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 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.

A General Method for Kinematic Analysis of Epicyclic Bevel Gear Trains Applied to Robotic Wrist Mechanisms

2013 ◽  
Author(s):  
Ilie Talpasanu
Keyword(s):  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Simple Procedure ◽  
Bevel Gear ◽  
Efficient Computation ◽  
General Applicability ◽  
Cycle Basis ◽  
Angular Velocities ◽  
Gear Trains ◽  
Robotic Wrist

This 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 relative and absolute 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 as illustrated by numerical examples of robotic wrist mechanisms.

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.

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.

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.

Innovation Synthesis of Basic Configurationof Epicyclic Gear Trains with Three-Degrees of Freedom

2011 ◽  
Vol 199-200 ◽  
pp. 358-364
Author(s):  
Heng Bin Ren ◽  
Mao Lin Huang
Keyword(s):  
Degrees Of Freedom ◽  
Synthesis Method ◽  
Kinematic Chain ◽  
Practical Application ◽  
New Approach ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Train System ◽  
Three Degrees Of Freedom ◽  
Basic Configuration

Epicyclical gear trains with three-degrees of freedom have found its wide application as the development of new technique. Currently, nearly all domestic researches on epicyclical gear trains with three or more degrees of freedom are aimed at the practical application, and scare works systematically investigate basic configuration and synthesis of the train system. An innovation synthesis method is proposed based on the compound joint kinematic chain and the substitution of low pair with high pair for epicyclical gear trains with three-degrees of freedom, and the possible independent basic configurations of epicyclical gear trains with three-degrees of freedom are obtained by applying the proposed method and the utilization of the method is also discussed. The method provides not only a new approach for innovation synthesis of epicyclical gear trains but also a few basic configurations of epicyclical gear trains with three-degrees of freedom for practice design.

A Study of the Duality Between Epicyclic Gear Trains and Beam Systems

2006 ◽  
Author(s):  
Gordon P. Pennock ◽  
Jeremiah J. Alwerdt
Keyword(s):  
Gear Train ◽  
Specific Design ◽  
Beam System ◽  
Dual Beam ◽  
Epicyclic Gear ◽  
Angular Velocities ◽  
Gear Trains ◽  
Design Requirements ◽  
Primary Contribution ◽  
Insight Into

This paper provides geometric insight into the duality between the kinematics of epicyclic gear trains and the statics of beam systems. The two devices have inherent geometrical relationships that allow the angular velocities of the gears in a gear train to be investigated from a knowledge of the forces acting on the dual beam system, and vice-versa. The primary contribution of the paper is the application of this duality to obtain the dual beam system for a given compound epicyclic gear train. The paper develops a systematic procedure to transform between the first-order kinematics of a gear train and the statics of the dual beam system. This provides a simple and intuitive approach to study the speed ratios of an epicyclic gear train and the force ratios of the dual beam system. The speed ratios are expressed in terms of kinematic coefficients, which are a function of the position of the input gear and provide insight into the gear train geometry. Several numerical examples of simple and compound epicyclic gear trains are presented to demonstrate the simplicity of the proposed approach. The analytical equations that are developed in the paper can be incorporated, in a straightforward manner, into a spreadsheet that is oriented towards an epicyclic gear train satisfying specific design requirements.

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