A General Method of Kinematic Analysis of Parallel Axes Epicyclic Gear Trains Based on Graph-Cycle Matroid Theory

2005 ◽  
Author(s):  
Ilie Talpasanu ◽  
T. C. Yih ◽  
P. A. Simionescu
Keyword(s):  
Kinematic Analysis ◽  
Matroid Theory ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Cycle Matroid ◽  
General Method

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.

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.

scholarly journals Kinematic Analysis of Spatial Geared Mechanisms

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Julie Penaud ◽  
Daniel Alazard ◽  
Alexandre Amiez
Keyword(s):  
Adjacency Matrix ◽  
Kinematic Analysis ◽  
Polar Coordinates ◽  
Constraint Matrix ◽  
New Approach ◽  
Bevel Gears ◽  
Gear Trains ◽  
Complex Coefficients ◽  
Two Degree Of Freedom ◽  
General Method

In this paper, a general method for kinematic analysis of complex gear mechanisms, including bevel gear trains and noncollinear input and output axes, is presented. This new approach is based on the nullspace of the kinematic constraint matrix computed from the mechanism graph or its adjacency matrix. The novelty is that the elements of the adjacency matrix are weighted with complex coefficients allowing bevel gears to be taken into account and the angular velocity of each link to be directly expressed using polar coordinates. This approach is illustrated on a two-degree-of-freedom car differential and applied to a helicopter main gear box. A MATLAB open source software was developed to implement this method.

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.

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 General Method for Kinematic Analysis of Robotic Wrist Mechanisms

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Ilie Talpasanu
Keyword(s):  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Simple Procedure ◽  
Efficient Computation ◽  
General Applicability ◽  
Cycle Basis ◽  
Angular Velocities ◽  
Gear Trains ◽  
Cycle Matroid ◽  
Robotic Wrist

Abstract The paper presents a novel and simple technique for the kinematic analysis of bevel gear trains (BGT). The approach is based on edge-oriented graphs for efficient computation of BGT’s absolute and relative velocities of links using incidence matrices. The kinematic equations are generated in matrix form using a cycle basis from a cycle matroid. The set of independent equations is automatically obtained from matrix orthogonalities and not by taking derivatives. Equation coefficients are expressed as function of speed ratios and have minimal variables. Then the relationships between the output and input angular velocities can be determined. In addition, a simple procedure is demonstrated to check for mechanism singularities. The method presented here has general applicability and can be employed for spatial geared mechanisms with any number of gears and degrees of freedom (DOF) as illustrated by numerical examples of robotic wrist mechanisms.

Kinematic Analysis of Epicyclic Bevel Gear Trains With Matroid Method

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
Ilie Talpasanu ◽  
P. A. Simionescu
Keyword(s):  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Time Derivative ◽  
Oriented Graph ◽  
Bevel Gear ◽  
Efficient Computation ◽  
Cycle Basis ◽  
Angular Velocities ◽  
Gear Trains ◽  
Cycle Matroid

The paper presents a novel technique for the kinematic analysis of bevel gear trains using the incidence matrices of an edge-oriented graph of the mechanism. The kinematic equations are then obtained in matrix form using a cycle basis from a cycle matroid. These equations can be systematically generated, and allow for an efficient computation of the angular velocities of the gears and planet carriers of the mechanism without employing time derivative operations. As illustrated in the paper, the method is applicable to bevel gear trains of any number of gears or degrees of freedom.

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.

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