scholarly journals The Kinematic and Dynamic Modeling and Numerical Calculation of Robots with Complex Mechanisms Based on Lie Group Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-34
Author(s):  
Lu-Han Ma ◽  
Yong-Bo Zhong ◽  
Gong-Dong Wang ◽  
Nan Li
Keyword(s):  
Numerical Calculation ◽  
Lie Group ◽  
Dynamic Models ◽  
Lagrange Equation ◽  
Kinematic Parameter ◽  
Model Complexity ◽  
Calculation Error ◽  
Closed Chain ◽  
Complex Mechanisms ◽  
The Relationship

The kinematic and dynamic models of robots with complex mechanisms such as the closed-chain mechanism and the branch mechanism are often very complex and difficult to be calculated. Aiming at this issue, in this paper, the pose of the component in robots is represented by the Euclidean group and its subgroups with the proposed method. The component’s velocity is derived using the relationship between the Lie group and Lie algebra, and the acceleration and Jacobian matrix are then derived on this basis. The Lagrange equation is expressed by the obtained kinematic parameter expressions. Establishing the model with this method can obtain clear physical meaning and make the expressions uniform and easy to program, which is convenient for computer-aided calculation and parameterization. Calculating by the properties of the Lie group can reduce the calculation and model complexity, especially for calculating the velocity and acceleration, which reduces the calculation error and eases the calculation. Therefore, the proposed modeling and calculation method of kinematics and dynamics of robots is especially suitable for robots with complex mechanisms. As an example, the kinematic and dynamic model of the manipulator developed in our laboratory is established and a working process of it is numerically calculated. Then, the results of the numerical calculation are compared with the results of virtual prototype simulation in ADAMS to verify the correctness.

scholarly journals Kinematic Analysis of the Robot Having Closed Chain Mechanisms Based on an Improved Modeling Method and Lie Group Theory

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Lu-Han Ma ◽  
Yong-Bo Zhong ◽  
Gong-Dong Wang ◽  
Nan Li
Keyword(s):  
Numerical Calculation ◽  
Error Analysis ◽  
Motion Control ◽  
Lie Group ◽  
Kinematic Analysis ◽  
Kinematic Model ◽  
Modeling Method ◽  
Calibration Error ◽  
Kinematic Modeling ◽  
Closed Chain

The robot kinematic model is the basis of motion control, calibration, error analysis, etc. Considering these factors, the kinematic model needs to meet the requirements of completeness, model continuity, and minimality. DH model as the most widely used method to build robot kinematic model still has problems in completeness, model continuity, and calculation, especially for robots with complex mechanisms such as closed chain mechanism and branch mechanism. In this paper, an improved kinematic modeling method is proposed based on the cooperation of the DH model and the Hayati and Mirmirani model and considering the Lie group concept. The improved model is complete and continuous, and when combining with Lie group to calculate, it avoids numbers of trigonometric functions and antitrigonometric functions in the process so as to optimize the algorithm. With this method, the kinematic model of the closed chain cascade manipulator developed in our laboratory is established, and a working process of it is numerically calculated. The results of the numerical calculation are basically consistent with those of virtual prototype simulation, which means the established kinematic model is correct and the numerical calculation method can solve the problem correctly. The kinematic model and the results of the kinematic analysis provide a theoretical basis for the subsequent motion control, calibration, and error analysis of the robot.

scholarly journals Online Reviews and Product Sales: The Role of Review Visibility

2021 ◽  
Vol 16 (4) ◽  
pp. 638-669
Author(s):  
Miriam Alzate ◽  
Marta Arce-Urriza ◽  
Javier Cebollada
Keyword(s):  
Decision Making ◽  
Dynamic Models ◽  
Generalized Method Of Moments ◽  
Online Reviews ◽  
Consumer Decision Making ◽  
Product Sales ◽  
The Impact ◽  
The Relationship ◽  
The Empirical Analysis

When studying the impact of online reviews on product sales, previous scholars have usually assumed that every review for a product has the same probability of being viewed by consumers. However, decision-making and information processing theories underline that the accessibility of information plays a role in consumer decision-making. We incorporate the notion of review visibility to study the relationship between online reviews and product sales, which is proxied by sales rank information, studying three different cases: (1) when every online review is assumed to have the same probability of being viewed; (2) when we assume that consumers sort online reviews by the most helpful mechanism; and (3) when we assume that consumers sort online reviews by the most recent mechanism. Review non-textual and textual variables are analyzed. The empirical analysis is conducted using a panel of 119 cosmetic products over a period of nine weeks. Using the system generalized method of moments (system GMM) method for dynamic models of panel data, our findings reveal that review variables influence product sales, but the magnitude, and even the direction of the effect, vary amongst visibility cases. Overall, the characteristics of the most helpful reviews have a higher impact on sales.

A Generalized Performance Sensitivity Synthesis Methodology for Four-Bar Mechanisms

1992 ◽  
Author(s):  
Ming-Yih Lee ◽  
Arthur G. Erdman ◽  
Salaheddine Faik
Keyword(s):  
Solution Space ◽  
Design Solution ◽  
Link Length ◽  
Performance Sensitivity ◽  
Closed Chain ◽  
Synthesis Methodology ◽  
Position Synthesis ◽  
The Relationship ◽  
Accuracy Performance ◽  
Sensitivity Maps

Abstract A generalized accuracy performance synthesis methodology for planar closed chain mechanisms is proposed. The relationship between the sensitivity to variations of link lengths and the location of the moving pivots of four-link mechanisms is investigated for the particular objective of three and four position synthesis. In the three design positions case, sensitivity maps with isosensitivity curves plotted in the design solution space allow the designer to synthesize a planar mechanism with desired sensitivity value or to optimize sensitivity from a set of acceptable design solutions. In the case of four design positions, segments of the Burmester design curves that exhibit specified sensitivity to link length tolerance are identified. A performance sensitivity criterion is used as a convenient and a useful way of discriminating between many possible solutions to a given synthesis problem.

scholarly journals Effect of Thickness of Gravel Base and Asphalt Pavement on Road Deformation

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Dongliang He ◽  
Weijun Yang
Keyword(s):  
Numerical Calculation ◽  
Test Section ◽  
Asphalt Pavement ◽  
Road Surface ◽  
Vertical Deformation ◽  
The Road ◽  
Design Requirements ◽  
The Relationship

This study uses a test section of a highway, a study object, to explore the effect of thickness of the gravel base and asphalt layer on the vertical deformation of the road surface. The thickness of the asphalt layer and graded gravel base is changed. The nonlinear description equation of the relationship between the thickness (h1) of the asphalt layer and the vertical deformation (d1) is established: d1=a41−b4h1. The thickness of the asphalt pavement is then determined to reduce vertical deformation. Numerical calculation shows that the maximum vertical deformation of the foundation is within 8 mm, which is less than the 15 mm maximum vertical deformation of the embankment. This level meets the design requirements.

scholarly journals On Designing an Expert Diagnostic System of the Aircraft Turbine Engine Functional Units

2020 ◽  
Vol 50 (1) ◽  
pp. 171-192
Author(s):  
Henryk Borowczyk ◽  
Jarosław Spychała
Keyword(s):  
Dynamic Models ◽  
Diagnostic System ◽  
Compact Representation ◽  
Diagnostic Model ◽  
Diagnostic Systems ◽  
Turbine Engine ◽  
Flight Data ◽  
Diagnostic Parameters ◽  
Functional Units ◽  
The Relationship

AbstractThe paper presents issues related to the design of an expert diagnostic system of turbine engine functional units. Dedicated diagnostic stations and on-board flight data recorders are the sources of diagnostic signals. The signals were parameterized or identified dynamic models to get a compact representation in the form of a set of parameters. The set of diagnostic parameters was subjected to integer encoding. On this basis, a multi-valued diagnostic model describing the relationship between the set of faults and the set of symptoms (code values of diagnostic parameters) was determined. The proposed approach can be used in the design of expert diagnostic systems for propulsion units of any aircraft.

Revisited the Relationship Between Economic Growth and Transport Infrastructure in India: An Empirical Study

2021 ◽  
pp. 001946622110635
Author(s):  
Prabir Kumar Ghosh ◽  
Soumyananda Dinda
Keyword(s):  
Economic Growth ◽  
Dynamic Models ◽  
Composite Index ◽  
Principal Component ◽  
Transport Infrastructure ◽  
Positive Contribution ◽  
Model Framework ◽  
Vector Error Correction ◽  
Long Run ◽  
The Relationship

This study empirically re-examines the relationship between transport infrastructure and economic growth in India for the period 1990–2017. Multivariate dynamic models are applied to estimate the relationship between economic growth and different modes of transport infrastructure namely road, rail and air transports in the vector error correction model framework. The results reveal that road and air transports have significant positive contribution to economic growth in the long-run while rail transport is insignificant. This study further examines the said issue using unit free index variables and has constructed a composite index of transport infrastructure using principal component analysis to analyse the nexus between aggregate transport infrastructure and economic growth in India in the post globalisation era. The results of the study indicate the bidirectional causality between aggregate transport infrastructure and economic growth. Results of this study suggest incorporating feedback issue in policy formulations. JEL Codes: C22, O18, R4

scholarly journals Impact of coherence decay on wavepacket models for broadband shock-associated noise in supersonic jets

2019 ◽  
Vol 863 ◽  
pp. 969-993 ◽  
Author(s):  
Marcus H. Wong ◽  
Peter Jordan ◽  
Damon R. Honnery ◽  
Daniel Edgington-Mitchell
Keyword(s):  
Dynamic Models ◽  
Critical Role ◽  
Coherence Function ◽  
Supersonic Jets ◽  
Far Field ◽  
Shock Cell ◽  
Acoustic Spectrum ◽  
Flow Mechanisms ◽  
The Relationship ◽  
Field Sound

Motivated by the success of wavepackets in modelling the noise from subsonic and perfectly expanded supersonic jets, we apply the wavepacket model to imperfectly expanded supersonic jets. Recent studies with subsonic jets have demonstrated the importance of capturing the ‘jitter’ of wavepackets in order to correctly predict the intensity of far-field sound. Wavepacket jitter may be statistically represented using a two-point coherence function; accurate prediction of noise requires identification of this coherence function. Following the analysis of Cavalieri & Agarwal (J. Fluid Mech., vol. 748, 2014. pp. 399–415), we extend their methodology to model the acoustic sources of broadband shock-associated noise in imperfectly expanded supersonic jets using cross-spectral densities of the turbulent and shock-cell quantities. The aim is to determine the relationship between wavepacket coherence-decay and far-field broadband shock-associated noise, using the model as a vehicle to explore the flow mechanisms at work. Unlike the subsonic case where inclusion of coherence decay amplifies the sound pressure level over the whole acoustic spectrum, we find that it does not play such a critical role in determining the peak sound amplitude for shock-cell noise. When higher-order shock-cell modes are used to reconstruct the acoustic spectrum at higher frequencies, however, the inclusion of a jittering wavepacket is necessary. These results suggest that the requirement for coherence decay identified in prior broadband shock-associated noise (BBSAN) models is in reality the statistical signature of jittering wavepackets. The results from this modelling approach suggest that nonlinear jittering effects of wavepackets need to be included in dynamic models for broadband shock-associated noise.

Urban Spatial Structure and Travel in China

2019 ◽  
Vol 35 (1) ◽  
pp. 6-24 ◽  
Author(s):  
Lingqian Hu ◽  
Jiawen Yang ◽  
Tianren Yang ◽  
Yuanjie Tu ◽  
Jing Zhu
Keyword(s):  
Spatial Structure ◽  
Scoping Review ◽  
Contextual Factors ◽  
Mixed Effects ◽  
Empirical Literature ◽  
Future Research ◽  
Urban Structure ◽  
Urban Spatial Structure ◽  
Complex Mechanisms ◽  
The Relationship

This article first provides a critical scoping review of empirical literature on the relationship between urban structure and travel in China. The review finds that residential suburbanization alone increases travel, polycentric development has mixed effects, and jobs–housing balance reduces travel. Second, this article compares the empirical findings of the urban structure–travel relationships in China with those observed in other countries, and it identifies contextual factors that can explain the differing relationships in China. We suggest that future research improve data and methodology and broaden the research scope to investigate the complex mechanisms that affect the urban structure–travel relationship in China.

scholarly journals Lagrangians, Gauge Functions, and Lie Groups for Semigroup of Second-Order Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Z. E. Musielak ◽  
N. Davachi ◽  
M. Rosario-Franco
Keyword(s):  
Differential Equations ◽  
Lie Groups ◽  
Lie Group ◽  
Algebraic Structure ◽  
Second Order ◽  
Lagrangian Formalism ◽  
Group Approach ◽  
Second Order Differential Equations ◽  
Gauge Functions ◽  
The Relationship

A set of linear second-order differential equations is converted into a semigroup, whose algebraic structure is used to generate novel equations. The Lagrangian formalism based on standard, null, and nonstandard Lagrangians is established for all members of the semigroup. For the null Lagrangians, their corresponding gauge functions are derived. The obtained Lagrangians are either new or generalization of those previously known. The previously developed Lie group approach to derive some equations of the semigroup is also described. It is shown that certain equations of the semigroup cannot be factorized, and therefore, their Lie groups cannot be determined. A possible solution of this problem is proposed, and the relationship between the Lagrangian formalism and the Lie group approach is discussed.

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