# Mechanics

## Rotation

Rotation is defined as rigid movement having as fixed points a point called center (in two dimensions) or a straight line called axis (in three dimensions) of rotation. This movement shifts all points around the center, or axis, by a fixed angle. In other words a rotation is the movement of a body following a circular […]

## Roto-translation (rigid transformation)

The rigid transformation (or roto-translation motion) is the composition between reflection, translation, and rotation, and therefore it is an isometry, that is, a geometric transformation that leaves the distances unchanged. In other words, we can think of roto-translation as a rigid movement in which a geometric figure first rotates and then translates. The rototranslation motion of a rigid body

## Fracture mechanics

Fracture mechanics is the branch of mechanics concerned with the study of the effects of cracks and defects on the state of stress in a body. By applying the physics and mathematics of stress and strain to the microscopic level of defects in materials, it is possible to predict the macroscopic fracture behavior of bodies.

## Impedance

Impedance is the complex-valued generalization of resistance. It may refer to:

## Anelasticity

Anelasticity is a characteristic of viscoelastic materials that depends on some physical properties of the material itself. Anelasticity is the opposite of elasticity. An anelastic material subjected to stress undergoes deformations that are not proportional to the stresses and that do not disappear when the force is zeroed. In other words, an anelastic material will fully

## Motion

Motion is defined as the change in the position of an object over time and mathematically described in terms of displacement, distance, velocity, acceleration, speed, and time. When we talk about motion of points, we refer to points belonging to rigid bodies, intending to establish the connection between the motions of the two entities – point

## Newton’s laws of motion

The laws of motion (also called Newton’s laws of motion) are the physical principles on which Newtonian dynamics is based, and describe the relationships between the motion of a body and the entities that modify it. They are valid in inertial reference systems and accurately describe the behavior of bodies moving at speeds much slower

## Continuum mechanics

In physics, continuous body mechanics, or simply continuum mechanics, is the branch of classical mechanics and statistical mechanics that studies the behavior of continuous bodies, i.e., macroscopic physical systems in which the size of the observed phenomena is such that they are not affected by the molecular structure of the matter, and for which it

## Mechanics

Mechanics is divided into different branches according to the characteristics of the bodies it deals with; thus we speak of mechanics of material points, mechanics of rigid systems, mechanics of deformable systems, fluid mechanics, etc. At the macroscopic level, the study of the motion of bodies is carried out either within the framework of classical

## Worm gear

A worm gear is similar to a screw having single or multiple start threads, which form the teeth of the worm. The worm drives the worm gear or worm wheel to enable transmission of motion. The axes of worm and worm gear are at right angles to each other. Worms and worm wheels are not limited to

## Spur gear

Spur gears, or straight-cut gears, are the simplest and the most widely used gears that can achieve high accuracy with relatively easy production processes. The gear teeth are cut on the periphery and are parallel to the axis of the gear. Though the teeth are not straight-sided (but usually of special form to achieve a constant

## Shear strength

Shear strength is the strength of a material or component against the type of yield or structural failure when the material or component fails in shear. A shear load is a force that tends to produce a sliding failure on a material along a plane that is parallel to the direction of the force. When a

## Mechanical impedance

Mechanical impedance is a measure of how much a structure resists motion when subjected to a harmonic force. It relates forces with velocities acting on a mechanical system. The mechanical impedance of a point on a structure is the ratio of the force applied at a point to the resulting velocity at that point. The mechanical

## Kinematic pair

A kinematic pair is a connection between two physical objects that imposes constraints on their relative movement. In other words: two links or elements of a machine, when in contact with each other, are said to form a pair; if the relative motion between them is completely or successfully constrained (i.e. in a definite direction),

A kinematic link is defined as the part of the machine which has a relative motion with respect to some other part of the same machine is called kinematic link or element. Kinematic links can be divided into four types:

## Kinematic chain

In rational mechanics, the kinematic chain is the union of several members obtained with kinematic pairs, so that, fixed the relative velocity of a member to any other, result univocally determined the relative velocities of all other members, i.e. fixed one of the members, the system has only one degree of freedom. When the kinematic pairs are

## Indentation hardness

Indentation hardness, used in mechanical engineering to determine the hardness of a material to deformation. Several such tests exist, wherein the examined material is indented until an impression is formed; these tests can be performed on a macroscopic or microscopic scale. Nanoindentation, or nanopenetration, uses very small loading forces (down to nanonewtons) and is used

## Hypoid gear

Hypoid gears are similar to bevel gears, but the axes of the two connecting shafts do not intersect. They carry curved teeth, are stronger than the common types of bevel gears, and are quiet-running. These gears are mainly used in automobile rear axle drives. A hypoid gear is a spiral bevel gear with an axis that

## Herringbone gear

Herringbone gears have two sets of helical teeth, one right-hand and the other left-hand, machined side by side. Is a special type of gear that is a side-to-side (not face-to-face) combination of two helical gears of opposite hands. Viewed from above, each helical groove of this gear looks like the letter V, and many together form

## Helical gear

Helical or “dry fixed” gear, is a type of gear that offers a refinement over spur gears. The leading edges of the teeth are not parallel to the axis of rotation, but are set at an angle. Each tooth has a helical or spiral form. Since the gear is curved, this angling makes the tooth shape a

## Gear rack

The gear rack have the same sized and shaped teeth cut at equal distances along a flat surface or a straight rod. A gear rack is a cylindrical gear with the radius of the pitch cylinder being infinite. By meshing with a cylindrical gear pinion, it converts rotational motion into linear motion. Gear racks can be broadly divided

## Gear (cogwheel)

A gear (or cogwheel) it is the main element in a transmission system, in which teeth are cut around cylindrical or cone shaped surfaces with equal spacing; or in the case of a cogwheel, inserted teeth (called cogs). By meshing a pair of these elements, they are used to transmit rotations and forces from the driving shaft to

## Fracture toughness

Fracture toughness is a property that describes the ability of a material to resist fracture and is one of the essential properties of any material for many design applications. In materials science, fracture toughness is the critical stress intensity factor of a sharp crack, where crack propagation suddenly becomes rapid and unrestricted. The thickness of

## Fracture

In mechanics, fracture (or breakage) is a phenomenon that occurs as a result of stresses acting on the material and consists, at the macroscopic level, of the disintegration of the material itself (or object) into smaller fragments. This phenomenon is characterized by the disintegration of the chemical bonds that hold the constituent atoms of the

## Ductility

Ductility is a technological property of matter that indicates the ability of a body or material to deform plastically under load before breaking, which may be expressed as percent elongation or percent area reduction from a tensile test — for example, the ability to withstand plastic deformations. A body is much more ductile, the higher the

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