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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.
The ball screw was invented independently by H.M. Stevenson and D. Glenn who were issued in 1898 patents 601,451 and 610,044 respectively. Early precise screwshafts were produced by starting with a low-precision screwshaft, and then lapping the shaft with several spring-loaded nut laps [citation needed].
A full turn of the thimble 12 rotates the nut sleeve 13 and its two threads (20 tpi outside and 25 tpi inside) to move the rod 1 / 20 - 1 / 25 = 0.01 in (0.25 mm) relative to the barrel. Differential screw illustration from an 1817 machine design handbook. ab & ef have one thread pitch while cd has a different one.
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]
Cutting a single helical groove into a screw-stock cylinder yields what is referred to as a single-thread screw. Similarly, one may construct a double-thread screw provided that the helix angle of the two cuts is the same, and that the second cut is positioned in the uncut material between the grooves of the first.
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.
Bearing pressure for a cylinder-cylinder contact. In the case of a revolute joint or of a hinge joint, there is a contact between a male cylinder and a female cylinder.The complexity depends on the situation, and three cases are distinguished:
The Acme thread was developed in 1894 as a profile well suited to power screws that has various advantages over the square thread, [note 1] which had been the form of choice until then. It is easier to cut with either single-point threading or die than the square thread is (because the latter's shape requires tool bit or die tooth geometry that ...
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