Estudio de las curvas epicicloide y evolvente para formar el perfil de los engranajes que operan con distancia entre centros variable. // Study of the epicycloid and involute curves to form the profile of gears with variable center distance.

Authors

  • L. I. Negrín Hernández Departamento de Mecánica Aplicada y Dibujo, Facultad de Ing. Mecánica Universidad Central de Las Villas “Marta Abreu”, Santa Clara, Cuba. Telef: 53-422-81630, FAX: 53-422-81608
  • R. Franco Rodríguez Departamento de Mecánica Aplicada y Dibujo, Facultad de Ing. Mecánica Universidad Central de Las Villas “Marta Abreu”, Santa Clara, Cuba. Telef: 53-422-81630, FAX: 53-422-81608

Abstract

En este trabajo se realiza un estudio de las curvas epicicloidales y evolventes de círculo en sus formas generales, con el
objetivo de formar el perfil de trabajo de los dientes de los engranajes que operan con distancia entre centros variable. Se
parte de las expresiones generales de estas curvas y se desarrollan las fórmulas para determinar algunas propiedades de las
mismas, como el radio de curvatura, la involuta, etc. Aquí se realiza también la demostración de que la evolvente de círculo
es un caso particular de la epicicloide, demostración que no aparece en la literatura especializada. Con posterioridad se hace
una comparación teniendo en cuenta las propiedades cinemáticas de los engranajes formados por las diferentes curvas.
Como conclusiones del trabajo se plantea que la evolvente de círculo común tiene las mejores propiedades para engranajes
que trabajan con una variación de la distancia entre centros menor que el 5 %, mientras que la epicicloide alargada
garantiza un mejor funcionamiento para engranajes que trabajen con una variación entre el 5 y el 10 %.


Palabras claves: epicicloide, involuta, diente de engranaje, geometría de engranaje.

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Abstract:
In this work is carried out a study of the epicycloid and circle involutes curves in their general forms, with the objective of
forming the working profile of the gear teeth that operate with variable center distance. From the general expressions of
these curves and the formulas are developed formulae to determine some of their properties, as the curvature radius, the
involute, etc. It is also carried out the demonstration that the circle involute is a peculiar case of the epicycloid,
demonstration that does not appear in the specialized literature. Moreover, a comparison is made keeping in mind the
kinematics properties of gears formed by the different curves. As conclusions of the work is stated that the common circle
involute has the best properties for gears working with a variation of the center distance minor that 5%, while the extended
epicycloid guarantees a better operation for gears working with a variation between the 5 and 10%.


Key Words: epicycloid, involute, teeth working profile, gears teeth, gear geometry.

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How to Cite

1.
Negrín Hernández LI, Franco Rodríguez R. Estudio de las curvas epicicloide y evolvente para formar el perfil de los engranajes que operan con distancia entre centros variable. // Study of the epicycloid and involute curves to form the profile of gears with variable center distance. Ing. Mec. [Internet]. 2007 Sep. 1 [cited 2025 Sep. 13];10(3):71-6. Available from: https://ingenieriamecanica.cujae.edu.cu/index.php/revistaim/article/view/142

Issue

Vol. 10 No. 3 (2007): september-december

Section

Original article

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