Type Synthesis of Long Symmetric Planar Shape-Morphing Mechanism Arrays

2021 ◽  
Author(s):  
Craig Lusk
Keyword(s):  
Graph Theory ◽  
Complex Shape ◽  
Degree Of Freedom ◽  
Type Synthesis ◽  
Analysis Techniques ◽  
Shape Morphing ◽  
Symmetry Theory ◽  
Planar Shape ◽  
Synthesis Methodology

Abstract This paper describes a novel type synthesis methodology for creating planar shape-morphing mechanism chains of any length with specified mobility (degree-of-freedom). It is expected that this will be of use in designing complex shape-morphing objects. The methodology is based on using graph theory in conjunction with symmetry theory for borders (Frieze groups). It is shown that the methodology can produce chains of a variety of lengths and mobility, and these chains have symmetric topologies and that symmetric kinematics may be possible for some of the chains, which simplifies their analysis. Techniques for decreasing and increasing the mobility of the chains are discussed. Finally, a gallery of shape morphing chains is given to provide concrete illustrations of the diversity of designs generated using this methodology.

Design of Planar Shape-Morphing Mechanism Arrays Using Harmonic Mechanisms

2018 ◽  
Author(s):  
Craig Lusk
Keyword(s):  
Interesting Property ◽  
Small Degree ◽  
Design Concept ◽  
Degree Of Freedom ◽  
Planar Mechanism ◽  
Harmonic Motion ◽  
Musical Harmony ◽  
Shape Morphing ◽  
Planar Shape ◽  
Interference Mechanism

is paper introduces a design concept for planar mechanism arrays using an interesting property of mechanisms that I have termed mechanism harmony. Just as a theory of musical harmony allows for a large number of notes to be played without harsh-sounding interference, mechanism harmony allows mechanism links to be arrayed so that they move coherently and with a small degree of freedom. The concept of mechanism harmony is based on permuting the arrangement of the moving links. For a four-bar mechanism, this yields six (3!) different harmonic permutations of the link arrangement, and there are numerous ways that these six different mechanisms can be grouped together to tile the plane. This paper presents early findings on these groups, some prototypes showing arrays with harmonic motion, and discusses the possible significance of harmonic mechanisms for shape morphing mechanisms.

scholarly journals A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Yongquan Li ◽  
Yang Zhang ◽  
Lijie Zhang
Keyword(s):  
Closed Loop ◽  
Screw Theory ◽  
Line Graph ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Allocation Criteria ◽  
Grassmann Line Geometry ◽  
Moving Platform ◽  
Atlas Method

Abstract The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F&C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.

Type Synthesis of Compliant Mechanisms Employing a Simplified Approach to Segment Type

1994 ◽  
Author(s):  
Morgan D. Murphy ◽  
Ashok Midha ◽  
Larry L. Howell
Keyword(s):  
Rigid Body ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Type Synthesis ◽  
Simplified Approach ◽  
Design Procedures ◽  
Synthesis Techniques ◽  
Design Solutions ◽  
Synthesis Methodology

Abstract The formulation of design procedures for rigid-body mechanisms has benefited from the application of type-synthesis techniques. Therefore, with modifications to allow for inclusions of compliance, type synthesis is seen as a useful tool in the design of compliant mechanisms. Previous efforts have developed methods that result in a large number of possible design solutions to a given problem. This paper deals primarily with the development of a simplified compliant-mechanism type-synthesis methodology that limits the number of design solutions considered. The techniques are derived by modifying existing compliant mechanism type-synthesis techniques to yield a simpler model with greater pragmatic value.

Photothermally driven liquid crystal polymer actuators

2018 ◽  
Vol 2 (11) ◽  
pp. 1932-1943 ◽  
Author(s):  
Liangliang Dong ◽  
Yue Zhao
Keyword(s):  
Liquid Crystal ◽  
Complex Shape ◽  
Liquid Crystal Polymer ◽  
Photothermal Effect ◽  
Polymer Actuators ◽  
Shape Morphing ◽  
Crystal Polymer

Light-controlled liquid crystal polymer actuators using the photothermal effect are easy to make and capable of executing complex shape morphing or motion.

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.

scholarly journals Configuration synthesis of electric-drive transmissions for tracked vehicles

2018 ◽  
Vol 10 (1) ◽  
pp. 168781401774966
Author(s):  
Ming-Fei Gao ◽  
Ji-Bin Hu ◽  
Zeng-Xiong Peng
Keyword(s):  
Graph Theory ◽  
Electric Drive ◽  
Synthesis Method ◽  
Theory Model ◽  
Degree Of Freedom ◽  
Transmission Mechanism ◽  
Necessary Condition ◽  
Tracked Vehicles ◽  
Configuration Synthesis ◽  
Complex Transmission

This article focus on the configuration synthesis of electric-drive transmissions for tracked vehicles. First, a new graph theory model is proposed to represent the transmission mechanism, which makes the complex transmission system easier to understand. Second, a configuration synthesis method is proposed based on kinematics and statics, in which the speed degree of freedom and torque degree of freedom are considered as the constraints of configuration synthesis. Also, the expressions for speed degree of freedom and torque degree of freedom are derived. Third, based on the graph theory model, the necessary condition to achieve skid steering in the transmission of tracked vehicles is obtained. The results of this article can provides a theoretical basis for the design and analysis of transmission mechanism of tracked vehicles.

scholarly journals Type Synthesis of 5-DoF Parallel Mechanisms with Different Submechanisms

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Yi Lu ◽  
Yang Lu ◽  
Lijie Zhang ◽  
Nijia Ye ◽  
Bo Hu ◽  
...  
Keyword(s):  
Degree Of Freedom ◽  
Digital Topology ◽  
Parallel Mechanisms ◽  
Type Synthesis

The type synthesis of the 5-DoF (degree of freedom) parallel mechanisms with different submechanisms is studied by utilizing digital topology graphs (DTGs). The conditions for synthesizing the 5-DoF parallel mechanisms with different submechanisms using DTGs are determined. Many valid DTGs are derived from 17 different 5-DoF associated linkages, and the valid DTGs are transformed into revised DTGs. The subplanar and/or spatial parallel mechanisms in the 5-DoF parallel mechanisms are transformed into some simple equivalent limbs, and their equivalent relations and merits are analyzed. Using the derived valid DTGs and revised DTGs, many 5-DoF parallel mechanisms with different subserial or parallel mechanisms are synthesized, and they are simplified by replacing the complicated subparallel mechanisms with their simple equivalent limbs. Finally, their DoFs are calculated to verify the correctness and effectiveness of the proposed approach.

Type Synthesis and Application of Gear Linkage Transplanting Mechanisms Based on Graph Theory

2019 ◽  
Vol 62 (2) ◽  
pp. 515-528
Author(s):  
Liang Sun ◽  
Yuzhu Zhou ◽  
Xuan Chen ◽  
Chuanyu Wu
Keyword(s):  
Graph Theory ◽  
Structural Characteristics ◽  
Synthesis Method ◽  
Kinematic Chain ◽  
Gear Train ◽  
Type Synthesis ◽  
Linkage Mechanism ◽  
Topological Graph ◽  
Labeled Graphs ◽  
Motion Characteristics

Abstract. Type synthesis is an important step when designing innovations in mechanisms. To overcome the limitation of traditional gear train transplanting mechanisms in realizing a specific trajectory, a swinging linkage mechanism is introduced into the design of the transplanting mechanism. To design a crop-transplanting gear linkage mechanism (GLM), an automatic synthesis method based on graph theory is proposed in this article. First, the numbers of loops, links, joints and other parameters, along with unlabeled graphs, are calculated based on the structural characteristics of the GLM. The labeled graphs that correspond to the kinematic chain (KC) are then obtained by thickening the edges of the unlabeled graphs, and physically reasonable labeled graphs are derived from identification of the structural rationality of the corresponding structures. Based on the relative motion characteristics of the input and output links of the transplanting mechanisms, criteria for screening the gear linkage mechanisms represented by the labeled graphs are formulated, and the labeled graphs that are suitable for transplanting are calculated to enrich the configurations of the transplanting mechanisms. Finally, two examples are tested to verify the effectiveness of the proposed type synthesis method. Keywords: Gear linkage, Screening, Topological graph, Transplanting mechanism, Type synthesis.

scholarly journals Type Synthesis of Two DOF Hybrid Translational Parallel Manipulators

2016 ◽  
Vol 836 ◽  
pp. 48-53 ◽  
Author(s):  
Latifah Nurahmi ◽  
Stéphane Caro
Keyword(s):  
Screw Theory ◽  
Synthesis Method ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Type Synthesis ◽  
In Series ◽  
Actuation Scheme ◽  
Two Degree Of Freedom

This paper introduces a methodology for the type synthesis of two degree-of-freedom hybrid translational manipulators with identical legs. The type synthesis method is based upon the screw theory. Three types of two degree-of-freedom hybrid translational manipulators with identical legs are identified based upon their wrench decomposition. Each leg of the manipulators is composed of a proximal module and a distal module mounted in series. The assembly conditions and the validity of the actuation scheme are also defined. Eventually, some novel two degree-of-freedom hybrid translational manipulators are synthesized with the proposed procedure.

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