|
Kinematic Determinacy
Kinematic determinacy is a term used in structural mechanics to describe a structure where material compatibility conditions alone can be used to calculate deflections. A kinematically determinate structure can be defined as a structure where, if it is possible to find nodal displacements compatible with member extensions, those nodal displacements are unique. The structure has no possible mechanisms, i.e. nodal displacements, compatible with zero member extensions, at least to a first-order approximation. Mathematically, the mass matrix of the structure must have full rank. Kinematic determinacy can be loosely used to classify an arrangement of structural members as a ''structure'' (stable) instead of a ''mechanism'' (unstable). The principles of kinematic determinacy are used to design precision devices such as mirror mounts for optics, and precision linear motion bearings. See also * Statical determinacy * Precision engineering * Kinematic coupling Kinematic coupling describes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Mechanics
Structural mechanics or Mechanics of structures is the computation of deformations, deflections, and internal forces or stresses (''stress equivalents'') within structures, either for design or for performance evaluation of existing structures. It is one subset of structural analysis. Structural mechanics analysis needs input data such as structural loads, the structure's geometric representation and support conditions, and the materials' properties. Output quantities may include support reactions, stresses and displacements. Advanced structural mechanics may include the effects of stability and non-linear behaviors. Mechanics of structures is a field of study within applied mechanics that investigates the behavior of structures under mechanical loads, such as bending of a beam, buckling of a column, torsion of a shaft, deflection of a thin shell, and vibration of a bridge. There are three approaches to the analysis: the energy methods, flexibility method or direct stiffness ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mass Matrix
In analytical mechanics, the mass matrix is a symmetric matrix that expresses the connection between the time derivative \mathbf\dot q of the generalized coordinate vector of a system and the kinetic energy of that system, by the equation :T = \frac \mathbf^\textsf \mathbf \mathbf where \mathbf^\textsf denotes the transpose of the vector \mathbf. This equation is analogous to the formula for the kinetic energy of a particle with mass and velocity , namely :T = \frac m, \mathbf, ^2 = \frac \mathbf \cdot m\mathbf and can be derived from it, by expressing the position of each particle of the system in terms of . In general, the mass matrix depends on the state , and therefore varies with time. Lagrangian mechanics yields an ordinary differential equation (actually, a system of coupled differential equations) that describes the evolution of a system in terms of an arbitrary vector of generalized coordinates that completely defines the position of every particle in the system. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mirror Mount
A mirror mount is a device that holds a mirror. In optics research, these can be quite sophisticated devices, due to the need to be able to tip and tilt the mirror by controlled amounts, while still holding it in a precise position when it is not being adjusted. An optical mirror mount generally consists of a movable front plate which holds the mirror, and a fixed back plate with adjustment screws. Adjustment screws drive the front plate about the axes of rotation in the pitch (vertical) and yaw (horizontal) directions. An optional third actuator often enables z-axis translation. Precision mirror mounts can be quite expensive, and a notable amount of engineering goes into their design. Such sophisticated mounts are often required for lasers, interferometers, and optical delay lines. Types of mirror mount The most common type of mirror mount is the kinematic mount. This type of mount is designed according to the principles of kinematic determinacy. Typically, the movable fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Motion Bearing
A linear-motion bearing or linear slide is a bearing designed to provide free motion in one direction. There are many different types of linear motion bearings. Motorized linear slides such as machine slides, X-Y tables, roller tables and some dovetail slides are bearings moved by drive mechanisms. Not all linear slides are motorized, and non-motorized dovetail slides, ball bearing slides and roller slides provide low-friction linear movement for equipment powered by inertia or by hand. All linear slides provide linear motion based on bearings, whether they are ball bearings, dovetail bearings, linear roller bearings, magnetic or fluid bearings. X-Y tables, linear stages, machine slides and other advanced slides use linear motion bearings to provide movement along both X and Y multiple axis. Rolling-element bearing A rolling-element bearing is generally composed of a sleeve-like outer ring and several rows of balls retained by cages. The cages were originally machined from soli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statical Determinacy
In statics and structural mechanics, a structure is statically indeterminate when the static equilibrium equations force and moment equilibrium conditions are insufficient for determining the internal forces and reactions on that structure. Mathematics Based on Newton's laws of motion, the equilibrium equations available for a two-dimensional body are: : \sum \mathbf F = 0 : the vectorial sum of the forces acting on the body equals zero. This translates to: :: \sum \mathbf H = 0 : the sum of the horizontal components of the forces equals zero; :: \sum \mathbf V = 0 : the sum of the vertical components of forces equals zero; : \sum \mathbf M = 0 : the sum of the moments (about an arbitrary point) of all forces equals zero. In the beam construction on the right, the four unknown reactions are , , , and . The equilibrium equations are: : \begin \sum \mathbf V = 0 \quad & \implies \quad \mathbf V_A - \mathbf F_v + \mathbf V_B + \mathbf V_C = 0 \\ \sum \mathbf H = 0 \quad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Precision Engineering
Precision engineering is a subdiscipline of electrical engineering, software engineering, electronics engineering, mechanical engineering, and optical engineering concerned with designing machines, fixtures, and other structures that have exceptionally low tolerances, are repeatable, and are stable over time. These approaches have applications in machine tools, MEMS, NEMS, optoelectronics design, and many other fields. Overview Professors Hiromu Nakazawa and Pat McKeown provide the following list of goals for precision engineering: # Create a highly precise movement. # Reduce the dispersion of the product's or part's function. # Eliminate fitting and promote assembly, especially automatic assembly. # Reduce the initial cost. # Reduce the running cost. # Extend the life span. # Enable the design safety factor to be lowered. # Improve interchangeability of components so that corresponding parts made by other factories or firms can be used in their place. # Improve quality contro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinematic Coupling
Kinematic coupling describes fixtures designed to exactly constrain the part in question, providing precision and certainty of location. A canonical example of a kinematic coupling consists of three radial v-grooves in one part that mate with three hemispheres in another part. Each hemisphere has two contact points for a total of six contact points, enough to constrain all six of the part's degrees of freedom. An alternative design consists of three hemispheres on one part that fit respectively into a tetrahedral dent, a v-groove, and a flat. Background Kinematic couplings arose from the need of precision coupling between structural interfaces that were meant to be routinely taken apart and put back together. Kelvin Coupling The Kelvin coupling is named after William Thompson (Lord Kelvin) who published the design in 1868–71. It consists of three spherical surfaces that rest on a concave tetrahedron, a V-groove pointing towards the tetrahedron and a flat plate. The tetra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
