scholarly journals Closure to “Discussion of ‘An Application of the Linkage Characteristic Polynomial to the Topological Synthesis of Epicyclic Gear Trains’” (1987, ASME J. Mech. Transm. Autom. Des., 109, p. 337)

1987 ◽  
Vol 109 (3) ◽  
pp. 337-337
Author(s):  
Lung-Wen Tsai
Keyword(s):  
Characteristic Polynomial ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Topological Synthesis

scholarly journals An Application of the Linkage Characteristic Polynomial to the Topological Synthesis of Epicyclic Gear Trains

1987 ◽  
Vol 109 (3) ◽  
pp. 329-336 ◽  
Author(s):  
Lung-Wen Tsai
Keyword(s):  
Characteristic Polynomial ◽  
Random Number ◽  
Degree Of Freedom ◽  
Characteristic Polynomials ◽  
Systematic Procedure ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Isomorphic Graphs ◽  
Topological Synthesis

In this paper, a random number technique for computing the value of a linkage characteristic polynomial is shown to be an effective method for identifying isomorphic graphs. The technique has been applied to the topological synthesis of one-degree-of-freedon, epicyclic gear trains with up to six links. All the permissible graphs of epicyclic gear trains were generated by a systematic procedure, and the isomorphic graphs were identified by comparing the values of their corresponding linkage characteristic polynomials. It is shown that there are 26 nonisomorphic rotation graphs and 80 displacement nonisomorphic graphs from which all the six-link, one-degree-of-freedom, epicyclic gear trains can be derived.

Topological Synthesis of Epicyclic Gear Trains Using Vertex Incidence Polynomial

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Vinjamuri Venkata Kamesh ◽  
Kuchibhotla Mallikarjuna Rao ◽  
Annambhotla Balaji Srinivasa Rao
Keyword(s):  
High Velocity ◽  
Mechanical Energy ◽  
Gear Train ◽  
Recursive Method ◽  
Gear Pair ◽  
Simple Method ◽  
Epicyclic Gear ◽  
Thick Line ◽  
Gear Trains ◽  
Isomorphic Graphs

Epicyclic gear trains (EGTs) are used in the mechanical energy transmission systems where high velocity ratios are needed in a compact space. It is necessary to eliminate duplicate structures in the initial stages of enumeration. In this paper, a novel and simple method is proposed using a parameter, Vertex Incidence Polynomial (VIP), to synthesize epicyclic gear trains up to six links eliminating all isomorphic gear trains. Each epicyclic gear train is represented as a graph by denoting gear pair with thick line and transfer pair with thin line. All the permissible graphs of epicyclic gear trains from the fundamental principles are generated by the recursive method. Isomorphic graphs are identified by calculating VIP. Another parameter “Rotation Index” (RI) is proposed to detect rotational isomorphism. It is found that there are six nonisomorphic rotation graphs for five-link one degree-of-freedom (1-DOF) and 26 graphs for six-link 1-DOF EGTs from which all the nonisomorphic displacement graphs can be derived by adding the transfer vertices for each combination. The proposed method proved to be successful in clustering all the isomorphic structures into a group, which in turn checked for rotational isomorphism. This method is very easy to understand and allows performing isomorphism test in epicyclic gear trains.

Systematic Synthesis and Applications of Novel Multi-Degree-of-Freedom Differential Systems

1992 ◽  
Author(s):  
Sridhar Kota ◽  
Srinivas Bidare
Keyword(s):  
Degrees Of Freedom ◽  
Building Blocks ◽  
Degree Of Freedom ◽  
Differential Systems ◽  
Practical Applications ◽  
Epicyclic Gear ◽  
Differential Mechanism ◽  
Long Time ◽  
Gear Trains ◽  
Drive Systems

Abstract A two-degree-of-freedom differential system has been known for a long time and is widely used in automotive drive systems. Although higher degree-of-freedom differential systems have been developed in the past based on the well-known standard differential, the number of degrees-of-freedom has been severely restricted to 2n. Using a standard differential mechanism and simple epicyclic gear trains as differential building blocks, we have developed novel whiffletree-like differential systems that can provide n-degrees of freedom, where n is any integer greater than two. Symbolic notation for representing these novel differentials is also presented. This paper presents a systematic method of deriving multi-degree-of-freedom differential systems, a three and four output differential systems and some of their practical applications.

Meshing Efficiency Analysis of Two Degree-of-Freedom Epicyclic Gear Trains

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Essam Lauibi Esmail
Keyword(s):  
Reference Frame ◽  
Power Efficiency ◽  
Power Flow ◽  
Flow Direction ◽  
Efficiency Analysis ◽  
Degree Of Freedom ◽  
Gear Train ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Two Degree Of Freedom

The concept of potential power efficiency is introduced as the efficiency of an epicyclic gear train (EGT) measured in any moving reference frame. The conventional efficiency can be computed in a carrier-moving reference frame in which the gear carrier appears relatively fixed. In principle, by attaching the reference frame to an appropriate link, torques can be calculated with respect to each input, output, or (relatively) fixed link in the EGT. Once the power flow direction is obtained from the potential power ratio, the torque ratios are obtained from the potential power efficiencies, the particular expression of the efficiency of the EGT is found in a simple manner. A systematic methodology for the efficiency analysis of one and two degree-of-freedom (DOF) EGTs is described, and 14 ready-to-use efficiency formulas are derived for 2DOF gear pair entities (GPEs). This paper includes also a discussion on the redundancy of the efficiency formulas used for 1DOF GPEs. An incomplete in the efficiency formulas in previous literature, which make them susceptible to wrong application, is brought to light.

Degeneracy Detection in Epicyclic Gear Trains Using a Matroid-Based Algorithm

2020 ◽  
pp. 11-18
Author(s):  
Fernando V. Morlin ◽  
Andrea Piga Carboni ◽  
Marina Baldissera de Souza ◽  
Daniel Martins
Keyword(s):  
Epicyclic Gear ◽  
Gear Trains ◽  
Degeneracy Detection

A New Method of Design of Epicyclic Gear Trains

2013 ◽  
Vol 457-458 ◽  
pp. 707-712
Author(s):  
Pei Wen An ◽  
Zhong Liang Lv
Keyword(s):  
New Method ◽  
Combination Method ◽  
Engineering Practice ◽  
Type Number ◽  
Practical Application ◽  
Kinematic Chains ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Number Synthesis ◽  
Method Of Design

Epicyclic gear trains have been broadly applied in engineering practice. In this paper, kinematic chains (K.C.) with single-joint (S.J.) were applied to innovative synthesis of the epicyclic gear trains. The method of the innovative synthesis of the epicyclic gear trains was presented. Not only the epicyclic gear trains in common uses were obtained, but some new types of epicyclic gear trains that are got difficultly by means of conventional combination method were gained. Thereby, a new way has been offered for the innovative synthesis of the epicyclic gear trains, at the same time, a way has also been offered for practical application of some multi-link kinematic chains gained by using the theory of type-number synthesis of the K.C. with S.J.. Examples show that the method presented in this paper is right and feasible, and the method is efficient and practical for the innovative synthesis of the epicyclic gear trains.

Nomographs for Enumeration of Clutching Sequences Associated With Epicyclic-Type Automatic Transmission Mechanisms

2008 ◽  
Author(s):  
Essam L. Esmail
Keyword(s):  
Automatic Transmission ◽  
Root Cause ◽  
Transmission Mechanisms ◽  
Epicyclic Gear ◽  
Angular Velocities ◽  
Gear Mechanism ◽  
Gear Trains ◽  
Exact Size ◽  
Algorithmic Techniques ◽  
Transmission Gear

A new methodology for the enumeration of feasible clutching sequences for a given epicyclic gear mechanism (EGM) is presented using the kinematic nomographs of epicyclic-type transmission mechanisms. From such nomographs, the kinematic characteristics of an epicyclic gear mechanism can be expressed in terms of the gear ratios of its gear pairs. From a single nomograph, the angular velocities for all of the coaxial links can be estimated and compared directly without specifying the exact size of each gear. In addition, the angular velocities can be arranged in a descending sequence without using complicated artificial intelligence or algorithmic techniques. Then, a procedure for the enumeration of feasible clutching sequences associated with a transmission mechanism composed of two or more fundamental gear entities (FGEs) is developed. The reliability of the methodology is established by applying it to two transmission gear trains for which solutions are either fully or partially available in the literature. In the process, an incomplete in the results reported in previous literature is brought to light. And the root cause of this incompleteness is explored. The present methodology is judged to be more efficient for enumeration of all feasible clutching sequences of an EGM.

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