An Application of Generalized Kinematic Chains to the Structural Synthesis of Nonfractionated Epicyclic Gear Trains

1992 ◽  
Author(s):  
Cheng-Ho Hsu
Keyword(s):  
Degrees Of Freedom ◽  
Systematic Approach ◽  
Kinematic Chain ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Epicyclic Gear ◽  
Gear Trains ◽  
Three Degrees Of Freedom

Abstract This paper presents a systematic approach, which is based on the concept of generalization for the structural synthesis of geared kinematic chains for epicyclic gear trains with any number of degrees of freedom. First, the fundamental rules of generalized kinematic chains for nonfractionated epicyclic gear trains are investigated. Next, according to the numbers of gear pairs and degrees of freedom, acceptable kinematic chains for nonfractionated epicyclic gear trains are identified from an atlas of basic kinematic chains. Then, each acceptable kinematic chain is specialized to be epicyclic gear trains. Finally, geared kinematic chains for nonfractionated epicyclic gear trains with up to three degrees of freedom and four gear pairs have been susscessfully constructed.

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.

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.

scholarly journals Structural synthesis of plane kinematic chain inversions without detecting isomorphism

2021 ◽  
Vol 12 (2) ◽  
pp. 1061-1071
Author(s):  
Jinxi Chen ◽  
Jiejin Ding ◽  
Weiwei Hong ◽  
Rongjiang Cui
Keyword(s):  
Mechanism Design ◽  
Adjacency Matrix ◽  
Synthesis Method ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Synthesis Methods ◽  
Creative Design ◽  
Structural Synthesis ◽  
Kinematic Chains

Abstract. A plane kinematic chain inversion refers to a plane kinematic chain with one link fixed (assigned as the ground link). In the creative design of mechanisms, it is important to select proper ground links. The structural synthesis of plane kinematic chain inversions is helpful for improving the efficiency of mechanism design. However, the existing structural synthesis methods involve isomorphism detection, which is cumbersome. This paper proposes a simple and efficient structural synthesis method for plane kinematic chain inversions without detecting isomorphism. The fifth power of the adjacency matrix is applied to recognize similar vertices, and non-isomorphic kinematic chain inversions are directly derived according to non-similar vertices. This method is used to automatically synthesize 6-link 1-degree-of-freedom (DOF), 8-link 1-DOF, 8-link 3-DOF, 9-link 2-DOF, 9-link 4-DOF, 10-link 1-DOF, 10-link 3-DOF and 10-link 5-DOF plane kinematic chain inversions. All the synthesis results are consistent with those reported in literature. Our method is also suitable for other kinds of kinematic chains.

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.

PSEUDO PROBABILISTIC APPROACH TO TEST ISOMORPHISM AMONG KINEMATIC CHAINS

1997 ◽  
Vol 21 (2) ◽  
pp. 65-83 ◽  
Author(s):  
S. Shubhashis ◽  
M. Choubey ◽  
A.C. Rao
Keyword(s):  
Numerical Scheme ◽  
Degrees Of Freedom ◽  
Probabilistic Approach ◽  
Kinematic Chain ◽  
Single Degree Of Freedom ◽  
Reliable Test ◽  
Kinematic Chains ◽  
Single Degree ◽  
Unique Method ◽  
P Matrix

There is no dearth of methods to test isomorphism amongst kinematic chains. Search for a computationally easier, logically simple and unique method is still on. Present work is in quest of a reliable test to detect isomorphism among kinematic chains. Work presented here is more versatile as it incorporates more features of the kinematic chain which were not included earlier such as number and type of links, their relative dispositions in the kinematic chain, nature of adjacent links etc. The method proposed is based on the concept of pseudo-probability (pseudo means it appears to be, but not exactly. The approach does not follow in-toto the principles of probability and considerable liberty has been taken in interpreting the word probability hence the word pseudo is used along with the probability schemes). Using the resemblance of different coloured balls in an urn for the number and type of links in a kinematic chain, a matrix (named P-Matrix) representing the kinematic chain in totality is generated. For the sake of comparison a numerical scheme named, pseudo probability scheme, P-Scheme, is developed from the above P-Matrix and is used for testing isomorphism. In fact the method is more powerful in the sense that each row of the proposed P-Matrix is capable of representing the respective kinematic chain distinctly and can be used to compare the kinematic chains with same link assortments, uniquely. The proposed method, besides possessing the potential of testing the isomorphism among simple-joint, single degree of freedom kinematic chains is also capable of multi degrees of freedom and multiple-joint kinematic chains.

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.

Designing Statically Determinable Mechanisms of Technological Mechatronic Machines with Parallel Kinematics

2019 ◽  
Vol 20 (7) ◽  
pp. 428-436
Author(s):  
A. K. Tolstosheev ◽  
V. A. Tatarintsev
Keyword(s):  
Structural Analysis ◽  
Hierarchical Structure ◽  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Parallel Structure ◽  
Parallel Kinematics ◽  
Output Link ◽  
Parallel Connection ◽  
Kinematic Chains ◽  
Chain Increase

The work is devoted to improving the reliability and manufacturability of mechatronic machine designs with parallel kinematics by replacing statically indeterminable manipulators with statically determinable mechanisms. A technique is proposed in which the design of statically determinable manipulators of technological mechatronic machines with parallel kinematics is performed by modifying the structure of prototypes and includes three steps: identifying and analyzing redundant links, eliminating redundant links, checking the correctness of eliminating redundant links. To determine the number of degrees of freedom of the mechanism, identify redundant links, and verify the solution, the authors use the proposed methodology for structural analysis of parallel structure mechanisms. In structural analysis, a manipulator is represented by a hierarchical structure and is considered as a parallel connection of elementary mechanisms with an open kinematic chain; as a kinematic chain consisting of leading and driven parts; as a set of links and kinematic pairs; as a kinematic connection of the output link and the rack. The article implements the following techniques for eliminating redundant links: mobility increase in kinematic pairs; introduction of unloading links and passive kinematic pairs to the kinematic chain; exclusion of extra links and pairs from the kinematic chain; increase in mobility in some kinematic pairs simultaneously with the exclusion of other kinematic pairs that have become superfluous. The authors developed several variants of structural schemes of self-aligning manipulators based on the Orthoglide mechanism, which retain the basic functional proper ties of the prototype. To increase the number of self-aligning mechanism diagrams, the redistribution of mobilities and links within the connecting kinematic chain and between connecting kinematic chains is used. The proposed methodics allow to determine the number of degrees of freedom of the mechanism, the number and type of redundant links, eliminate redundant links and, on an alternative basis, build structural diagrams of statically determinable mechanisms of technological mechatronic machines with parallel kinematics.

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