Cam design by hyperbolic spline functions of fourth order

1999 ◽  
Vol 10 (4) ◽  
pp. 245-263
Author(s):  
L Kohaupt
Keyword(s):  
Fourth Order ◽  
Spline Functions ◽  
Cam Design

scholarly journals Bernstein Polynomials

2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Anandaram Mandyam N
Keyword(s):  
Fourth Order ◽  
Bernstein Polynomials ◽  
Basis Functions ◽  
Spline Functions ◽  
Bezier Curves ◽  
Bézier Curves ◽  
B Splines

Bernstein polynomials (aka, B-polys) have excellent properties allowing them to be used as basis functions in many applications of physics. In this paper, a brief tutorial description of their properties is given and then their use in obtaining B-polys, B-splines or Basis spline functions, Bezier curves and ODE solution curves, is computationally demonstrated.  An example is also described showing their application to solving a fourth-order BVP relating to the bending at the free end of a cantilever.

An Evaluation of Spline Functions for use in Cam Design

1985 ◽  
Vol 199 (3) ◽  
pp. 239-248 ◽  
Author(s):  
B L MacCarthy ◽  
N D Burns
Keyword(s):  
Polynomial Spline ◽  
Spline Functions ◽  
Design Problems ◽  
Quintic Spline ◽  
B Spline ◽  
Cam Design ◽  
Piecewise Function ◽  
Standard Design ◽  
Kinematic Motion ◽  
Special Case

This paper shows how spline functions can be employed for kinematic motion specification in cam design. The polynomial spline is introduced as a special case of a continuous piecewise function. Cubic and quintic splines are derived and their properties are discussed in the cam design context. It is shown how standard cam laws can be approximated extremely accurately with a small number of points and appropriate boundary conditions. The modified sinusoidal acceleration cam law is used as an example. The application of quintic splines to non-standard and special motions is discussed. The algebraic and B-spline representations of spline functions are compared. The former is considered preferable in this context and a list of useful algorithms is given. The real power of the spline function, in particular the algebraic quintic spline, is its simplicity, ease of computation and adaptability to non-standard design problems. The use of parametrized, deficient and exponential splines is proposed for specific applications.

scholarly journals Quasi-Interpolation in a Space of C2 Sextic Splines over Powell–Sabin Triangulations

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2276
Author(s):  
Salah Eddargani ◽  
María José Ibáñez ◽  
Abdellah Lamnii ◽  
Mohamed Lamnii ◽  
Domingo Barrera
Keyword(s):  
Fourth Order ◽  
Interior Point ◽  
Small Area ◽  
Spline Functions ◽  
Interpolation Operators ◽  
Marsden’S Identity

In this work, we study quasi-interpolation in a space of sextic splines defined over Powell–Sabin triangulations. These spline functions are of class C2 on the whole domain but fourth-order regularity is required at vertices and C3 regularity is imposed across the edges of the refined triangulation and also at the interior point chosen to define the refinement. An algorithm is proposed to define the Powell–Sabin triangles with a small area and diameter needed to construct a normalized basis. Quasi-interpolation operators which reproduce sextic polynomials are constructed after deriving Marsden’s identity from a more explicit version of the control polynomials introduced some years ago in the literature. Finally, some tests show the good performance of these operators.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

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