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Important theorems of screw theory include: the transfer principle proves that geometric calculations for points using vectors have parallel geometric calculations for lines obtained by replacing vectors with screws; [1] Chasles' theorem proves that any change between two rigid object poses can be performed by a single screw; Poinsot's theorem ...
The capstan equation [1] or belt friction equation, also known as Euler–Eytelwein formula [2] (after Leonhard Euler and Johann Albert Eytelwein), [3] relates the hold-force to the load-force if a flexible line is wound around a cylinder (a bollard, a winch or a capstan).
As an example, using a block and tackle with six rope sections and a 600 lb load, the operator of an ideal system would be required to pull the rope six feet and exert 100 lb F of force to lift the load one foot. Both the ratios F out / F in and V in / V out show that the IMA is six. For the first ratio, 100 lb F of force input results in 600 ...
Stress–strength analysis is the analysis of the strength of the materials and the interference of the stresses placed on the materials, where "materials" is not necessarily the raw goods or parts, but can be an entire system. Stress-Strength Analysis is a tool used in reliability engineering.
Strength depends upon material properties. The strength of a material depends on its capacity to withstand axial stress, shear stress, bending, and torsion.The strength of a material is measured in force per unit area (newtons per square millimetre or N/mm², or the equivalent megapascals or MPa in the SI system and often pounds per square inch psi in the United States Customary Units system).
Graph of Johnson's parabola (plotted in red) against Euler's formula, with the transition point indicated. The area above the curve indicates failure. The Johnson parabola creates a new region of failure. In structural engineering, Johnson's parabolic formula is an empirically based equation for calculating the critical buckling stress of a column.
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Where L e is the thread engagement length, A t is the tensile stress area, D is the major diameter of the screw, and p is the pitch. This equation only holds true if the screw and female thread materials are the same. If they are not the same, then the following equations can be used to determine the additional thread length that is required: [14]