Symbolic Notation and Kinematic Equations of Motion of the Twenty-Two Basic Spur Planetary Gear Trains

Abstract

This paper introduces a symbolic notation for describing two degree-of-freedom spur planetary gear trains with the configuration of two central gears, one carrier or arm, and at least one planet gear. This simple notation is then used to write the kinematic equation of motion for this type of planetary gear train without the need to develop any intermediate equations. It is also shown that, there are exactly 22 basic spur planetary gear trains with this configuration and not 34 as Levai [1] previously found. These 22 planetary gear trains are illustrated along with their symbolic notation and kinematic equation of motion.

Symbolic Notation of Planetary Gear Trains by Canonical Number Approach (Max Code)

“…A scheme of symbolic notations proposed by Gibson and Kramer [7] is used for identifying the type of gear pair (internal, external, compound, etc.). According to this capital letter 'E' is used to central external gear and the capital letter 'I' is used to denote a central internal gear.…”

“…Concept of symbolic notations, by Gibson and Kramer [7], is converted for getting more powerful codes with 'Max Code' concept.…”

Nomographs for Kinematics, Statics and Power Flow Analysis of Epicyclic Gear Trains

“…1. For the kinematic analysis of epicyclic gear trains (EGMs), various approaches such as the relative velocity method [3][4][5], energy method [6], bond graph method [7], vector-loop method [8,9] and the nomograph method [10][11][12] have been proposed. Freudenstein and Yang [13] introduced the concept of fundamental circuit to analyze EGTs.…”

Teaching Planetary Gear Trains with the Aid of Nomographs

“…Any straight line through the input operating velocities of the EGT will intersect other axes at the operating velocities of the links representing those axes. To compare the results of this methodology with others [2,[4][5][6][7][8][9][10], algebraic expressions for the velocity ratios of this FGE can be written as follows: …”

“…For the kinematic analysis of EGMs, various approaches such as the relative velocity method [3][4][5], energy method [6], bond graph method [7], vector-loop method [8,9], and the nomograph method [10][11][12] have been proposed. Freudenstein and Yang [13] introduced the concept of fundamental circuit to analyze EGTs.…”