On the Application of Kinematic Units to the Topological Analysis of Geared Mechanisms

2000 ◽  
Vol 123 (2) ◽  
pp. 240-246 ◽  
Author(s):  
Chia-Pin Liu ◽  
Dar-Zen Chen
Keyword(s):  
Topological Analysis ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Systematic Method ◽  
Input And Output

Based on the concept of kinematic fractionation, a systematic method for the topological analysis of geared mechanisms is presented in this paper. It is shown that a geared kinematic chain (GKC) can be regarded as a combination of kinematic unit(s). By identifying the embedded kinematic units, kinematic insight in the GKC can be exposed. The disclosed information leads to straightforward and promising rules to prevent redundant links. These rules form the basis of a by-inspection procedure to determine admissible assignments of the ground, input and output links in a GKC. Admissible assignments of the ground, input and output links of one degree-of-freedom 5 link GKCs are determined as an illustrative example.

Topological Analysis of Single-Degree-of-Freedom Planetary Gear Trains

1991 ◽  
Vol 113 (1) ◽  
pp. 10-16 ◽  
Author(s):  
D. G. Olson ◽  
A. G. Erdman ◽  
D. R. Riley
Keyword(s):  
Topological Analysis ◽  
Planetary Gear ◽  
Degree Of Freedom ◽  
Graph Representation ◽  
Straightforward Manner ◽  
Single Degree Of Freedom ◽  
Kinematic Chains ◽  
Planetary Gear Trains ◽  
Input And Output ◽  
Gear Trains

Graph theory has been demonstrated by many researchers to be useful during the conceptual phase of mechanism design. For the particular class of mechanisms known as planetary gear trains, the graph representation has been used primarily for “topological synthesis,” the enumeration of kinematic chains satisfying the requirements for planetary gear trains. The subsequent “topological analysis” steps resulting in the specification of ground, input, and output links, have received very little attention in the literature, perhaps because the conventional graph representation for topological analysis, and utilizes a new graph representation which enables these steps to be performed in a straightforward manner. It is shown that among the thirteen distinct displacement graphs representing planetary geared kinematic chains with five links and one degree-of-freedom, only four distinct planetary gear trains result after assigning the ground, input, and output links subject to meaningful topological requirements.

Structure Based Grading of Kinematic Chains

2014 ◽  
Vol 575 ◽  
pp. 501-506 ◽  
Author(s):  
Shubhashis Sanyal ◽  
G.S. Bedi
Keyword(s):  
Structural Properties ◽  
Structural Property ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Kinematic Chains ◽  
Structural Differences ◽  
The Individual ◽  
Independent Loops

Kinematic chains differ due to the structural differences between them. The location of links, joints and loops differ in each kinematic chain to make it unique. Two similar kinematic chains will produce similar motion properties and hence are avoided. The performance of these kinematic chains also depends on the individual topology, i.e. the placement of its entities. In the present work an attempt has been made to compare a family of kinematic chains based on its structural properties. The method is based on identifying the chains structural property by using its JOINT LOOP connectivity table. Nomenclature J - Number of joints, F - Degree of freedom of the chain, N - Number of links, L - Number of basic loops (independent loops plus one peripheral loop).

A Method for Detection of Distinct Mechanisms of a Planar Kinematic Chain

1988 ◽  
Vol 12 (1) ◽  
pp. 15-20 ◽  
Author(s):  
L.K. Patel ◽  
A.C. Rao
Keyword(s):  
Efficient Method ◽  
Numerical Scheme ◽  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
A Chain

This paper presents a computationally simple and efficient method for identification of distinct mechanisms of a planar kinematic chain having a single degree of freedom. It is proposed that velocity diagrams for all the inversions of a chain be drawn and the possible isomorphism among these velocity diagrams be detected. From the velocity diagram, a motion transfer point matrix can be prepared resulting in the development of a numerical scheme to be associated with a mechanism. Identical schemes lead to detection of isomorphism between mechanisms. The main advantage of this method is that, apart form detecteing isomorphism, it indicates which of the inversions is better kinematically e.g. higher the total number of vectors, better is the mechanism.

A Novel Method for Constructing Multi-Mode Deployable Polyhedron Mechanisms Using Symmetric Spatial RRR Compositional Units

2018 ◽  
Author(s):  
Jieyu Wang ◽  
Xianwen Kong
Keyword(s):  
Kinematic Chain ◽  
Degree Of Freedom ◽  
Single Loop ◽  
Kinematic Chains ◽  
The Third ◽  
Motion Modes ◽  
3D Printed ◽  
Novel Method ◽  
Multi Mode ◽  
Motion Mode

A novel construction method is proposed to construct multimode deployable polyhedron mechanisms (DPMs) using symmetric spatial RRR compositional units, a serial kinematic chain in which the axes of the first and the third revolute (R) joints are perpendicular to the axis of the second R joint. Single-loop deployable linkages are first constructed using RRR units and are further assembled into polyhedron mechanisms by connecting single-loop kinematic chains using RRR units. The proposed mechanisms are over-constrained and can be deployed through two approaches. The prism mechanism constructed using two Bricard linkages and six RRR limbs has one degree-of-freedom (DOF). When removing three of the RRR limbs, the mechanism obtains one additional 1-DOF motion mode. The DPMs based on 8R and 10R linkages also have multiple modes, and several mechanisms are variable-DOF mechanisms. The DPMs can switch among different motion modes through transition positions. Prototypes are 3D-printed to verify the feasibility of the mechanisms.

scholarly journals Development and evaluation of a handheld type 6 DoF midair haptic device using asymmetric vibration and a presentation force vectoring mechanism

2021 ◽  
Author(s):  
Yuto Okuda ◽  
Shunsuke Komizunai ◽  
Atsushi Konno
Keyword(s):  
Inverse Problem ◽  
Problem Solving ◽  
Degree Of Freedom ◽  
Haptic Device ◽  
Input And Output ◽  
User Test ◽  
Original Presentation ◽  
Force Sense ◽  
Asymmetric Vibration

Abstract This paper describes a handheld type aerial haptic device with 6 DoF (degree of freedom) using pseudo-haptics by asymmetric vibration. By introducing a original presentation force vectoring mechanism, 6 DoF force sense presentation and compactness suitable for handheld use with a small number of vibrators are realized together. In addition, a relationship between the drive input and output (presentation force sense) of the developed device is formulated, and its inverse problem solving method for obtaining the drive input that realizes a desired presentation force sense is derived. Furthermore, a user test clarified the direction in which this device can / cannot effectively exert force.

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.

Conditions for Self-Locking in Planetary Gear Trains

2006 ◽  
Vol 129 (9) ◽  
pp. 960-968 ◽  
Author(s):  
David R. Salgado ◽  
J. M. del Castillo
Keyword(s):  
Planetary Gear ◽  
Degree Of Freedom ◽  
The Self ◽  
Gear Train ◽  
Planetary Gear Train ◽  
Analytical Expression ◽  
Planetary Gear Trains ◽  
Input And Output ◽  
Approximate Relationship ◽  
Gear Trains

The objective of the present work is to determine the conditions that have to be satisfied for a planetary gear train of one degree of freedom to be self-locking. All planetary gear trains of up to six members are considered. As a result, we show the constructional solutions of planetary gear trains exhibiting self-locking. Unlike other studies, the self-locking conditions are obtained systematically from the analytical expression for the product of the efficiency of a given train by the efficiency of the train resulting from interchanging its input and output axes. Finally, a proof is given of an approximate relationship between these two efficiencies.

Structural Analysis and Mobility Test of Fourteen Links Kinematic Chain Using Graph Theory

2014 ◽  
Vol 592-594 ◽  
pp. 1165-1169
Author(s):  
Preeti Gulia ◽  
V.P. Singh
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Incidence Matrix ◽  
Reliable Method ◽  
Kinematic Chain ◽  
Polynomial Equation ◽  
Degree Of Freedom ◽  
Mobility Test ◽  
Structural Problems ◽  
Algebraic Test

The present work is focused on the graph theory which is used for structural analysis of kinematic chain and identification of degree of freedom. A method based on graph theory is proposed in this paper to solve structural problems by using a suitable example of fourteen links kinematic chain. Purpose of this paper is to give an easy and reliable method for structural analysis of fourteen links kinematic chain. Here, a simple incidence matrix is used to represent the kinematic chain. The proposed method is applied for determining the characteristic polynomial equation of fourteen links kinematic chain. An algebraic test based on graph theory is also used for identifying degree of freedom of kinematic chain whether it is total, partial or fractionated degree of freedom.

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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