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The hinge theorem holds in Euclidean spaces and more generally in simply connected non-positively curved space forms.. It can be also extended from plane Euclidean geometry to higher dimension Euclidean spaces (e.g., to tetrahedra and more generally to simplices), as has been done for orthocentric tetrahedra (i.e., tetrahedra in which altitudes are concurrent) [2] and more generally for ...
A twist-hinge dissection is one which use a three-dimensional "hinge" which is placed on the edges of pieces rather than their vertices, allowing them to be "flipped" three-dimensionally. [ 10 ] [ 11 ] As of 2002, the question of whether any two polygons must have a common twist-hinged dissection remains unsolved.
This means if the influence line for a reaction is asked for, simply start by pretending the beam is no longer attached to the reaction in question and is free to rotate about the other support. If the influence line for a moment is desired, pretend the point in question is a hinge and the subsequent two sides can rotate about their supports.
In case of four-bar linkage coupler cognates, the Roberts–Chebyshev Theorem, after Samuel Roberts and Pafnuty Chebyshev, [1] states that each coupler curve can be generated by three different four-bar linkages. These four-bar linkages can be constructed using similar triangles and parallelograms, and the Cayley diagram (named after Arthur ...
In the study of mechanisms, a four-bar linkage, also called a four-bar, is the simplest closed-chain movable linkage.It consists of four bodies, called bars or links, connected in a loop by four joints.
A M/EI diagram is a moment diagram divided by the beam's Young's modulus and moment of inertia. To make use of this comparison we will now consider a beam having the same length as the real beam, but referred here as the "conjugate beam." The conjugate beam is "loaded" with the M/EI diagram derived from the load on the real beam.
Himmelblau's function-- Hindley–Milner type system-- Hindmarsh–Rose model-- Hindu–Arabic numeral system-- Hindu units of time-- Hindustani numerals-- Hinge theorem-- Hinged dissection-- Hippopede-- Hiptmair–Xu preconditioner-- Hironaka decomposition-- Hironaka's example-- Hiroshima Mathematical Journal-- Hiroyuki Goto-- Hirsch ...
Macaulay's method (the double integration method) is a technique used in structural analysis to determine the deflection of Euler-Bernoulli beams.Use of Macaulay's technique is very convenient for cases of discontinuous and/or discrete loading.