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A plane curve with non-vanishing curvature has zero torsion at all points. Conversely, if the torsion of a regular curve with non-vanishing curvature is identically zero, then this curve belongs to a fixed plane. The curvature and the torsion of a helix are constant. Conversely, any space curve whose curvature and torsion are both constant and ...
A curve is called a general helix or cylindrical helix [4] if its tangent makes a constant angle with a fixed line in space. A curve is a general helix if and only if the ratio of curvature to torsion is constant. [5] A curve is called a slant helix if its principal normal makes a constant angle with a fixed line in space. [6]
The normal curvature, k n, is the curvature of the curve projected onto the plane containing the curve's tangent T and the surface normal u; the geodesic curvature, k g, is the curvature of the curve projected onto the surface's tangent plane; and the geodesic torsion (or relative torsion), τ r, measures the rate of change of the surface ...
Torsion of a square section bar Example of torsion mechanics. In the field of solid mechanics, torsion is the twisting of an object due to an applied torque [1] [2].Torsion could be defined as strain [3] [4] or angular deformation [5], and is measured by the angle a chosen section is rotated from its equilibrium position [6].
In mathematics, a conical spiral, also known as a conical helix, [1] is a space curve on a right circular cone, whose floor projection is a plane spiral. If the floor projection is a logarithmic spiral , it is called conchospiral (from conch ).
A space curve; the vectors T, N, B; and the osculating plane spanned by T and N. In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space, or the geometric properties of the curve itself irrespective of any motion.
The torsion form, an alternative characterization of torsion, applies to the frame bundle FM of the manifold M. This principal bundle is equipped with a connection form ω , a gl ( n )-valued one-form which maps vertical vectors to the generators of the right action in gl ( n ) and equivariantly intertwines the right action of GL( n ) on the ...
The efficiency can be plotted versus the helix angle for a constant friction, as shown in the adjacent diagram. The maximum efficiency is a helix angle between 40 and 45 degrees, however a reasonable efficiency is achieved above 15°. Due to difficulties in forming the thread, helix angle greater than 30° are rarely used.