The Direct Kinematics of Objects Suspended From Cables

2010 ◽  
Author(s):  
Qimi Jiang ◽  
Vijay Kumar
Keyword(s):  
Nonlinear System ◽  
Case Studies ◽  
Horizontal Plane ◽  
Regular Polygon ◽  
Polynomial Equation ◽  
Search Algorithms ◽  
Cable System ◽  
Equilibrium Configurations ◽  
Position And Orientation ◽  
Direct Kinematics

This work addresses the problem for determining the position and orientation of an object with regular polygon suspended from n cables with the same length when the n robots form a regular polygon on the horizontal plane. First, an analytic algorithm based on resultant elimination is presented to determine all possible equilibrium configurations of the planar 4-bar linkage. As the nonlinear system can be reduced to a polynomial equation in one unknown with a degree 8, this algorithm is more efficient than numerical search algorithms. Then, considering that the motion of the 3D cable system in its vertical planes of symmetry can be regarded as the motion of an equivalent planar 4-bar linkage, the proposed algorithm is used to solve the direct kinematic problem of objects suspended from multiple cables. Then, case studies with three to six cables are conducted for demonstration. Finally, experiments are conducted for validation.

Determination and Stability Analysis of Equilibrium Configurations of Objects Suspended From Multiple Aerial Robots

2012 ◽  
Vol 4 (2) ◽  
Author(s):  
Qimi Jiang ◽  
Vijay Kumar
Keyword(s):  
Stability Analysis ◽  
Hessian Matrix ◽  
Polynomial Equation ◽  
Search Algorithms ◽  
Cable System ◽  
Aerial Robots ◽  
Equilibrium Configurations ◽  
Position And Orientation ◽  
The Stability ◽  
Direct Kinematics

This work addresses the problem for determining the position and orientation of objects suspended with n cables from n aerial robots. This is actually the direct kinematics problem of the 3D cable system. First, the problem is formulated based on the static equilibrium condition. Then, an analytic algorithm based on resultant elimination is proposed to determine all possible equilibrium configurations of the planar 4-bar linkage. As the nonlinear system can be reduced to a polynomial equation in one unknown with a degree 8, this algorithm is more efficient than numerical search algorithms. Considering that the motion of a 3D cable system in its vertical planes of symmetry can be regarded as the motion of an equivalent planar 4-bar linkage, the proposed algorithm is used to solve the direct kinematics problem of objects suspended from multiple aerial robots. Case studies with three to six robots are conducted for demonstration. Then, approaches for stability analysis based on Hessian matrix are developed, and the stability of obtained equilibrium configurations is analyzed. Finally, experiments are conducted for validation.

scholarly journals The Comparison of Docking Search Algorithms and Scoring Functions

2017 ◽  
pp. 820-849
Author(s):  
Marjana Novič ◽  
Tjaša Tibaut ◽  
Marko Anderluh ◽  
Jure Borišek ◽  
Tihomir Tomašič
Keyword(s):  
Organic Chemistry ◽  
Molecular Docking ◽  
Case Studies ◽  
Experimental Work ◽  
Cathepsin K ◽  
Docking Studies ◽  
Search Algorithms ◽  
Scoring Functions ◽  
Basic Information

This chapter, composed of two parts, firstly provides molecular docking overview and secondly two molecular docking case studies are described. In overview, basic information about molecular docking are presented such as description of search algorithms and scoring functions applied in various docking programs. Brief description of methods utilized in some of the most popular docking programs also applied in our experimental work is provided. AutoDock, CDOCKER, GOLD, FlexX and FRED were used for docking studies of the DC-SIGN protein, while GOLD was further used for docking studies of cathepsin K protein. Methods and results of our studies with their contribution to science and medicine are presented. Content of the chapter is therefore appropriate for public of Medicinal and Organic Chemistry as an overview of docking studies, and also for Computational Chemists at the beginning of their work as the introduction to application of molecular docking programs.

The Comparison of Docking Search Algorithms and Scoring Functions

2016 ◽  
pp. 99-127 ◽  
Author(s):  
Marjana Novič ◽  
Tjaša Tibaut ◽  
Marko Anderluh ◽  
Jure Borišek ◽  
Tihomir Tomašič
Keyword(s):  
Organic Chemistry ◽  
Molecular Docking ◽  
Case Studies ◽  
Experimental Work ◽  
Cathepsin K ◽  
Docking Studies ◽  
Search Algorithms ◽  
Scoring Functions ◽  
Basic Information

This chapter, composed of two parts, firstly provides molecular docking overview and secondly two molecular docking case studies are described. In overview, basic information about molecular docking are presented such as description of search algorithms and scoring functions applied in various docking programs. Brief description of methods utilized in some of the most popular docking programs also applied in our experimental work is provided. AutoDock, CDOCKER, GOLD, FlexX and FRED were used for docking studies of the DC-SIGN protein, while GOLD was further used for docking studies of cathepsin K protein. Methods and results of our studies with their contribution to science and medicine are presented. Content of the chapter is therefore appropriate for public of Medicinal and Organic Chemistry as an overview of docking studies, and also for Computational Chemists at the beginning of their work as the introduction to application of molecular docking programs.

Molecular Docking at a Glance

2016 ◽  
pp. 1-38
Author(s):  
Maryam Hamzeh-Mivehroud ◽  
Babak Sokouti ◽  
Siavoush Dastmalchi
Keyword(s):  
Molecular Docking ◽  
Case Studies ◽  
Scientific Community ◽  
Docking Studies ◽  
Search Algorithms ◽  
Steady Increase ◽  
Scoring Functions ◽  
Exponential Expansion ◽  
And Performance ◽  
Computational Resources

The current chapter introduces different aspects of molecular docking technique in order to give an overview to the readers about the topics which will be dealt with throughout this volume. Like many other fields of science, molecular docking studies has experienced a lagging period of slow and steady increase in terms of acquiring attention of scientific community as well as its frequency of application, followed by a pronounced era of exponential expansion in theory, methodology, areas of application and performance due to developments in related technologies such as computational resources and theoretical as well as experimental biophysical methods. In the following sections the evolution of molecular docking will be reviewed and its different components including methods, search algorithms, scoring functions, validation of the methods, and area of applications plus few case studies will be touched briefly.

scholarly journals Nonlinear System Identification in coherence with Nonlinearity measure for Dynamic Physical systems- Case Studies

2021 ◽  
Author(s):  
Joanofarc Xavier ◽  
Rames C Panda ◽  
SK Patnaik
Keyword(s):  
Nonlinear Dynamics ◽  
System Identification ◽  
Nonlinear System ◽  
Case Studies ◽  
Nonlinear System Identification ◽  
Least Square ◽  
Measurement Tool ◽  
Identification Methods ◽  
Physical Systems ◽  
Highly Nonlinear

Abstract With the recent success of using the time series to vast applications, one would expect its boundless adaptation to problems like nonlinear control and nonlinearity quantification. Though there exist many system identification methods, finding suitable method for identifying a given process is still cryptic. Moreover, to this notch, research on their usage to nonlinear system identification and classification of nonlinearity remains limited. This article hovers around the central idea of developing a ‘kSINDYc’ (key term based Sparse Identification of Nonlinear Dynamics with control) algorithm to capture the nonlinear dynamics of typical physical systems. Furthermore, existing two reliable identification methods namely NL2SQ (Nonlinear least square method) and N3ARX (Neural network based nonlinear auto regressive exogenous input scheme) are also considered for all the physical process-case studies. The primary spotlight of present research is to encapsulate the nonlinear dynamics identified for any process with its nonlinearity level through a mathematical measurement tool. The nonlinear metric Convergence Area based Nonlinear Measure (CANM) calculates the process nonlinearity in the dynamic physical systems and classifies them under mild, medium and highly nonlinear categories. Simulation studies are carried-out on five industrial systems with divergent nonlinear dynamics. The user can make a flawless choice of specific identification methods suitable for given process by finding the nonlinear metric (Δ0). Finally, parametric sensitivity on the measurement has been studied on CSTR and Bioreactor to evaluate the efficacy of kSINDYc on system identification.

A New Algebraic Solution to Inverse Static Force Analysis of a Special Planar Three-Spring System

2016 ◽  
Author(s):  
Ying Zhang ◽  
Qizheng Liao ◽  
Shimin Wei ◽  
Feng Wei ◽  
Duanling Li
Keyword(s):  
Polynomial Equation ◽  
Algebraic Solution ◽  
Static Force ◽  
Force Analysis ◽  
Elimination Algorithm ◽  
Equilibrium Configurations ◽  
Spring System ◽  
Univariate Polynomial ◽  
Variable Substitution ◽  
Resultant Matrix

In this paper, we present a new algebraic elimination algorithm for the inverse static force analysis of a special planar three-spring system. The system consists of three linear springs joined to the ground at the two fixed pivots and connected to the two moving pivots at the platform. When exerted by specified static force, the goal of inverse static analysis is to determine all the equilibrium configurations. First of all, a system of seven polynomial equations in seven variables is established based on the geometric constraint and static force balancing. Then, four basic constraint equations in four variables are obtained by variable substitution. Next, a 20 by 20 resultant matrix is reduced by means of three consecutive Sylvester elimination process. Finally, a 54th-degree univariate polynomial equation is directly derived without extraneous roots in the computer algebra system Mathematica 9.0. At last, a numerical example is given to verify the elimination procedure.

Workspace analysis and performance of a binary actuated parallel manipulator with flexural joints

2003 ◽  
Vol 217 (3) ◽  
pp. 313-330 ◽  
Author(s):  
E Ottaviano ◽  
G Carbone ◽  
M Ceccarelli
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Parallel Manipulator ◽  
Mechanical Design ◽  
Parallel Architecture ◽  
Workspace Analysis ◽  
Position And Orientation ◽  
And Performance ◽  
Direct Kinematics ◽  
Flexural Joints

In this paper the design of a miniaturized parallel architecture is investigated in terms of basic performances concerning mobility and workspace characteristics. The miniature requirements have been achieved with a milli-scaled parallel manipulator requiring flexural joints and binary actuation with shape memory alloy wires or small pneumatic pistons. The mechanical design is analysed by considering the mobility of the flexural joints in order to size them and model the kinematics of the joints. The reachability is analysed through a suitable formulation of the direct kinematics by also taking into account binary actuation. Workspace performance has been determined in terms of position and orientation capabilities.

scholarly journals Impact of Selected Electrical Cables Slope on Flame Out Time and Flame Spread

2019 ◽  
Vol 27 (44) ◽  
pp. 41-47
Author(s):  
Aleš Nečas ◽  
Jozef Martinka ◽  
Igor Wachter ◽  
Tomáš Štefko ◽  
Martina Hladová ◽  
...  
Keyword(s):  
Cross Section ◽  
Flame Spread ◽  
Horizontal Plane ◽  
Spread Rate ◽  
Cable System ◽  
Vertical Orientation ◽  
Electrical Cable ◽  
Horizontal Orientation ◽  
Electrical Cables ◽  
The Impact

Abstract The aim of the research described in this paper was to study the impact of the electrical cables slope on the flame out time and the flame spread rate. Measured cables were thermally loaded by methanol flame (diameter of the container was 106 mm) at seven different slopes with respect to the horizontal plane (the slopes were 0° – horizontal orientation, 15°, 30°, 45°, 60°, 75° and 90° - vertical orientation). The first tested electrical cable was a copper three-core power one resistant to the flame spread with circuit integrity of the cable system during 30 minutes under fire (cross-section of each core was 1.5 mm2). The second tested electrical cable was a copper two-core signal one resistant to the flame spread with circuit integrity of the cable system during 30 minutes under fire (cross-section of each core was 0.5 mm2). The first electrical cable did not show reaction to fire class. The reaction to fire class of the second tested cable was B2ca, s1, d1, a1. The obtained results proved that slope had virtually no impact on the flame out time and the flame spread over the tested cable surface (tested cables of all slopes stopped burning after 1 to 5 seconds after methanol flame burned out). Likewise, the flame spread was only negligibly beyond the border of flame action for each cable slope.

Chapter 2. CNF Encodings

2021 ◽  
Author(s):  
Steven Prestwich
Keyword(s):  
Normal Form ◽  
Case Studies ◽  
Search Algorithm ◽  
Empirical Work ◽  
Combinatorial Problem ◽  
Conjunctive Normal Form ◽  
Search Algorithms ◽  
File Format ◽  
Sources Of Error ◽  
Algorithm Implementation

Before a combinatorial problem can be solved by current SAT methods, it must usually be encoded in conjunctive normal form, which facilitates algorithm implementation and allows a common file format for problems. Unfortunately there are several ways of encoding most problems and few guidelines on how to choose among them, yet the choice of encoding can be as important as the choice of search algorithm. This chapter reviews theoretical and empirical work on encoding methods, including the use of Tseitin encodings, the encoding of extensional and intensional constraints, the interaction between encodings and search algorithms, and some common sources of error. Case studies are used for illustration.

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