Manual

TEACHING PLANETARY GEAR TRAINS WITH THE AID OF
NOMOGRAPHS
ESSAM LAUIBI ESMAIL
Lecturer
College of Engineering/University of Qadisyah

ABSTRACT
Planetary gear trains (PGTs) are introduced to undergraduate mechanical engineering students in the course of Theory of Machines. The 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 unified general formulation for simultaneously visualizing velocities, torques and power flow through a train is presented on a single nomograph. Therefore, the increasing complex mechanical systems, such as automotive transmissions, are much easier to understand. Nomographs of Fundemental Gear Entities (FGEs) are constructed based on the nomographs of their fundamental circuits, without specifying the exact gear dimensions. They are then unified in one system nomograph. Nomographs are promising to provide designers an efficient tool for the design of geared mechanisms.
KEYWORDS: Fundamental Circuit, Fundamental Geared Entity, Graph Theory,
Mechanisms, Nomograph, Power Flow, Planetary Gear trains, One-Degree of Freedom.
NOMENCLATURE
B
Brake
C
Clutch
E
Distance from origin to the point of intersection of the horizontal axis connecting the zeros of the three axes of a nomograph with the straight line passing through operating velocities of a fundamental circuit
EGM
Epicyclic gear mechanism
EGT
Epicyclic gear train
FC k k th Fundamental circuit
FGE
Fundamental gear entity
GKC
Geared kinematic chain
Gear ratio defined by a planet gear p with respect to a sun or ring gear x.
N p,x
N p , x = ± Z p / Z x , where Z p and Z x denote the numbers of teeth on

OWC
PGT
z

R x,y
S

the planet and the sun or ring gear, respectively, and the positive or negative signs depend on whether x is a ring or sun gear.
One way clutch
Planetary gear train
Velocity ratio between links x and y with

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