Simplified Kinematic Analysis of Bevel Epicyclic Gear Trains With Application to Power-Flow and Efficiency Analyses

2005 ◽  
Vol 127 (2) ◽  
pp. 278-286 ◽  
Author(s):  
Carl A. Nelson ◽  
Raymond J. Cipra
Keyword(s):  
Graph Theory ◽  
Kinematic Analysis ◽  
Power Flow ◽  
Computer Software ◽  
Input And Output ◽  
Automatic Transmissions ◽  
Epicyclic Gear ◽  
Analysis Technique ◽  
Angular Velocities ◽  
Gear Trains

A kinematic analysis technique is introduced to find the angular velocities of all links in bevel epicyclic gear trains. The method relies on previous work in graph theory. It improves on existing techniques used for analysis of planar geared mechanisms in its ability to accurately solve the kinematics of spatial geared mechanisms, particularly bevel gear trains, in a simpler manner. Usefulness of the method is demonstrated through its application to power-flow and efficiency analyses as well as its implementation in computer software. This discussion is limited to gear trains whose input and output axes are collinear, such as automotive automatic transmissions.

scholarly journals Kinematic Analysis of Tendon-Driven Robotic Mechanisms Using Graph Theory

1989 ◽  
Vol 111 (1) ◽  
pp. 59-65 ◽  
Author(s):  
Lung-Wen Tsai ◽  
Jyh-Jone Lee
Keyword(s):  
Graph Theory ◽  
Kinematic Analysis ◽  
Graph Representation ◽  
Kinematic Structure ◽  
Kinematic Chains ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Robotic Devices

The kinematic structure of tendon-driven robotic mechanisms has been investigated with the aid of graph theory. The correspondence between the graph representation of the kinematic structure and the mechanism has been established. We have shown that the kinematic structure of tendon-driven kinematic chains is similar to that of epicyclic gear trains. We also have shown that, using the concept of fundamental circuits, the displacement equations of tendon-driven robotic mechanisms can be systematically derived from the kinematic structure. The theory has been demonstrated by the kinematic analysis of three articulated robotic devices.

Application of Matroid Method in Kinematic Analysis of Parallel Axes Epicyclic Gear Trains

2006 ◽  
Vol 128 (6) ◽  
pp. 1307-1314 ◽  
Author(s):  
Ilie Talpasanu ◽  
T. C. Yih ◽  
P. A. Simionescu
Keyword(s):  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Oriented Graph ◽  
General Applicability ◽  
Epicyclic Gear ◽  
Angular Velocities ◽  
Gear Trains ◽  
Transfer Method ◽  
Cycle Matroid ◽  
Mobile Links

A novel method for kinematic analysis of parallel-axes epicyclic gear trains is presented, called the incidence and transfer method, which uses the incidence matrices associated with the edge-oriented graph associated to the mechanism and the transfer joints (teeth contact joints). Relative to such joints, a set of independent equations can be generated for calculating the angular positions, velocities, and accelerations. Complete kinematic equations are obtained in matrix form using a base of circuits from a cycle matroid. The analysis uses the relationships between the number of mobile links, number of joints, and number of circuits in the base of circuits, together with the Latin matrix (whose entries are function of the absolute values of the partial gear ratios of the transmission). Calculating the rank of the Latin matrix can identify singularities, like groups of gears that rotate as a whole. Relationships between the output and input angular velocities and accelerations are then determined in a matrix-based approach without using any derivative operations. The proposed method has general applicability and can be employed for systems with any number of gears and degrees of freedom, as illustrated by the numerical examples presented.

A Simplified Approach for Force and Power-Flow Analysis of Compound Epicyclic Spur-Gear Trains

1992 ◽  
Author(s):  
L. Saggere ◽  
D. G. Olson
Keyword(s):  
Graph Theory ◽  
Kinematic Analysis ◽  
Power Flow ◽  
Flow Analysis ◽  
Spur Gear ◽  
Gear Train ◽  
Force Analysis ◽  
Power Flow Analysis ◽  
Torque Analysis ◽  
Gear Trains

Abstract After conceptual design and dimensional synthesis of a compound epicyclic gear train (EGT), its performance evaluation involves kinematic analysis, force analysis, torque analysis, and power-flow analysis. In recent years, graph theory has proven to be a powerful symbolic representation for design of mechanisms. Application of graph theory for the topological representation and kinematic analysis of EGTs is quite well established. However, graph theory based methods for power-flow and force analysis lack certain features, making them unsuitable or difficult to implement in a general purpose program for automatic design of EGTs. The traditional approach has been to perform force and torque analysis first, and then use the results to perform power-flow analysis. This paper presents a novel, systematic approach in which power-flow analysis is performed first, and then the results are used to determine the inter-link forces in epicyclic spur-gear trains. This method is based only on the graph of the gear-train and the angular velocities of the elements, and hence, is more suitable for automatic computation, simpler to implement in a program, and also avoids requiring the formulation of tedious torque equilibrium equations. A numerical example is presented to illustrate the simplicity and generality of the method.

Similarity and Equivalence of Nutating Mechanisms to Bevel Epicyclic Gear Trains

2003 ◽  
Author(s):  
Carl A. Nelson ◽  
Raymond J. Cipra
Keyword(s):  
Kinematic Analysis ◽  
Power Flow ◽  
Bevel Gear ◽  
Static Force ◽  
Main Motivation ◽  
Kinematic Characteristics ◽  
Epicyclic Gear ◽  
Speed Reducer ◽  
Gear Trains

This paper addresses similarities between various nutating or wobbling mechanisms, especially kinematic similarities. A case is made for the generalization of several mechanisms into a mechanism “class” having common kinematic characteristics. This mechanism class is shown to be typified by bevel epicyclic gear trains. It is proposed that not only kinematic analysis, but static-force, power-flow, and efficiency analyses of mechanisms belonging to this “class” can be simplified by modeling them as bevel-gear trains. Simplified kinematic, force, and efficiency analyses are demonstrated for a novel wobbling speed reducer using this concept of “equivalent” geared mechanisms. The reduction in complexity of these analyses is the main motivation for this work.

A review of graph theory application research in gears

2015 ◽  
Vol 230 (10) ◽  
pp. 1697-1714 ◽  
Author(s):  
Hui-Ling Xue ◽  
Geng Liu ◽  
Xiao-Hui Yang
Keyword(s):  
Graph Theory ◽  
Power Flow ◽  
Planetary Gear ◽  
Mechanical Efficiency ◽  
Gear Train ◽  
Synthesis Process ◽  
Epicyclic Gear ◽  
Analysis And Synthesis ◽  
Theory Application ◽  
Gear Trains

Graph theory has been applied to gear train analysis and synthesis for many years, and it is an effective and systematic modeling approach in the design process of gear transmission. Based on more than 100 references listed in this paper, a review about the graph-based method for kinematic and static force analysis, power flow, and mechanical efficiency computation is presented. The method is based on the concept of fundamental circuit corresponding to a basic epicyclic gear train. A 1-dof epicyclic gear train and a two-stage planetary gear train are used to illustrate the application of this method. Besides, isomorphism identification in the synthesis process and enumeration of 1-dof epicyclic gear train graphs are surveyed particularly. Also, the computerized methods for detection of redundant gears and degenerate structures in epicyclic gear trains are reviewed, respectively.

Similarity and Equivalence of Nutating Mechanisms to Bevel Epicyclic Gear Trains for Modeling and Analysis

2005 ◽  
Vol 127 (2) ◽  
pp. 269-277 ◽  
Author(s):  
Carl A. Nelson ◽  
Raymond J. Cipra
Keyword(s):  
Kinematic Analysis ◽  
Power Flow ◽  
Similarity Index ◽  
Static Force ◽  
Modeling And Analysis ◽  
Epicyclic Gear ◽  
Speed Reducer ◽  
Gear Trains ◽  
Degree Of Similarity

This paper addresses similarities between various nutating or wobbling mechanisms, in particular kinematic similarities. A case is made for the generalization of these mechanisms into a mechanism “class” having common kinematic characteristics, which is typified by bevel epicyclic gear trains. A similarity index is proposed to describe the quality of kinematic similarity, with the best degree of similarity termed “equivalence.” It is proposed that kinematic analysis of mechanisms belonging to this “class” can be simplified by modeling them as bevel-gear trains, and that static-force, power-flow, and efficiency analyses can also be greatly simplified in the case of “equivalent” mechanisms. Simplified kinematic, force, and efficiency analyses are demonstrated for a unique wobbling speed reducer using this new concept of equivalent geared mechanisms.

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.

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.

Generation of Epicyclic Gear Trains of One Degree of Freedom

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Y. V. D. Rao ◽  
A. C. Rao
Keyword(s):  
Graph Theory ◽  
Adjacency Matrix ◽  
Kinematic Chain ◽  
Planetary Gear ◽  
Degree Of Freedom ◽  
Planetary Gear Trains ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Hamming Matrix

New planetary gear trains (PGTs) are generated using graph theory. A geared kinematic chain is converted to a graph and a graph in turn is algebraically represented by a vertex-vertex adjacency matrix. Checking for isomorphism needs to be an integral part of the enumeration process of PGTs. Hamming matrix is written from the adjacency matrix, using a set of rules, which is adequate to detect isomorphism in PGTs. The present work presents the twin objectives of testing for isomorphism and compactness using the Hamming matrices and moment matrices.

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