Structural Synthesis Method of Planar Mechanisms Using the Assur-group Based Adjacency Matrix

2012 ◽  
Vol 48 (13) ◽  
pp. 13 ◽  
Author(s):  
Shujun LI
Keyword(s):  
Adjacency Matrix ◽  
Synthesis Method ◽  
Structural Synthesis ◽  
Planar Mechanisms ◽  
Assur Group

Assur-Group Inferred Structural Synthesis for Planar Mechanisms

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Shujun Li ◽  
Hongguang Wang ◽  
Jian S. Dai
Keyword(s):  
Adjacency Matrix ◽  
Synthesis Method ◽  
Matrix Group ◽  
Structural Synthesis ◽  
Planar Mechanisms ◽  
Comprehensive List ◽  
Assur Group ◽  
The Given ◽  
First Time ◽  
Metamorphic Mechanisms

In order to obtain a comprehensive list of possible mechanisms with various choices of both R and P pairs and mechanism inversion of planar mechanisms, a new structural synthesis method is developed by integrating Assur groups (AGs) as elements in the newly developed group-based adjacency matrix. This extended adjacency matrix is proposed with the diagonal elements representing three fundamental elements as the frame link, driving link, AG and augmented AG (AAG) if metamorphic mechanisms are to be synthesized. The off-diagonal elements provide information on group combination and connection forms of the above three fundamental elements and that on the associated kinematic pairs. Based on the extended adjacency matrix, all assembly modes for the given AGs can be established and isomorphism mechanisms can be identified at the same time. Considering all types of the AGs in the extended adjacency matrix, group permutation and combination are used and connection forms are generated including variation of the driving link and mechanism inversion. The structural synthesis is then extending to generating a comprehensive list of types of mechanisms and illustrated by the synthesis for class II 6-bar planar mechanisms with both R and P pairs, generating a list of 588 types of mechanisms that are derived for the first time. The paper further applies the approach to metamorphic mechanisms, and obtained five connection forms of the 7-bar 2DOF metamorphic mechanisms.

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.

Automatic Structural Synthesis of the Whole Family of Planar 3-Degrees of Freedom Closed Loop Mechanisms

2013 ◽  
Vol 5 (4) ◽  
Author(s):  
Huafeng Ding ◽  
Peng Huang ◽  
Jingfang Liu ◽  
Andrés Kecskeméthy
Keyword(s):  
Degrees Of Freedom ◽  
Closed Loop ◽  
Synthesis Method ◽  
Synthesis Process ◽  
Structural Synthesis ◽  
Planar Mechanisms ◽  
Systematic Method ◽  
Automatic Synthesis ◽  
Heavy Load ◽  
Structure Representation

Conception of the kinematic structures with better performance has been a challenging, yet pivotal issue, since the beginning of the design of mechanisms or robots. This paper proposes a systematic method to synthesize and classify automatically all the valid kinematic structures of planar 3-DOF closed loop mechanisms or robots. First, after the structure representation graphs of planar mechanisms or robots are addressed, the unique representation of both contracted graphs and topological graphs is proposed and used to detect isomorphism in the synthesis process. Then the valid atlas database of the contracted graphs for planar 3-DOF closed loop mechanisms or robots up to 16-link is built. Based on the atlas database, an automatic synthesis method is proposed to synthesize all the kinematic structures of planar 3-DOF closed loop mechanisms or robots, and the complete atlas database with all the valid kinematic structures classified for planar 3-DOF closed loop mechanisms or robots up to 16-link is established. The creative design of 3-DOF heavy-load hydraulic robots is conducted to show the usefulness of the established atlas database.

A New Approach for Exact/Approximate Point Synthesis of Planar Mechanisms

2005 ◽  
Author(s):  
Ahmad Smaili ◽  
Nadim Diab
Keyword(s):  
Synthesis Method ◽  
Dimensional Synthesis ◽  
Gradient Search ◽  
Planar Mechanisms ◽  
Simple Method ◽  
New Approach ◽  
Optimum Synthesis ◽  
Approximate Synthesis ◽  
Optimum Solution ◽  
Synthesis Approach

The aim of this article is to provide a simple method to solve the mixed exact-approximate dimensional synthesis problem of planar mechanism. The method results in a mechanism that can traverse a closed path with the choice of any number of exact points while the rest are approximate points. The algorithm is based on optimum synthesis rather than on precision position methods. Ant-gradient search is applied on an objective function based on log10 of the error between the desired positions and those generated by the optimum solution. The log10 function discriminates on the side of generating miniscule errors (on the order of 10−14) at the exact points while allowing for higher errors at the approximate positions. The algorithm is tested by way of five examples. One of these examples was used to test exact/approximate synthesis method based on precision point synthesis approach.

Optimum Synthesis of Planar Mechanisms for Path Generation Based on a Combined Discrete Fourier Descriptor

2015 ◽  
Vol 7 (4) ◽  
Author(s):  
Wen-Yi Lin
Keyword(s):  
Synthesis Method ◽  
Optimization Method ◽  
Path Generation ◽  
Fourier Descriptor ◽  
Planar Mechanisms ◽  
Two Phase ◽  
Phase Synthesis ◽  
Optimum Synthesis ◽  
Centroid Distance ◽  
The One

A two-phase synthesis method is described, which is capable of solving quite challenging path generation problems. A combined discrete Fourier descriptor (FD) is proposed for shape optimization, and a geometric-based approach is used for the scale–rotation–translation synthesis. The combined discrete FD comprises three shape signatures, i.e., complex coordinates (CCs), centroid distance (CD), and triangular centroid area (TCA), which can capture greater similarity of shape. The genetic algorithm–differential evolution (GA–DE) optimization method is used to solve the optimization problem. The proposed two-phase synthesis method, based on the combined discrete FD, successfully solves the challenging path generation problems with a relatively small number of function evaluations. A more accurate path shape can be obtained using the combined FD than the one-phase synthesis method. The obtained coupler curves approximate the desired paths quite well.

STRUCTURAL SYNTHESIS OF ACTUATORS OF STIRRED TANKS WITH IRREGULAR MOTION OF IMPELLER

2019 ◽  
Author(s):  
А.А. ПРИХОДЬКО ◽  
А.А. КОПТЕВА
Keyword(s):  
Initial Conditions ◽  
Structural Parameters ◽  
Synthesis Method ◽  
System Of Equations ◽  
Structural Synthesis ◽  
Stirred Tanks ◽  
Irregular Motion ◽  
The Relationship ◽  
Independent Loops ◽  
Planetary Mechanism

Предложено синтезировать зубчатые исполнительные механизмы перемешивающих устройств с неравномерным движением рабочего органа. В качестве метода синтеза применена структурная математическая модель в виде системы уравнений, описывающей взаимосвязи между количественным и качественным составом звеньев n и кинематических пар p будущего механизма, его подвижностью W, количеством замкнутых независимых контуров k, присоединений к стойке S и другими структурными параметрами. Начальные условия заданы с целью получения одноподвижных (W 1) плоских (П 3) механизмов с одним (k 1) и двумя (k 2) замкнутыми независимыми контурами. По результатам решения системы уравнений построены две схемы механизмов зубчатая передача (p1 2 p2 1 n2 2 S 2) и планетарный механизм с внешним зацеплением (p1 3 p2 2 n2 2 n3 1 S 3). Анализ синтезированных схем показал, что применение в их составе эллиптических зубчатых колес позволяет получить различные виды неравномерного движения выходного звена и, соответственно, закрепленного на нем рабочего органа. Преимущества предлагаемых перемешивающих устройств простота проектирования, надежность и компактность. It is proposed to synthesize gear actuators of stirred tanks with irregular motion of the impeller, since they allow providing higher intensity of mixing in the reactor. As a synthesis method, a structural mathematical model is used in a system of equations form that describes the relationship between the quantitative and qualitative composition of the links n and kinematic pairs p of the future mechanism, its mobility W, the number of closed independent loops k and connections to the rack S and other structural parameters. The initial conditions are specified with the aim of obtaining oneDOF (W 1) flat (P 3) mechanisms with one (k 1) and two (k 2) closed independent loops. Based on the results of solving the system of equations, two schemes of mechanisms were constructed: a gear (p1 2 p2 1 n2 2 S 2) and a planetary mechanism with external gearing (p1 3 p2 2 n2 2 n3 1 S 3). The analysis of the obtained schemes showed that the use of elliptical gears in their schemes allows to obtain various types of irregular motion of the output link and, accordingly, the impeller fixed on it. The advantages of the proposed stirred tank actuators are ease of design, reliability and compactness.

Automated Synthesis of Planar Mechanisms With Revolute, Prismatic and Pin-in-Slot Joints

2015 ◽  
Author(s):  
Weifeng Huang ◽  
Matthew I. Campbell
Keyword(s):  
Synthesis Method ◽  
Automated Synthesis ◽  
Planar Mechanisms ◽  
Revolute Joint ◽  
Synthesis Approach

This paper presents a graph synthesis approach to planar N-bar mechanisms with revolute (R), prismatic (P), and RP (pin-in-slot) joints. This novel graph synthesis method extends the enumeration to define the possible topologies for mechanisms with any mix of R-, P-, and RP-joints. Each topology is explicitly defined as a graph which can be viewed and simulated within an online kinematic simulator. This method successfully produces the same number of topologies for 6, 8, 10, and 12-bar revolute joint mechanisms as those shown in the existing literature. It explicitly calculates all topologies for 6, 8, and 10 bars with a mix of the three joint-types.

A Single Universal Construction Rule for the Structural Synthesis of Mechanisms

2016 ◽  
Author(s):  
Elad Hahn ◽  
Offer Shai
Keyword(s):  
Synthesis Method ◽  
Building Blocks ◽  
Construction Rule ◽  
Synthesis Methods ◽  
Rigidity Theory ◽  
Structural Synthesis ◽  
Graph Representations ◽  
Synthesis Of Mechanisms ◽  
Different Types ◽  
Universal Construction

In the field of structural synthesis of mechanisms several synthesis methods have been developed using different approaches. One of the more interesting approaches was that of bottom-up construction via the combination of modular structural groups, known as Assur groups. This approach is combined with new graph representations of mechanisms taken from rigidity theory, capable of representing all the different types of planar and spatial mechanisms. With the strong mathematical base of rigidity theory, a new synthesis method is proposed based on Assur groups, which are reformulated in terms of graph theory and renamed Assur Graphs. Using a single universal construction rule, Assur Graphs of different types and of any number of links are constructed, creating a complete set of building blocks for the synthesis of feasible mechanisms. As its name implies, the single universal construction is applicable for mechanisms of all types of joints and links, for planar or spatial motion.

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