Teaching Planetary Gear Trains with the Aid of Nomographs

Abstract

Planetary gear trains (PGTs) are introduced to undergraduate mechanical engineering students in the course of eory of Machines. e complexity of the traditional methods for analyzing PGTs has kept many from becoming familiar with the capability of PGTs in mechanisms and machine design. In this paper a uni�ed general formulation for simultaneously visualizing velocities, torques, and power �ow through a train is presented on a single nomograph. erefore, the increasing complex mechanical systems, such as automotive transmissions, are much easier to understand. Nomographs of Fundamental Gear Entities (FGEs) are constructed based on the nomographs of their fundamental circuits, without specifying the exact gear dimensions. ey are then uni�ed in one system nomograph. Nomographs are promising to provide designers with an efficient tool for the design of geared mechanisms.

Power Flow in Coupled Three-Row Series-Parallel Planetary Gear System, Part I: Without Power Losses

“…In practice, the Willis formula [12][13][14][15][16][17]163,178] is often used for this purpose, although graph methods (linear, contour, signal flow, bond graphs, matroids, and hypergraphs) are gaining more and more recognition, thanks to their advantages [143,162,[164][165][166][167][168][169][171][172][173][174][175][176][177][179][180][181][182][183][184][185][186]189,192,194]. The nomograph method and, especially, the lever analogy are also promising as universal methods for kinematics, statics, and power flow analysis of the most complex PSHEV planetary transmission [88,[118][119][120][121]126,[128][129][130]160,161,164,188]. The...…”

A universal kinematic analysis of geared mechanisms

“…2a contains five GPEs: two internal GPEs (7,2,3) and (7,11,3), and three external GPEs (7, 1, 3), (7,8,3), and (8,5,3), while the simple planetary gear train shown in Fig. 2b contains three GPEs: one internal GPE (9, 4, 5) and two external GPEs (9, 1, 5) and (9,14,5). The Humbage bevel gear train shown in Fig.…”

“…The following review on the kinematic of PGTs cannot be considered complete since a review of all contributions in this field is not the objective of this work. Many efforts are made to develop effective approaches to the kinematic analysis of PGTs [1][2][3][4][5][6]. Freudenstein et al [7] used efficiently the concept of fundamental circuit for the kinematic of PGTs.…”