![]() ![]() ![]() Involute spline where the sides of the equally spaced grooves are involute, as with an involute gear, but not as tall. There are several types of splines: Parallel key spline where the sides of the equally spaced grooves are parallel in both directions, radial and axial. An alternative to splines is a keyway and key, though splines provide a longer fatigue life, and can carry significantly greater torques for the size. Adjacent images in the section below show a transmission input shaft with male splines and a clutch plate with mating female splines in the center hub, where the smooth tip of the axle would be supported in a pilot bearing in the flywheel (not pictured). On a drive shaft that matches with groove in a mating piece and transfer torque to it, maintaining the angular correspondence between them.įor instance, a gear mounted on a shaft might use a male spline on the shaft that matches the female spline on the gear. In this case, a spline is a piecewise polynomial function.Ridges or teeth on a drive shaft that transfer torque to interlocking components We begin by limiting our discussion to polynomials in one variable. ( February 2009) ( Learn how and when to remove this template message) There might be a discussion about this on the talk page. ![]() This article may be confusing or unclear to readers. For the rest of this section, we focus entirely on one-dimensional, polynomial splines and use the term "spline" in this restricted sense. For a number of meaningful definitions of the roughness measure, the spline functions are found to be finite dimensional in nature, which is the primary reason for their utility in computations and representation. Smoothing splines may be viewed as generalizations of interpolation splines where the functions are determined to minimize a weighted combination of the average squared approximation error over observed data and the roughness measure. Spline functions for interpolation are normally determined as the minimizers of suitable measures of roughness (for example integral squared curvature) subject to the interpolation constraints. The data may be either one-dimensional or multi-dimensional. The term "spline" is used to refer to a wide class of functions that are used in applications requiring data interpolation and/or smoothing. The term spline comes from the flexible spline devices used by shipbuilders and draftsmen to draw smooth shapes. 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. In the computer science subfields of computer-aided design and computer graphics, the term spline more frequently refers to a piecewise polynomial ( parametric) curve. In interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, even when using low degree polynomials, while avoiding Runge's phenomenon for higher degrees. In mathematics, a spline is a special function defined piecewise by polynomials. Triple knots at both ends of the interval ensure that the curve interpolates the end points Single knots at 1/3 and 2/3 establish a spline of three cubic polynomials meeting with C 2 parametric continuity. ![]()
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