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Kinematic synthesis
And kinematic synthesis is the collection of techniques for designing those elements of these machines that achieve required output forces and movement for a given input. Applications of kinematic synthesis include determining: the topology and dimensions of a linkage system to achieve a specified task; the size and sh...
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Duality (mechanical engineering)
In mechanical engineering, many terms are associated into pairs called duals. A dual of a relationship is formed by interchanging force (stress) and deformation (strain) in an expression. Here is a partial list of mechanical dualities: force — deformation stress — strain stiffness method — flexibility method
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Mechanical efficiency
In mechanical engineering, mechanical efficiency is a dimensionless number that measures the efficiency of a mechanism or machine in transforming the power input to the device to power output. A machine is a mechanical linkage in which force is applied at one point, and the force does work moving a load at another poin...
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Mechanical efficiency
All real machines lose energy to friction; the energy is dissipated as heat. Therefore, their power output is less than their power input Power output = Power input − Frictional power loss {\displaystyle {\text{Power output}}={\text{Power input}}-{\text{Frictional power loss}}} Therefore, the efficiency of all real mac...
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Random vibration
In mechanical engineering, random vibration is motion which is non-deterministic, meaning that future behavior cannot be precisely predicted. The randomness is a characteristic of the excitation or input, not the mode shapes or natural frequencies. Some common examples include an automobile riding on a rough road, wave...
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Random vibration
Mathematically, random vibration is characterized as an ergodic and stationary process. A measurement of the acceleration spectral density (ASD) is the usual way to specify random vibration. The root mean square acceleration (Grms) is the square root of the area under the ASD curve in the frequency domain.
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Random vibration
The Grms value is typically used to express the overall energy of a particular random vibration event and is a statistical value used in mechanical engineering for structural design and analysis purposes. While the term power spectral density (PSD) is commonly used to specify a random vibration event, ASD is more appro...
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Ultimate failure
An example of this would be stretching a clay pot or rod, when it is stretched it will not neck or elongate, but merely break into two or more pieces. While applying a tensile stress to a ductile material, instead of immediately breaking the material will instead elongate. The material will begin by elongating uniforml...
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Remontoire
In mechanical horology, a remontoire (from the French remonter, meaning 'to wind') is a small secondary source of power, a weight or spring, which runs the timekeeping mechanism and is itself periodically rewound by the timepiece's main power source, such as a mainspring. It was used in a few precision clocks and watch...
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Electronic interlocking
In mechanical interlocking plants, a locking bed is constructed, consisting of steel bars forming a grid. The levers that operate switches, derails, signals or other appliances are connected to the bars running in one direction. The bars are constructed so that if the function controlled by a given lever conflicts with...
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State Variable
In mechanical systems, the position coordinates and velocities of mechanical parts are typical state variables; knowing these, it is possible to determine the future state of the objects in the system. In thermodynamics, a state variable is an independent variable of a state function. Examples include internal energy, ...
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State Variable
Heat and work are not state functions, but process functions. In electronic/electrical circuits, the voltages of the nodes and the currents through components in the circuit are usually the state variables. In any electrical circuit, the number of state variables are equal to the number of (independent) storage element...
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Bit-paired keyboard
As a result, implementing an electromechanical keyboard that produced an ASCII encoding but had conventional typewriter key mappings would require significant complexity due to key-specific shift mechanisms for digits and symbol keys. This could be avoided by changing the key mappings to correspond to the ASCII table, ...
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Fabric filter
In mechanical-shaker baghouses, tubular filter bags are fastened onto a cell plate at the bottom of the baghouse and suspended from horizontal beams at the top. Dirty gas enters the bottom of the baghouse and passes through the filter, and the dust collects on the inside surface of the bags. Cleaning a mechanical-shake...
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Air gap capacitor
In mechanically controlled variable capacitors, the distance between the plates, or the amount of plate surface area which overlaps, can be changed. The most common form arranges a group of semicircular metal plates on a rotary axis ("rotor") that are positioned in the gaps between a set of stationary plates ("stator")...
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Air gap capacitor
Various forms of reduction gear mechanisms are often used to achieve finer tuning control, i.e. to spread the variation of capacity over a larger angle, often several turns. Maximum capacitance is achieved when the plates are "meshed" together, that is, they are inter-laced. Minimum capacitance is achieved when the pla...
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Air gap capacitor
Measurement of the capacitance of a rotary capacitor A vacuum variable capacitor uses a set of plates made from concentric cylinders that can be slid in or out of an opposing set of cylinders (sleeve and plunger). These plates are then sealed inside of a non-conductive envelope such as glass or ceramic and placed under...
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Air gap capacitor
A screw shaft is attached to the plunger; when the shaft is turned the plunger moves in or out of the sleeve and the value of the capacitor changes. The vacuum not only increases the working voltage and current handling capacity of the capacitor, it also greatly reduces the chance of arcing across the plates. The most ...
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Air gap capacitor
Vacuum variables can also be more convenient; since the elements are under a vacuum, the working voltage can be higher than an air variable the same size, allowing the size of the vacuum capacitor to be reduced. Very cheap variable capacitors are constructed from layered aluminium and plastic foils that are variably pr...
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Air gap capacitor
These so-called squeezers cannot provide a stable and reproducible capacitance, however. A variant of this structure that allows for linear movement of one set of plates to change the plate overlap area is also used and might be called a slider. This has practical advantages for makeshift or home construction, and may ...
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Drag area
In mechanics and aerodynamics, the drag area of an object represents the effective size of the object as it is "seen" by the fluid flow around it. The drag area is usually expressed as a product C d A , {\displaystyle C_{d}A,} where A {\displaystyle A} is a representative area of the object, and C d {\displaystyle C_{d...
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Mechanical resonance
In mechanics and construction a resonance disaster describes the destruction of a building or a technical mechanism by induced vibrations at a system's resonant frequency, which causes it to oscillate. Periodic excitation optimally transfers to the system the energy of the vibration and stores it there. Because of this...
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Pure shear
In mechanics and geology, pure shear is a three-dimensional homogeneous flattening of a body. It is an example of irrotational strain in which body is elongated in one direction while being shortened perpendicularly. For soft materials, such as rubber, a strain state of pure shear is often used for characterizing hyper...
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Set of 3D rotations
In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space R 3 {\displaystyle \mathbb {R} ^{3}} under the operation of composition.By definition, a rotation about the origin is a transformation that preserves the origin, Euc...
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Set of 3D rotations
It is compact and has dimension 3. Rotations are linear transformations of R 3 {\displaystyle \mathbb {R} ^{3}} and can therefore be represented by matrices once a basis of R 3 {\displaystyle \mathbb {R} ^{3}} has been chosen. Specifically, if we choose an orthonormal basis of R 3 {\displaystyle \mathbb {R} ^{3}} , eve...
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Set of 3D rotations
The group SO(3) can therefore be identified with the group of these matrices under matrix multiplication. These matrices are known as "special orthogonal matrices", explaining the notation SO(3). The group SO(3) is used to describe the possible rotational symmetries of an object, as well as the possible orientations of...
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Strain rate
In mechanics and materials science, strain rate is the time derivative of strain of a material. Strain rate has dimension of inverse time and SI units of inverse second, s−1 (or its multiples). The strain rate at some point within the material measures the rate at which the distances of adjacent parcels of the material...
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Strain rate
It is zero if these distances do not change, as happens when all particles in some region are moving with the same velocity (same speed and direction) and/or rotating with the same angular velocity, as if that part of the medium were a rigid body. The strain rate is a concept of materials science and continuum mechanic...
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Shock (mechanics)
In mechanics and physics, shock is a sudden acceleration caused, for example, by impact, drop, kick, earthquake, or explosion. Shock is a transient physical excitation. Shock describes matter subject to extreme rates of force with respect to time. Shock is a vector that has units of an acceleration (rate of change of v...
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Shock (mechanics)
The unit g (or g) represents multiples of the standard acceleration of gravity and is conventionally used. A shock pulse can be characterised by its peak acceleration, the duration, and the shape of the shock pulse (half sine, triangular, trapezoidal, etc.). The shock response spectrum is a method for further evaluatin...
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Simple Harmonic Motion
In mechanics and physics, simple harmonic motion (sometimes abbreviated SHM) is a special type of periodic motion an object experiences due to a restoring force whose magnitude is directly proportional to the distance of the object from an equilibrium position and acts towards the equilibrium position. It results in an...
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Simple Harmonic Motion
The motion is sinusoidal in time and demonstrates a single resonant frequency. Other phenomena can be modeled by simple harmonic motion, including the motion of a simple pendulum, although for it to be an accurate model, the net force on the object at the end of the pendulum must be proportional to the displacement (an...
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Heat load
In mechanics and thermodynamics, thermal stress is mechanical stress created by any change in temperature of a material. These stresses can lead to fracturing or plastic deformation depending on the other variables of heating, which include material types and constraints. Temperature gradients, thermal expansion or con...
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Heat load
This type of stress is highly dependent on the thermal expansion coefficient which varies from material to material. In general, the greater the temperature change, the higher the level of stress that can occur. Thermal shock can result from a rapid change in temperature, resulting in cracking or shattering.
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Stiffening
In mechanics, "stiffening" beams brings anti-buckling, anti-wrinkling, desired shaping, reinforcement, repair, strength, enhanced function, extended utility, longer beam life, safety, etc. Stiffening of fluid or rigid beams is used in medical arts, aerospace, aviation, sports, bookbinding, art, architecture, natural pl...
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Avicennian logic
In mechanics, Avicenna, in The Book of Healing, developed a theory of motion, in which he made a distinction between the inclination (tendency to motion) and force of a projectile, and concluded that motion was a result of an inclination (mayl) transferred to the projectile by the thrower, and that projectile motion in...
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Avicennian logic
It is unclear if Buridan was influenced by Avicenna, or by Philoponus directly.In optics, Avicenna was among those who argued that light had a speed, observing that "if the perception of light is due to the emission of some sort of particles by a luminous source, the speed of light must be finite." He also provided a w...
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Sommerfeld effect
In mechanics, Sommerfeld effect is a phenomenon arising from feedback in the energy exchange between vibrating systems: for example, when for the rocking table, under given conditions, energy transmitted to the motor resulted not in higher revolutions but in stronger vibrations of the table. It is named after Arnold So...
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Dirac observables
In mechanics, a constant of motion is a quantity that is conserved throughout the motion, imposing in effect a constraint on the motion. However, it is a mathematical constraint, the natural consequence of the equations of motion, rather than a physical constraint (which would require extra constraint forces). Common e...
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Couple (mechanics)
In mechanics, a couple is a system of forces with a resultant (a.k.a. net or sum) moment of force but no resultant force.A better term is force couple or pure moment. Its effect is to impart angular momentum but no linear momentum.
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Couple (mechanics)
In rigid body dynamics, force couples are free vectors, meaning their effects on a body are independent of the point of application. The resultant moment of a couple is a special case of moment. A couple has the property that it is independent of reference point.
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Cylinder stress
In mechanics, a cylinder stress is a stress distribution with rotational symmetry; that is, which remains unchanged if the stressed object is rotated about some fixed axis. Cylinder stress patterns include: circumferential stress, or hoop stress, a normal stress in the tangential (azimuth) direction. axial stress, a no...
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Cylinder stress
In a straight, closed pipe, any force applied to the cylindrical pipe wall by a pressure differential will ultimately give rise to hoop stresses. Similarly, if this pipe has flat end caps, any force applied to them by static pressure will induce a perpendicular axial stress on the same pipe wall. Thin sections often ha...
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Cylinder stress
In thick-walled pressure vessels, construction techniques allowing for favorable initial stress patterns can be utilized. These compressive stresses at the inner surface reduce the overall hoop stress in pressurized cylinders. Cylindrical vessels of this nature are generally constructed from concentric cylinders shrunk...
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Diaphragm (mechanical device)
In mechanics, a diaphragm is a sheet of a semi-flexible material anchored at its periphery and most often round in shape. It serves either as a barrier between two chambers, moving slightly up into one chamber or down into the other depending on differences in pressure, or as a device that vibrates when certain frequen...
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Diaphragm (mechanical device)
The action of the diaphragm is very similar to the action of a plunger with the exception that a diaphragm responds to changes in pressure rather than the mechanical force of the shaft. A diaphragm pressure tank is a tank which has pressurant sealed inside on one side of the diaphragm. It is favored in certain applicat...
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Material displacement gradient tensor
In mechanics, a displacement field is an assignment of displacement vectors for all points in a region or body that are displaced from one state to another. A displacement vector specifies the position of a point or a particle in reference to an origin or to a previous position. For example, a displacement field may be...
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Micromixer
In mechanics, a micromixer is a device based on mechanical microparts used to mix fluids. This device represents a key technology to fields such as chemical industry, pharmaceutical industry, analytical chemistry, biochemical analysis, and high-throughput synthesis, since it makes use of the miniaturization of the flui...
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Body moment
In mechanics, a moment is a measure of the turning effect of a force about some point in space. In most practical examples, moments are the results of forces acting at a distance from the point of interest. The stress on the body on which the force acts is then symmetric. If the moment results from a strong body force,...
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Six-bar linkage
In mechanics, a six-bar linkage is a mechanism with one degree of freedom that is constructed from six links and seven joints. An example is the Klann linkage used to drive the legs of a walking machine. In general, each joint of a linkage connects two links, and a binary link supports two joints.
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Six-bar linkage
If we consider a hexagon constructed from six binary links with six of the seven joints forming its vertices, then the seventh joint can be added to connect two sides of the hexagon to form a six-bar linkage with two ternary links connected by one joint. This type of six-bar linkage is said to have the Watt topology.A ...
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Diffeomorphism
In mechanics, a stress-induced transformation is called a deformation and may be described by a diffeomorphism. A diffeomorphism f: U → V {\displaystyle f:U\to V} between two surfaces U {\displaystyle U} and V {\displaystyle V} has a Jacobian matrix D f {\displaystyle Df} that is an invertible matrix. In fact, it is re...
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Variable-mass system
In mechanics, a variable-mass system is a collection of matter whose mass varies with time. It can be confusing to try to apply Newton's second law of motion directly to such a system. Instead, the time dependence of the mass m can be calculated by rearranging Newton's second law and adding a term to account for the mo...
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Centripetal acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the orientation of the net force acting on that object.
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Centripetal acceleration
The magnitude of an object's acceleration, as described by Newton's Second Law, is the combined effect of two causes: the net balance of all external forces acting onto that object — magnitude is directly proportional to this net resulting force; that object's mass, depending on the materials out of which it is made — ...
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Centripetal acceleration
The acceleration of the vehicle in its current direction of motion is called a linear (or tangential during circular motions) acceleration, the reaction to which the passengers on board experience as a force pushing them back into their seats. When changing direction, the effecting acceleration is called radial (or cen...
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Centripetal acceleration
Such negative accelerations are often achieved by retrorocket burning in spacecraft. Both acceleration and deceleration are treated the same, as they are both changes in velocity. Each of these accelerations (tangential, radial, deceleration) is felt by passengers until their relative (differential) velocity are neutra...
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Equilibrant force
In mechanics, an equilibrant force is a force which brings a body into mechanical equilibrium. According to Newton's second law, a body has zero acceleration when the vector sum of all the forces acting upon it is zero: ∑ F = m a ; ∑ F = 0 ⇒ a = 0 {\displaystyle \sum \mathbf {F} =m\mathbf {a} ;\quad \sum \mathbf {F} =0...
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Mechanical impact
In mechanics, an impact is when two bodies collide. During this collision, both bodies decelerate. The deceleration causes a high force or shock, applied over a short time period. A high force, over a short duration, usually causes more damage to both bodies than a lower force applied over a proportionally longer durat...
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Mechanical impact
At normal speeds, during a perfectly inelastic collision, an object struck by a projectile will deform, and this deformation will absorb most or all of the force of the collision. Viewed from a conservation of energy perspective, the kinetic energy of the projectile is changed into heat and sound energy, as a result of...
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Mechanical impact
A high-velocity collision (an impact) does not provide sufficient time for these deformations and vibrations to occur. Thus, the struck material behaves as if it were more brittle than it would otherwise be, and the majority of the applied force goes into fracturing the material. Or, another way to look at it is that m...
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Mechanical impact
Impact resistance decreases with an increase in the modulus of elasticity, which means that stiffer materials will have less impact resistance. Resilient materials will have better impact resistance. Different materials can behave in quite different ways in impact when compared with static loading conditions.
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Mechanical impact
Ductile materials like steel tend to become more brittle at high loading rates, and spalling may occur on the reverse side to the impact if penetration doesn't occur. The way in which the kinetic energy is distributed through the section is also important in determining its response. Projectiles apply a Hertzian contac...
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Physical compression
In mechanics, compression is the application of balanced inward ("pushing") forces to different points on a material or structure, that is, forces with no net sum or torque directed so as to reduce its size in one or more directions. It is contrasted with tension or traction, the application of balanced outward ("pulli...
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Physical compression
In uniaxial compression, the forces are directed along one direction only, so that they act towards decreasing the object's length along that direction. The compressive forces may also be applied in multiple directions; for example inwards along the edges of a plate or all over the side surface of a cylinder, so as to ...
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Physical compression
If the stress vector itself is opposite to x {\displaystyle x} , the material is said to be under normal compression or pure compressive stress along x {\displaystyle x} . In a solid, the amount of compression generally depends on the direction x {\displaystyle x} , and the material may be under compression along some ...
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Physical compression
This is the only type of static compression that liquids and gases can bear. It affects the volume of the material, as quantified by the bulk modulus and the volumetric strain. The inverse process of compression is called decompression or dilation, in which the object enlarges or increases in volume. In a mechanical wa...
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Compressive strength
In mechanics, compressive strength (or compression strength) is the capacity of a material or structure to withstand loads tending to reduce size (as opposed to tensile strength which withstands loads tending to elongate). In other words, compressive strength resists compression (being pushed together), whereas tensile...
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Friction torque
In mechanics, friction torque is the torque caused by the frictional force that occurs when two objects in contact move. Like all torques, it is a rotational force that may be measured in newton meters or pounds-feet.
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Paul Émile Appell
In mechanics, he proposed an alternative formulation of analytical mechanics known as Appell's equation of motion. He discovered a physical interpretation of the imaginary period of the doubly periodic function whose restriction to real arguments describes the motion of an ideal pendulum.
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Logarithmic strain
In mechanics, strain is defined as relative deformation, compared to a reference position configuration. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or...
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Logarithmic strain
Strain can be formulated as the spatial derivative of displacement: where I is the identity tensor. The displacement of a body may be expressed in the form x = F(X), where X is the reference position of material points of the body; displacement has units of length and does not distinguish between rigid body motions (tr...
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Logarithmic strain
Physical insight into strains can be gained by observing that a given strain can be decomposed into normal and shear components. The amount of stretch or compression along material line elements or fibers is the normal strain, and the amount of distortion associated with the sliding of plane layers over each other is t...
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Suspension (mechanics)
In mechanics, suspension is a system of components allowing a machine (normally a vehicle) to move smoothly with reduced shock. Types may include: car suspension, four-wheeled motor vehicle suspension motorcycle suspension, two-wheeled motor vehicle suspension Motorcycle fork, a component of motorcycle suspension syste...
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Joule (unit)
In mechanics, the concept of force (in some direction) has a close analogue in the concept of torque (about some angle): A result of this similarity is that the SI unit for torque is the newton-metre, which works out algebraically to have the same dimensions as the joule, but they are not interchangeable. The General C...
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Joule (unit)
By contrast, torque is a vector – the cross product of a force vector and a distance vector. Torque and energy are related to one another by the equation where E is energy, τ is (the vector magnitude of) torque, and θ is the angle swept (in radians). Since plane angles are dimensionless, it follows that torque and ener...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Velocity vs. time graph
In mechanics, the derivative of the position vs. time graph of an object is equal to the velocity of the object. In the International System of Units, the position of the moving object is measured in meters relative to the origin, while the time is measured in seconds. Placing position on the y-axis and time on the x-a...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Velocity vs. time graph
Here s {\displaystyle s} is the position of the object, and t {\displaystyle t} is the time. Therefore, the slope of the curve gives the change in position divided by the change in time, which is the definition of the average velocity for that interval of time on the graph. If this interval is made to be infinitesimall...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Velocity vs. time graph
A similar fact also holds true for the velocity vs. time graph. The slope of a velocity vs. time graph is acceleration, this time, placing velocity on the y-axis and time on the x-axis. Again the slope of a line is change in y {\displaystyle y} over change in x {\displaystyle x}: a = Δ y Δ x = Δ v Δ t {\displaystyle a=...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Velocity vs. time graph
This slope therefore defines the average acceleration over the interval, and reducing the interval infinitesimally gives d v d t {\displaystyle {\begin{matrix}{\frac {dv}{dt}}\end{matrix}}} , the instantaneous acceleration at time t {\displaystyle t} , or the derivative of the velocity with respect to time (or the seco...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Velocity vs. time graph
(Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.) The same multiplication rule holds true for acceleration vs. time graphs. When acceleration is multiplied
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Left eigenvector
In mechanics, the eigenvectors of the moment of inertia tensor define the principal axes of a rigid body. The tensor of moment of inertia is a key quantity required to determine the rotation of a rigid body around its center of mass.
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Flexural modulus
In mechanics, the flexural modulus or bending modulus is an intensive property that is computed as the ratio of stress to strain in flexural deformation, or the tendency for a material to resist bending. It is determined from the slope of a stress-strain curve produced by a flexural test (such as the ASTM D790), and us...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Flexural modulus
For a 3-point test of a rectangular beam behaving as an isotropic linear material, where w and h are the width and height of the beam, I is the second moment of area of the beam's cross-section, L is the distance between the two outer supports, and d is the deflection due to the load F applied at the middle of the beam...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Net force
In mechanics, the net force is the sum of all the forces acting on an object. For example, if two forces are acting upon an object in opposite directions, and one force is greater than the other, the forces can be replaced with a single force that is the difference of the greater and smaller force. That force is the ne...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Net force
When the net force is applied at a specific point on an object, the associated torque can be calculated. The sum of the net force and torque is called the resultant force, which causes the object to rotate in the same way as all the forces acting upon it would if they were applied individually.It is possible for all th...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Net force
In some texts, the terms resultant force and net force are used as if they mean the same thing. This is not always true, especially when in complex topics like the motion of spinning objects or situations where everything is perfectly balanced, known as static equilibrium. In these cases, it's important to understand t...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Neutral plane
In mechanics, the neutral plane or neutral surface is a conceptual plane within a beam or cantilever. When loaded by a bending force, the beam bends so that the inner surface is in compression and the outer surface is in tension. The neutral plane is the surface within the beam between these zones, where the material o...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Neutral plane
To show that every beam must have a neutral plane, the material of the beam can be imagined to be divided into narrow fibers parallel to its length. When the beam is bent, at any given cross-section the region of fibers near the concave side will be under compression, while the region near the convex side will be under...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Normal force
In mechanics, the normal force F n {\displaystyle F_{n}} is the component of a contact force that is perpendicular to the surface that an object contacts, as in Figure 1. In this instance normal is used in the geometric sense and means perpendicular, as opposed to the common language use of normal meaning "ordinary" or...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Normal force
The normal force is one type of ground reaction force. If the person stands on a slope and does not sink into the ground or slide downhill, the total ground reaction force can be divided into two components: a normal force perpendicular to the ground and a frictional force parallel to the ground. In another common situ...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Centimeter gram second system of units
In mechanics, the quantities in the CGS and SI systems are defined identically. The two systems differ only in the scale of the three base units (centimetre versus metre and gram versus kilogram, respectively), with the third unit (second) being the same in both systems. There is a direct correspondence between the bas...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Series and parallel springs
In mechanics, two or more springs are said to be in series when they are connected end-to-end or point to point, and it is said to be in parallel when they are connected side-by-side; in both cases, so as to act as a single spring: More generally, two or more springs are in series when any external stress applied to th...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Virtual work
In mechanics, virtual work arises in the application of the principle of least action to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement is different for different displacements. Among all the possible displacements that a particle may f...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Virtual work
This displacement is therefore the displacement followed by the particle according to the principle of least action. The work of a force on a particle along a virtual displacement is known as the virtual work. Historically, virtual work and the associated calculus of variations were formulated to analyze systems of rig...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Implementability (mechanism design)
In mechanism design, implementability is a property of a social choice function. It means that there is an incentive-compatible mechanism that attains ("implements") this function. There are several degrees of implementability, corresponding to the different degrees of incentive-compatibility, e.g: A function is domina...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Implementability (mechanism design)
A function is Bayesian-Nash implementable if it is attainable by a mechanism which is Bayesian-Nash-incentive-compatible.See for a recent reference. In some textbooks, the entire field of mechanism design is called Implementation theory. == References ==
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Monotonicity (mechanism design)
In mechanism design, monotonicity is a property of a social choice function. It is a necessary condition for being able to implement the function using a strategyproof mechanism. Its verbal description is: If changing one agent's type (while keeping the types of other agents fixed) changes the outcome under the social ...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Single-crossing condition
In mechanism design, the term single-crossing condition (often referred to as the Spence-Mirrlees property for Michael Spence and James Mirrlees, sometimes as the constant-sign assumption) refers to the requirement that the isoutility curve for agents of different types cross only once. This condition guarantees that t...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus
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Media planning
And finally, the consumer is on the final step of buying cycle the purchase, with the help of frequent advertisement. Without the good amount of frequency, a consumer would be very unlikely to get to the purchasing step. Thus, frequency is important because consistence advertisement reinforces top of mind brand awarene...
https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus