hill — Online link from Cornell University.
  6. J. J. Uicker, G. R. Pennock, and J. E. Shigley, Theory of Machines and Mechanisms, Fifth Ed., Oxford University Press, 2016.