The image curve of the motion of the planet in a spherical epicyclic gear train

Q. Ge; J. M. McCarthy

doi:10.1115/DETC1987-0101

The image curve of the motion of the planet in a spherical epicyclic gear train

Q. Ge
, J. M. McCarthy

Mechanical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

This paper uses the Euler parameters of the motion of t?e planet of a spherical epicyclic gear train to obtain. a curve on the surface of a hypersphere in four dimensions. This curve, called the image curve, represents the rotational motion of the planet as it rolls without slipping on the fixed gear. Two image curve~ are obtained for two different choices of moving and fixed reference frames and it is shown that they are related by an orthogonal transformation in four dimensional space. The differential properties of the image curve are computed and it is found that the curvature is constant and the torsion is periodic in the motion parameter. A reference position is chosen and the canonical frame and instantaneous invariants of the motion are determined in terms of the dimensions of the gear train.

Original language	English
Title of host publication	Robotics, Mechanisms, and Machine Systems
Publisher	American Society of Mechanical Engineers (ASME)
Pages	363-368
Number of pages	6
ISBN (Electronic)	9780791897744
DOIs	https://doi.org/10.1115/DETC1987-0101
State	Published - 1987
Event	ASME 1987 Design Technology Conferences, DETC 1987 - Boston, United States Duration: Sep 27 1987 → Sep 30 1987

Publication series

Name	Proceedings of the ASME Design Engineering Technical Conference
Volume	2

Conference

Conference	ASME 1987 Design Technology Conferences, DETC 1987
Country/Territory	United States
City	Boston
Period	09/27/87 → 09/30/87

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10.1115/DETC1987-0101

Cite this

@inproceedings{0e39ae46d7c04609b03081cf3627ed1a,

title = "The image curve of the motion of the planet in a spherical epicyclic gear train",

abstract = "This paper uses the Euler parameters of the motion of t?e planet of a spherical epicyclic gear train to obtain. a curve on the surface of a hypersphere in four dimensions. This curve, called the image curve, represents the rotational motion of the planet as it rolls without slipping on the fixed gear. Two image curve\textasciitilde{} are obtained for two different choices of moving and fixed reference frames and it is shown that they are related by an orthogonal transformation in four dimensional space. The differential properties of the image curve are computed and it is found that the curvature is constant and the torsion is periodic in the motion parameter. A reference position is chosen and the canonical frame and instantaneous invariants of the motion are determined in terms of the dimensions of the gear train.",

author = "Q. Ge and McCarthy, \{J. M.\}",

note = "Publisher Copyright: {\textcopyright} 1987 American Society of Mechanical Engineers (ASME). All rights reserved.; ASME 1987 Design Technology Conferences, DETC 1987 ; Conference date: 27-09-1987 Through 30-09-1987",

year = "1987",

doi = "10.1115/DETC1987-0101",

language = "English",

series = "Proceedings of the ASME Design Engineering Technical Conference",

publisher = "American Society of Mechanical Engineers (ASME)",

pages = "363--368",

booktitle = "Robotics, Mechanisms, and Machine Systems",

}

Ge, Q & McCarthy, JM 1987, The image curve of the motion of the planet in a spherical epicyclic gear train. in Robotics, Mechanisms, and Machine Systems. Proceedings of the ASME Design Engineering Technical Conference, vol. 2, American Society of Mechanical Engineers (ASME), pp. 363-368, ASME 1987 Design Technology Conferences, DETC 1987, Boston, United States, 09/27/87. https://doi.org/10.1115/DETC1987-0101

The image curve of the motion of the planet in a spherical epicyclic gear train. / Ge, Q.; McCarthy, J. M.
Robotics, Mechanisms, and Machine Systems. American Society of Mechanical Engineers (ASME), 1987. p. 363-368 (Proceedings of the ASME Design Engineering Technical Conference; Vol. 2).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - The image curve of the motion of the planet in a spherical epicyclic gear train

AU - Ge, Q.

AU - McCarthy, J. M.

PY - 1987

Y1 - 1987

N2 - This paper uses the Euler parameters of the motion of t?e planet of a spherical epicyclic gear train to obtain. a curve on the surface of a hypersphere in four dimensions. This curve, called the image curve, represents the rotational motion of the planet as it rolls without slipping on the fixed gear. Two image curve~ are obtained for two different choices of moving and fixed reference frames and it is shown that they are related by an orthogonal transformation in four dimensional space. The differential properties of the image curve are computed and it is found that the curvature is constant and the torsion is periodic in the motion parameter. A reference position is chosen and the canonical frame and instantaneous invariants of the motion are determined in terms of the dimensions of the gear train.

AB - This paper uses the Euler parameters of the motion of t?e planet of a spherical epicyclic gear train to obtain. a curve on the surface of a hypersphere in four dimensions. This curve, called the image curve, represents the rotational motion of the planet as it rolls without slipping on the fixed gear. Two image curve~ are obtained for two different choices of moving and fixed reference frames and it is shown that they are related by an orthogonal transformation in four dimensional space. The differential properties of the image curve are computed and it is found that the curvature is constant and the torsion is periodic in the motion parameter. A reference position is chosen and the canonical frame and instantaneous invariants of the motion are determined in terms of the dimensions of the gear train.

UR - https://www.scopus.com/pages/publications/85105384941

U2 - 10.1115/DETC1987-0101

DO - 10.1115/DETC1987-0101

M3 - Conference contribution

AN - SCOPUS:85105384941

T3 - Proceedings of the ASME Design Engineering Technical Conference

SP - 363

EP - 368

BT - Robotics, Mechanisms, and Machine Systems

PB - American Society of Mechanical Engineers (ASME)

T2 - ASME 1987 Design Technology Conferences, DETC 1987

Y2 - 27 September 1987 through 30 September 1987

ER -

The image curve of the motion of the planet in a spherical epicyclic gear train

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