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

Abstract

In the present work, the concept of 'Max Code' approach is used for establishing identification code of planetary gear spur trains. Such a representation provides an expression rather than an unique number. An attempt is made here to establish these expressions for distinct single and two degrees of freedom planetary gear trains. The concept of maximum code (Max Code), as a canonical number is to introduce a symbolic notation for describing two degrees of freedom spur planetary gear trains with the configuration of two central gears, one carrier or arm and at least one planet gear. Properties of canonical number, relevant to kinematic chains, are discussed and an algorithm based on one available in graph theoretic literature exemplifying for establishment of maximum codes of planetary gear-trains. The maximum code being unique and decodable and promises in cataloguing (store and retrieval) of planetary gear trains.

Topological Synthesis of Planetary Gear Trains

“…Chatterjee and Tsai [8] compared some conventional graph representation and used basic kinematic units to combine planetary mechanisms. Other synthetic methods includes: max code [9] , kinematic fractionation [10][11][12] , graph theory based on loops [13][14] , genetic algorithm [15] , simplified structural graph and structural chain graph [16] , kinematic chain graph [17] , etc.…”

“…References [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], which are associated with the characteristic of gear trains (e.g. the characteristic of the structural components, kinetic characteristics, etc.…”

Classification and Synthesis of Planetary Gear Trains

“…But they contain less the characteristics of the integral structure of planetary mechanisms. On the other hand, general synthesis methods about PGTs are: structural graph and chain [1], innovated synthetic method based on kinematic chain [4], graph based on the description of kinematic characteristics [5], canonical number [6], topological graph by using kinematic fractionation [7][8][9], the graphic means using loops [10][11], etc. In reference [4], An Peiwen and Huang Maolin put forward the structural principle and synthesis corresponding method; they also found that PGTs can be obtained by the evolvement of single and compound chains.…”