Glossary of engineering: M–Z

1. structural components such as frame members, bearings, axles, splines, fasteners, seals, and lubricants,
2. mechanisms that control movement in various ways such as gear trains, belt or chain drives, linkages, cam and follower systems, including brakes and clutches, and
3. control components such as buttons, switches, indicators, sensors, actuators and computer controllers.[1]

While generally not considered to be a machine element, the shape, texture and color of covers are an important part of a machine that provide a styling and operational interface between the mechanical components of a machine and its users.

${\displaystyle \rho ={\frac {m}{V}}}$

${\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}}$

is a matrix with two rows and three columns; one say often a "two by three matrix", a "2×3-matrix", or a matrix of dimension 2×3.

Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra. Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. For example, matrix multiplication represents composition of linear maps.

• Gears and gear trains;
• Belts and chain drives;
• Cams and followers;
• Linkages;
• Friction devices, such as brakes or clutches;
• Structural components such as a frame, fasteners, bearings, springs, or lubricants;
• Various machine elements, such as splines, pins, or keys.

${\displaystyle M={\frac {\max x+\min x}{2}}.}$

The mid-range is closely related to the range, a measure of statistical dispersion defined as the difference between maximum and minimum values. The two measures are complementary in sense that if one knows the mid-range and the range, one can find the sample maximum and minimum values.

${\displaystyle \operatorname {MH} (X)={\overline {Q_{1,3}(X)}}={\frac {Q_{1}(X)+Q_{3}(X)}{2}}={\frac {P_{25}(X)+P_{75}(X)}{2}}=M_{25}(X)}$

The midhinge is related to the interquartile range (IQR), the difference of the third and first quartiles (i.e. ${\displaystyle IQR=Q_{3}-Q_{1}}$), which is a measure of statistical dispersion. The two are complementary in sense that if one knows the midhinge and the IQR, one can find the first and third quartiles.

The use of the term "hinge" for the lower or upper quartiles derives from John Tukey's work on exploratory data analysis in the late 1970s,[60] and "midhinge" is a fairly modern term dating from around that time. The midhinge is slightly simpler to calculate than the trimean (${\displaystyle TM}$), which originated in the same context and equals the average of the median (${\displaystyle {\tilde {X}}=Q_{2}=P_{50}}$) and the midhinge.

${\displaystyle \operatorname {MH} (X)=2\operatorname {TM} (X)-\operatorname {med} (X)=2{\frac {Q_{1}+2Q_{2}+Q3}{4}}-Q_{2}}$

${\displaystyle h\mathbf {b_{1}} +k\mathbf {b_{2}} +\ell \mathbf {b_{3}} }$

${\displaystyle \mathbf {b_{i}} }$

${\displaystyle h\mathbf {a_{1}} +k\mathbf {a_{2}} +\ell \mathbf {a_{3}} }$

• the notation {hkℓ} denotes the set of all planes that are equivalent to (hkℓ) by the symmetry of the lattice.

In the context of crystal directions (not planes), the corresponding notations are:

• [hkℓ], with square instead of round brackets, denotes a direction in the basis of the direct lattice vectors instead of the reciprocal lattice; and
• similarly, the notation <hkℓ> denotes the set of all directions that are equivalent to [hkℓ] by symmetry.

${\displaystyle \delta \ {\stackrel {\text{def}}{=}}\ {\frac {\text{stress}}{\text{strain}}}}$

${\displaystyle \delta }$

${\displaystyle \mathbf {P}$ :{\begin{pmatrix}x\\y\\z\end{pmatrix}}\mapsto {\begin{pmatrix}-x\\-y\\-z\end{pmatrix}}.}

It can also be thought of as a test for chirality of a physical phenomenon, in that a parity inversion transforms a phenomenon into its mirror image. All fundamental interactions of elementary particles, with the exception of the weak interaction, are symmetric under parity. The weak interaction is chiral and thus provides a means for probing chirality in physics. In interactions that are symmetric under parity, such as electromagnetism in atomic and molecular physics, parity serves as a powerful controlling principle underlying quantum transitions.

A matrix representation of P (in any number of dimensions) has determinant equal to −1, and hence is distinct from a rotation, which has a determinant equal to 1. In a two-dimensional plane, a simultaneous flip of all coordinates in sign is not a parity transformation; it is the same as a 180°-rotation.

${\displaystyle F=C-P+2.}$

It was derived by American physicist Josiah Willard Gibbs in his landmark paper titled On the Equilibrium of Heterogeneous Substances, published in parts between 1875 and 1878.[113]

${\displaystyle v_{\text{RMS}}={\sqrt {3RT \over M}}}$

${\displaystyle E_{\mathrm {rotational} }={\frac {1}{2}}I\omega ^{2}}$

where

${\displaystyle \omega \ }$ is the angular velocity

${\displaystyle I\ }$ is the moment of inertia around the axis of rotation

${\displaystyle E\ }$ is the kinetic energy

${\displaystyle \omega _{\text{cyc}}}$

${\displaystyle \omega _{\text{cyc}}}$

${\displaystyle v=2\pi r\omega _{\text{cyc}}}$

${\displaystyle v=r\omega _{\text{rad}}}$

An algebraic rearrangement of this equation allows us to solve for rotational speed:

${\displaystyle \omega _{\text{cyc}}=v/2\pi r}$

${\displaystyle \omega _{\text{rad}}=v/r}$

Thus, the tangential speed will be directly proportional to r when all parts of a system simultaneously have the same ω, as for a wheel, disk, or rigid wand. The direct proportionality of v to r is not valid for the planets, because the planets have different rotational speeds (ω).

Rotational speed can measure, for example, how fast a motor is running. Rotational speed and angular speed are sometimes used as synonyms, but typically they are measured with a different unit. Angular speed, however, tells the change in angle per time unit, which is measured in radians per second in the SI system. Since there are 2π radians per cycle, or 360 degrees per cycle, we can convert angular speed to rotational speed by

${\displaystyle \omega _{\text{cyc}}=\omega _{\text{rad}}/2\pi \,}$

and

${\displaystyle \omega _{\text{cyc}}=\omega _{\text{deg}}/360\,}$

where

• ${\displaystyle \omega _{\text{cyc}}\,}$ is rotational speed in cycles per second
• ${\displaystyle \omega _{\text{rad}}\,}$ is angular speed in radians per second
• ${\displaystyle \omega _{\text{deg}}\,}$ is angular speed in degrees per second

For example, a stepper motor might turn exactly one complete revolution each second. Its angular speed is 360 degrees per second (360°/s), or 2π radians per second (2π rad/s), while the rotational speed is 60 rpm.

• a shear stress over a distance in a thin-walled structure (in solid mechanics);[169]
• the flow induced by a force (in a fluid).

• Lever
• Wheel and axle
• Pulley
• Inclined plane
• Wedge
• Screw

1. The laws of physics are invariant (that is, identical) in all inertial frames of reference (that is, frames of reference with no acceleration).
2. The speed of light in vacuum is the same for all observers, regardless of the motion of the light source or observer.

${\displaystyle j^{\star }}$

${\displaystyle j^{\star }=\sigma T^{4}.}$

The constant of proportionality σ, called the Stefan–Boltzmann constant, is derived from other known physical constants. Since 2019, the value of the constant is

${\displaystyle \sigma ={\frac {2\pi ^{5}k^{4}}{15c^{2}h^{3}}}=5.670374\ldots \times 10^{-8}\,\mathrm {W\,m^{-2}\,K^{-4}} ,}$

where k is the Boltzmann constant, h is the Planck constant, and c is the speed of light in vacuum. The radiance from a specified angle of view (watts per square metre per steradian) is given by

${\displaystyle L={\frac {j^{\star }}{\pi }}={\frac {\sigma }{\pi }}T^{4}.}$

A body that does not absorb all incident radiation (sometimes known as a grey body) emits less total energy than a black body and is characterized by an emissivity, ${\displaystyle \varepsilon <1}$:

${\displaystyle j^{\star }=\varepsilon \sigma T^{4}.}$

The radiant emittance ${\displaystyle j^{\star }}$ has dimensions of energy flux (energy per unit time per unit area), and the SI units of measure are joules per second per square metre, or equivalently, watts per square metre. The SI unit for absolute temperature T is the kelvin. ${\displaystyle \varepsilon }$ is the emissivity of the grey body; if it is a perfect blackbody, ${\displaystyle \varepsilon =1}$. In the still more general (and realistic) case, the emissivity depends on the wavelength, ${\displaystyle \varepsilon =\varepsilon (\lambda )}$.

To find the total power radiated from an object, multiply by its surface area, ${\displaystyle A}$:

${\displaystyle P=Aj^{\star }=A\varepsilon \sigma T^{4}.}$

${\displaystyle \mathbf {v} (t)=v(t){\frac {\mathbf {v} (t)}{v(t)}}=v(t)\mathbf {u} _{\mathrm {t} }(t),}$

with v(t) equal to the speed of travel along the path, and

${\displaystyle \mathbf {u} _{\mathrm {t} }={\frac {\mathbf {v} (t)}{v(t)}}\ ,}$

a unit vector tangent to the path pointing in the direction of motion at the chosen moment in time. Taking into account both the changing speed v(t) and the changing direction of u_t, the acceleration of a particle moving on a curved path can be written using the chain rule of differentiation[217] for the product of two functions of time as:

${\displaystyle {\begin{alignedat}{3}\mathbf {a} &={\frac {d\mathbf {v} }{dt}}\\&={\frac {dv}{dt}}\mathbf {u} _{\mathrm {t} }+v(t){\frac {d\mathbf {u} _{\mathrm {t} }}{dt}}\\&={\frac {dv}{dt}}\mathbf {u} _{\mathrm {t} }+{\frac {v^{2}}{r}}\mathbf {u} _{\mathrm {n} }\ ,\end{alignedat}}}$

where u_n is the unit (inward) normal vector to the particle's trajectory (also called the principal normal), and r is its instantaneous radius of curvature based upon the osculating circle at time t. These components are called the tangential acceleration and the normal or radial acceleration (or centripetal acceleration in circular motion, see also circular motion and centripetal force).

• The equivalent voltage V_th is the voltage obtained at terminals A–B of the network with terminals A–B open circuited.
• The equivalent resistance R_th is the resistance that the circuit between terminals A and B would have if all ideal voltage sources in the circuit were replaced by a short circuit and all ideal current sources were replaced by an open circuit.
• If terminals A and B are connected to one another, the current flowing from A to B will be V_th/R_th. This means that R_th could alternatively be calculated as V_th divided by the short-circuit current between A and B when they are connected together.

In circuit theory terms, the theorem allows any one-port network to be reduced to a single voltage source and a single impedance.

${\displaystyle \Delta {\bar {S}}_{\text{vap}}\approx 10.5R.}$

A similar way of stating this (Trouton's ratio) is that the latent heat is connected to boiling point roughly as

${\displaystyle {\frac {L_{\text{vap}}}{T_{\text{boiling}}}}\approx 85{-}88\ {\frac {\text{J}}{{\text{K}}\cdot {\text{mol}}}}.}$

${\displaystyle PV=nRT}$

To account for the volume that a real gas molecule takes up, the Van der Waals equation replaces V in the ideal gas law with ${\displaystyle (V_{m}-b)}$, where V_m is the molar volume of the gas and b is the volume that is occupied by one mole of the molecules. This leads to:[255]

${\displaystyle P(V_{m}-b)=RT}$

The second modification made to the ideal gas law accounts for the fact that gas molecules do in fact interact with each other (they usually experience attraction at low pressures and repulsion at high pressures) and that real gases therefore show different compressibility than ideal gases. Van der Waals provided for intermolecular interaction by adding to the observed pressure P in the equation of state a term ${\displaystyle a/V_{m}^{2}}$, where a is a constant whose value depends on the gas. The Van der Waals equation is therefore written as:[255]

${\displaystyle \left(P+a{\frac {1}{V_{m}^{2}}}\right)(V_{m}-b)=RT}$

and, for n moles of gas, can also be written as the equation below:

${\displaystyle \left(P+a{\frac {n^{2}}{V^{2}}}\right)(V-nb)=nRT}$

where V_m is the molar volume of the gas, R is the universal gas constant, T is temperature, P is pressure, and V is volume. When the molar volume V_m is large, b becomes negligible in comparison with V_m, a/V_m² becomes negligible with respect to P, and the Van der Waals equation reduces to the ideal gas law, PV_m=RT.[255]

• If two non-collinear members meet in an unloaded joint, both are zero-force members.
• If three members meet in an unloaded joint of which two are collinear, then the third member is a zero-force member.

Reasons for Zero-force members in a truss system

• These members contribute to the stability of the structure, by providing buckling prevention for long slender members under compressive forces
• These members can carry loads in the event that variations are introduced in the normal external loading configuration.