An Analytic Expression for the Inverse Involute
Joint Authors
Rosado, Alberto López
Muñoz, Federico Prieto
Fernández, Roberto Alvarez
Source
Mathematical Problems in Engineering
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-09-29
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
This article introduces new types of rational approximations of the inverse involute function, widely used in gear engineering, allowing the processing of this function with a very low error.
This approximated function is appropriate for engineering applications, with a much reduced number of operations than previous formulae in the existing literature, and a very efficient computation.
The proposed expressions avoid the use of iterative methods.
The theoretical foundations of the approximation theory of rational functions, the Chebyshev and Jacobi polynomials that allow these approximations to be obtained, are presented in this work, and an adaptation of the Remez algorithm is also provided, which gets a null error at the origin.
This way, approximations in ranges or degrees different from those presented here can be obtained.
A rational approximation of the direct involute function is computed, which avoids the computation of the tangent function.
Finally, the direct polar equation of the circle involute curve is approximated with some application examples.
American Psychological Association (APA)
Rosado, Alberto López& Muñoz, Federico Prieto& Fernández, Roberto Alvarez. 2019. An Analytic Expression for the Inverse Involute. Mathematical Problems in Engineering،Vol. 2019, no. 2019, pp.1-9.
https://search.emarefa.net/detail/BIM-1195197
Modern Language Association (MLA)
Rosado, Alberto López…[et al.]. An Analytic Expression for the Inverse Involute. Mathematical Problems in Engineering No. 2019 (2019), pp.1-9.
https://search.emarefa.net/detail/BIM-1195197
American Medical Association (AMA)
Rosado, Alberto López& Muñoz, Federico Prieto& Fernández, Roberto Alvarez. An Analytic Expression for the Inverse Involute. Mathematical Problems in Engineering. 2019. Vol. 2019, no. 2019, pp.1-9.
https://search.emarefa.net/detail/BIM-1195197
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1195197