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Splines are popular curves in these subfields because of the simplicity of their construction, their ease and accuracy of evaluation, and their capacity to approximate complex shapes through curve fitting and interactive curve design. The term spline comes from the flexible spline devices used by shipbuilders and draftsmen to draw smooth shapes.
A spline is a ridge or tooth [1] [2] [3] on a drive shaft that matches with a groove in a mating piece and transfers torque to it, maintaining the angular correspondence between them. For instance, a gear mounted on a shaft might use a male spline on the shaft that matches the female spline on the gear.
In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. That is, instead of fitting a single, high-degree polynomial to all of the values at once, spline interpolation fits low-degree polynomials to small subsets of the ...
A B-spline function is a combination of flexible bands that is controlled by a number of points that are called control points, creating smooth curves. These functions are used to create and manage complex shapes and surfaces using a number of points. B-spline function and Bézier functions are applied extensively in shape optimization methods. [5]
The major axis of the flex spline's ellipse rotates with wave generator, so the points where the teeth mesh revolve around the center point at the same rate as the wave generator's shaft. The key to the design of the strain wave gear is that there are fewer teeth (often for example two fewer) on the flex spline than there are on the circular ...
Bézier surfaces are a species of mathematical spline used in computer graphics, computer-aided design, and finite element modeling. As with Bézier curves, a Bézier surface is defined by a set of control points. Similar to interpolation in many respects, a key difference is that the surface does not, in general, pass through the central ...
A spline. A spline consists of a long strip fixed in position at a number of points whose tension creates a smooth curve passing through those points, for the purpose of transferring that curve to another material. [1] Before computers were used for creating engineering designs, drafting tools were employed by designers drawing by hand. [2]
The coupling is defined by the groove count, the outer diameter of the cylindrical feature, the bottom angle of the grooves (to the axis of the cylindrical feature), and their depth. Hirth joints are designed as mating pairs and, unlike splines, there is no standardised off-the-shelf sizing system for them.