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Inengineering, amechanism is adevice that transforms input forces and movement into a desired set of output forces and movement. Mechanisms generally consist of moving components which may includeGears andgear trains;Belts andchain drives;cams andfollowers;Linkages; Friction devices, such asbrakes orclutches; Structural components such as a frame, fasteners, bearings, springs, or lubricants; Variousmachine elements, such as splines, pins, or keys.
German scientistFranz Reuleaux definesmachine 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 ofmachine is generally interpreted to meanmechanism.
The combination of force and movement definespower, 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 amechanical system ormachine. Sometimes an entire machine may be referred to as a mechanism; examples are thesteering mechanism in acar, or thewinding mechanism of awristwatch.However, typically, a set of multiple mechanisms is called a machine.
From the time ofArchimedes to theRenaissance, mechanisms were viewed as constructed fromsimple machines, such as thelever,pulley,screw,wheel and axle,wedge, andinclined plane.Reuleaux focused on bodies, calledlinks, and the connections between these bodies, calledkinematic pairs, or joints.
To use geometry to study the movement of a mechanism, its links are modelled asrigid 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.
Reuleaux called the ideal connections between linkskinematic pairs. He distinguished betweenhigher pairs, with line contact between the two links, andlower 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 acam joint. Similarly, the contact between the involute curves that form the meshing teeth of two gears are cam joints.
Akinematic 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 agraph by representing the links of the mechanism as edges and the joints as vertices of the graph. This version of thekinematic diagram has proven effective in enumerating kinematic structures in the process of machine design.[1]
An important consideration in this design process is thedegree of freedom of the system of links and joints, which is determined using theChebychev–Grübler–Kutzbach criterion.
While all mechanisms in a mechanical system are three-dimensional, they can be analysed usingplane 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 aplanar mechanism. The kinematic analysis of planar mechanisms uses the subset ofSpecial Euclidean groupSE, 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 thex andy coordinates of the origin of a coordinate frame inM,[clarification needed] measured from the origin of a coordinate frame inF, and the angle measured from thex-axis inF to thex-axis inM.[clarification needed] This is often described saying a body in the plane has threedegrees 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 as 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.
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 thegimbaledgyroscope. These devices are calledspherical 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)[clarification needed] of rotations in three-dimensional space. Other examples of spherical mechanisms are theautomotive differential and the robotic wrist.
Therotation group SO(3) is three-dimensional. An example of the three parameters that specify a spatial rotation are theroll, pitch and yaw angles used to define the orientation of an aircraft.
A mechanism in which a body moves through a general spatial movement is called aspatial 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 byrod ends, also called spherical joints orball 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, andhumanoid robotic systems are also examples of spatial mechanisms.
Bennett's linkage is an example of a spatialoverconstrained mechanism, which is constructed from four hinged joints.
The groupSE(3)[clarification needed] 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.
Alinkage 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 planarfour-bar linkage. There are, however, many more special linkages:
Acompliant 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 asflexure joints) are a subset of compliant mechanisms that produce a geometrically well-defined motion (rotation) on application of a force.
Acam andfollower 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 thecam andfollower determines the movement of the mechanism. In general a cam and follower mechanism's energy is transferred from cam to follower. Thecamshaft 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.
The transmission of rotation between contacting toothed wheels can be traced back to theAntikythera mechanism ofGreece and thesouth-pointing chariot of China. Illustrations by theRenaissance scientistGeorgius Agricola show gear trains with cylindrical teeth. The implementation of theinvolute tooth yielded a standard gear design that provides a constant speed ratio. Some important features of gears and gear trains are:
The design of mechanisms to achieve a particular movement and force transmission is known as thekinematic 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]
