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Screw theory is the algebraic calculation of pairs of vectors, also known as dual vectors [1] – such as angular and linear velocity, or forces and moments – that arise in the kinematics and dynamics of rigid bodies. [2] [3]
A screw axis is associated with each pair of vectors in the algebra of screws, also known as screw theory. [3] The spatial movement of a body can be represented by a continuous set of displacements. Because each of these displacements has a screw axis, the movement has an associated ruled surface known as a screw surface.
Principal view of the pumping action of a twin-screw pump with a six-lobe female screw and a five-lobe male screw. A compressor (as opposed to a pump) would be shaped the same way, except that the shape of the lobes would change along the length of the screw, so that the volume of the trapped pockets would get squeezed smaller as they get closer to the exhaust port.
The screw was also apparently applied to drilling and moving materials (besides water) around this time, when images of augers and drills began to appear in European paintings. [12] The complete dynamic theory of simple machines, including the screw, was worked out by Italian scientist Galileo Galilei in 1600 in Le Meccaniche ("On Mechanics").
The Newton–Euler equations are used as the basis for more complicated "multi-body" formulations (screw theory) that describe the dynamics of systems of rigid bodies connected by joints and other constraints. Multi-body problems can be solved by a variety of numerical algorithms.
The screw thread concept seems to have occurred first to Archimedes, who briefly wrote on spirals as well as designed several simple devices applying the screw principle. Leonardo da Vinci understood the screw principle, and left drawings showing how threads could be cut by machine. In the 1500s, screws appeared in German watches, and were used ...
The screw pump is the oldest positive displacement pump. [1] The first records of a water screw, or screw pump, date back to Hellenistic Egypt before the 3rd century BC. [1] [3] The Egyptian screw, used to lift water from the Nile, was composed of tubes wound round a cylinder; as the entire unit rotates, water is lifted within the spiral tube to the higher elevation.
FACT combines principles of screw theory, linear algebra, projective geometry, and exact-constraint design. The methodology employs a library of vector spaces derived from these principles and represented by geometric shapes. These shapes are categorized into freedom spaces, constraint spaces, and actuation spaces, each serving a unique purpose ...