Mobility Analysis of the Threefold-Symmetric Bricard Linkage and Its Network

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Xiaoke Song ◽  
Hongwei Guo ◽  
Ruiwei Liu ◽  
Fei Meng ◽  
Qiping Chen ◽  
...  
Keyword(s):  
Graph Theory ◽  
Screw Theory ◽  
Analysis Method ◽  
Mobility Analysis ◽  
Topological Constraint ◽  
Constraint Matrix ◽  
Matrix Rank ◽  
Constraint Graph ◽  
The Matrix ◽  
Mechanical Networks

Abstract In this study, the mobility of the threefold-symmetric Bricard linkage and its network are analyzed using screw theory. First, the screw motion equation of the linkage is derived. By applying the modified Grübler–Kutzbach criterion, we deduce that the degree of freedom (DOF) of the linkage is equal to 1. Then, we analyze the mechanical network constructed of threefold-symmetric Bricard linkages and provide its topological constraint graph. Using graph theory and screw theory, the constraint matrix of the mechanical network is obtained. Then, we solve the matrix rank via linear column transformation. Results show that the DOF of the mechanical network is equal to 1. The mobility analysis method of the mechanical network proposed in this study facilitates the solution of the constraint matrix rank and can be used as a reference for other mechanical networks constructed of single-loop linkages.

Kinematics and mobility analysis of carton folds in packing manipulation based on the mechanism equivalent

2002 ◽  
Vol 216 (10) ◽  
pp. 959-970 ◽  
Author(s):  
J S Dai ◽  
J Rees Jones
Keyword(s):  
Graph Theory ◽  
Closed Form ◽  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Mobility Analysis ◽  
Mathematical Basis ◽  
Packaging Process ◽  
Kinematic Geometry ◽  
Position And Orientation

The process of erecting and closing a carton in packing manipulation is seen as a succession of folds in position and orientation from one distinct configuration to another. Permitted manipulations and changes in shape are governed by the geometry of crease lines, dimensions and profiles of the panels. The possibility for panels to fold into successive distinct configurations is determined by the kinematic geometry. This paper presents a mathematical basis which determines the mobility of distinct configurations of a carton to include the degrees of freedom dominating the manipulation and the overconstraint configurations in an erected and closed form, and proposes the kinematic analysis of a carton during packing manipulation. Use is made of the concept of line vectors and screw theory associated with graph theory. The analysis helps to explain some configurations which show how a carton can fold and opens up the way of describing manipulation in the packaging process.

scholarly journals Mobility and Constraint Analysis of Interconnected Hybrid Flexure Systems Via Screw Algebra and Graph Theory

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Frederick Sun ◽  
Jonathan B. Hopkins
Keyword(s):  
Graph Theory ◽  
Compliant Mechanisms ◽  
Screw Theory ◽  
Mobility Analysis ◽  
Element Analysis ◽  
Constraint Analysis ◽  
Computationally Expensive ◽  
Precision Motion ◽  
Automated Tool ◽  
General Method

This paper introduces a general method for analyzing flexure systems of any configuration, including those that cannot be broken into parallel and serial subsystems. Such flexure systems are called interconnected hybrid flexure systems because they possess limbs with intermediate bodies that are connected by flexure systems or elements. Specifically, the method introduced utilizes screw algebra and graph theory to help designers determine the freedom spaces (i.e., the geometric shapes that represent all the ways a body is permitted to move) for all the bodies joined together by compliant flexure elements within interconnected hybrid flexure systems (i.e., perform mobility analysis of general flexure systems). This method also allows designers to determine (i) whether such systems are under-constrained or not and (ii) whether such systems are over-constrained or exactly constrained (i.e., perform constraint analysis of general flexure systems). Although many flexure-based precision motion stages, compliant mechanisms, and microarchitectured materials possess topologies that are highly interconnected, the theory for performing the mobility and constraint analysis of such interconnected flexure systems using traditional screw theory does not currently exist. The theory introduced here lays the foundation for an automated tool that can rapidly generate the freedom spaces of every rigid body within a general flexure system without having to perform traditional computationally expensive finite element analysis. Case studies are provided to demonstrate the utility of the proposed theory.

Large deployable network constructed by Altmann linkages

2016 ◽  
Vol 231 (2) ◽  
pp. 341-355 ◽  
Author(s):  
Xiaoke Song ◽  
Hongwei Guo ◽  
Bing Li ◽  
Rongqiang Liu ◽  
Zongquan Deng
Keyword(s):  
Theoretical Approach ◽  
Large Scale ◽  
Screw Theory ◽  
Motion Equation ◽  
Motion Simulation ◽  
Single Loop ◽  
Screw Motion ◽  
Revolute Joints ◽  
Constraint Graph ◽  
Mechanical Networks

This study proposes a large-scale modular deployable mechanical network constructed by networking Altmann linkages, which are spatial single-loop mechanisms with six revolute joints and four bars, and develops a theoretical approach to verify the feasibility of the networking method. First, the screw motion equation of the linkage is derived, and the deployability of the linkage is demonstrated through a motion simulation. Second, using the overlapping-unit method, a deployable mechanical network is constructed. The constraint graph of the mechanical network is deduced subsequently. The mobility of the mechanical network is proved by screw theory, which demonstrates the feasibility of the networking method. Then, the motion of the mechanical network is simulated and it is found to have excellent deployability. Finally, a prototype of the mechanical network is fabricated. Results show that spatial single-loop linkages can construct modular deployable mechanical networks with the overlapping-unit method under appropriate connections. This networking method can be verified with the theoretical approach proposed in this work.

Mobility Analysis of Interconnected Hybrid Flexure Systems Using Screw Algebra and Graph Theory

2016 ◽  
Author(s):  
Frederick Sun ◽  
Jonathan B. Hopkins
Keyword(s):  
Finite Element Analysis ◽  
Graph Theory ◽  
Compliant Mechanisms ◽  
Screw Theory ◽  
Mobility Analysis ◽  
Element Analysis ◽  
Computationally Expensive ◽  
Precision Motion ◽  
Automated Tool ◽  
General Method

This paper introduces a general method for determining the mobility analysis of flexure systems of any complexity, including those that can’t be broken into parallel and serial flexure subsystems. Such systems are called interconnected hybrid flexure systems because they possess limbs with intermediate bodies that are connected by flexure systems or elements. The method in this paper utilizes screw algebra and graph theory to enable designers to determine the freedom spaces (i.e., the geometric shapes that represent all the ways a body is permitted to move) for all the bodies joined together by compliant flexure elements within interconnected hybrid flexure systems. Although many flexure-based precision motion stages, compliant mechanisms, and microarchitectured materials possess topologies that are highly interconnected, the theory for performing a mobility analysis of such interconnected flexure systems using traditional screw theory does not currently exist. The theory introduced here lays the foundation for an automated tool that can rapidly generate the freedom spaces of every rigid body within a general flexure system without having to perform traditional computationally expensive finite element analysis. Case studies are provided in the paper to demonstrate the utility of the proposed theory.

scholarly journals Dilution of QuEChERS Extracts Without Cleanup Improves Results in the UHPLC-MS/MS Multiresidue Analysis of Pesticides in Tomato

2021 ◽  
Author(s):  
Fabiane M. Stringhini ◽  
Lucila C. Ribeiro ◽  
Graziela I. Rocha ◽  
Juliana D. de B. Kuntz ◽  
Renato Zanella ◽  
...  
Keyword(s):  
Matrix Effect ◽  
Practical Method ◽  
Analysis Method ◽  
Multiresidue Analysis ◽  
Limit Of Quantification ◽  
Chromatography Tandem Mass Spectrometry ◽  
The Matrix ◽  
Liquid Chromatography Tandem Mass ◽  
Ultrahigh Performance Liquid Chromatography ◽  
Positive Results

AbstractTomato is well-known to be one of the most cultivated and consumed vegetables worldwide and frequently contain pesticide residues. Therefore, a simple multiresidue method was established and validated to determine 129 pesticides and metabolites in tomato samples using a modified acetate QuEChERS without cleanup for sample preparation and determination by ultrahigh-performance liquid chromatography tandem mass spectrometry (UHPLC-MS/MS). Dilution of the raw extract in different proportions of mobile phase was evaluated and a dilution of 10 times presented adequate results improving analysis performance while minimizing the matrix effect. Validation performed according to SANTE guideline presented satisfactory results. Practical method limit of quantification was 0.01 mg kg−1 for most compounds. Recoveries between 70 and 120% with precision ≤ 20% were found for most compounds and spike levels evaluated. Matrix effect results were not significant for most part of compounds. Method proved to be simple, robust, and effective to be applied in routine analysis. Method applicability was performed by analysis of samples commercialized in Brazil and positive results were found demonstrating the importance of the proposed method.

scholarly journals Calculating the Energy Spectrum of Complex Low-Dimensional Heterostructures in the Electric Field

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Svetlana N. Khonina ◽  
Sergey G. Volotovsky ◽  
Sergey I. Kharitonov ◽  
Nikolay L. Kazanskiy
Keyword(s):  
Steady State ◽  
Electric Field ◽  
Ground State ◽  
State Energy ◽  
Airy Functions ◽  
Piecewise Constant ◽  
Matrix Rank ◽  
The Matrix ◽  
Constant Potential ◽  
Low Dimensional

An algorithm for solving the steady-state Schrödinger equation for a complex piecewise-constant potential in the presence of theE-field is developed and implemented. The algorithm is based on the consecutive matching of solutions given by the Airy functions at the band boundaries with the matrix rank increasing by no more than two orders, which enables the characteristic solution to be obtained in the convenient form for search of the roots. The algorithm developed allows valid solutions to be obtained for the electric field magnitudes larger than the ground-state energy level, that is, when the perturbation method is not suitable.

scholarly journals A Positive Combinatorial Formula for the Complexity of the $q$-Analog of the $n$-Cube

10.37236/2389 ◽  
2012 ◽  
Vol 19 (2) ◽  
Author(s):  
Murali Krishna Srinivasan
Keyword(s):  
Graph Theory ◽  
Explicit Formula ◽  
Classical Result ◽  
Spanning Trees ◽  
Combinatorial Formula ◽  
Algebraic Graph Theory ◽  
The Matrix ◽  
Number Of Spanning Trees

The number of spanning trees of a graph $G$ is called the complexity of $G$. A classical result in algebraic graph theory explicitly diagonalizes the Laplacian of the $n$-cube $C(n)$  and yields, using the Matrix-Tree theorem, an explicit formula for $c(C(n))$. In this paper we explicitly block diagonalize the Laplacian of the $q$-analog $C_q(n)$ of $C(n)$ and use this, along with the Matrix-Tree theorem, to give a positive combinatorial formula for $c(C_q(n))$. We also explain how setting $q=1$ in the formula for $c(C_q(n))$ recovers the formula for $c(C(n))$.

An Iterative Approach to Dynamic Elastic-Plastic Analysis

1998 ◽  
Vol 65 (4) ◽  
pp. 811-819 ◽  
Author(s):  
F. Giambanco ◽  
L. Palizzolo ◽  
L. Cirone
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Degrees Of Freedom ◽  
Linear Complementarity ◽  
Iterative Approach ◽  
Loading History ◽  
Constraint Matrix ◽  
Elastic Plastic ◽  
Recursive Solution ◽  
The Matrix

The step-by-step analysis of structures constituted by elastic-plastic finite elements, subjected to an assigned loading history, is here considered. The structure may possess dynamic and/or not dynamic degrees-of-freedom. As it is well-known, at each step of analysis the solution of a linear complementarity problem is required. An iterative method devoted to solving the relevant linear complementarity problem is presented. It is based on the recursive solution of a linear complementarity, problem in which the constraint matrix is block-diagonal and deduced from the matrix of the original linear complementarity problem. The convergence of the procedure is also proved. Some particular cases are examined. Several numerical applications conclude the paper.

Actuating Input Selection of 5-UPS/PRPU Parallel Machine Tool

2005 ◽  
Author(s):  
Jian-She Gao ◽  
Ren-Cheng Zheng ◽  
Yong-Sheng Zhao
Keyword(s):  
Parallel Mechanism ◽  
Basic Problem ◽  
Screw Theory ◽  
Parallel Machine ◽  
Condition Numbers ◽  
Constraint Matrix ◽  
Input Selection ◽  
Moving Platform ◽  
Parallel Machine Tool ◽  
Selection Of

The actuating input selection is an important basic problem for the parallel mechanism. Based on the screw theory, the constraint screw can be got after locking a kinematic pair in any limb, which can be taken as actuating wrench acted on the moving platform of the parallel mechanism. The constraint screw matrix is composed of the structure constraint screws and the constraint screws of the actuating pairs. The reasonableness of input selection can be judged by the rank of the constraint matrix. The performance of the combinations of actuating inputs is evaluated by the condition numbers of the force constraint matrix and the torque constraint matrix respectively. The theory presented is validated by the simulation and the maching test.

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