Novel use of the Monte-Carlo methods to visualize singularity configurations in serial manipulators

2021 ◽  
Vol 15 (2) ◽  
pp. 7948-7963
Author(s):  
Mohamed Aboelnasr ◽  
Hussein M Bahaa ◽  
Ossama Mokhiamar
Keyword(s):  
Monte Carlo ◽  
Numerical Methods ◽  
Curve Fitting ◽  
Jacobian Matrix ◽  
Forward Kinematics ◽  
Graphical Methods ◽  
Kinematic Singularity ◽  
Serial Manipulators ◽  
Serial Robots ◽  
Contour Plots

This paper analyses the problem of the kinematic singularity of 6 DOF serial robots by extending the use of Monte-Carlo numerical methods to visualize singularity configurations. To achieve this goal, first, forward kinematics and D-H parameters have been derived for the manipulator. Second, the derived equations are used to generate and visualize a workspace that gives a good intuition of the motion shape of the manipulator. Third, the Jacobian matrix is computed using graphical methods, aiming to locate positions that cause singularity. Finally, the data obtained are processed in order to visualize the singularity and to design a trajectory free of singularity. MATLAB robotics toolbox, Symbolic toolbox, and curve fitting toolbox are the MATLAB toolboxes used in the calculations. The results of the surface and contour plots of the determinate of the Jacobian matrix behavior lead to design a manipulator’s trajectory free of singularity and show the parameters that affect the manipulator’s singularity and its behavior in the workspace.

Numerical Methods for the Kinetic Theory of Fluids

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Molecular Dynamics ◽  
Monte Carlo ◽  
Numerical Methods ◽  
Kinetic Theory ◽  
Computational Efficiency ◽  
Lattice Boltzmann ◽  
Direct Simulation Monte Carlo ◽  
Particle Methods ◽  
Direct Simulation ◽  
Simulation Monte Carlo

This chapter provides a bird’s eye view of the main numerical particle methods used in the kinetic theory of fluids, the main purpose being of locating Lattice Boltzmann in the broader context of computational kinetic theory. The leading numerical methods for dense and rarified fluids are Molecular Dynamics (MD) and Direct Simulation Monte Carlo (DSMC), respectively. These methods date of the mid 50s and 60s, respectively, and, ever since, they have undergone a series of impressive developments and refinements which have turned them in major tools of investigation, discovery and design. However, they are both very demanding on computational grounds, which motivates a ceaseless demand for new and improved variants aimed at enhancing their computational efficiency without losing physical fidelity and vice versa, enhance their physical fidelity without compromising computational viability.

Solitons propagation dynamics in a saturable PT-symmetric fractional medium

2021 ◽  
Author(s):  
Davood Hajitaghi Tehrani ◽  
Mehdi Solaimani ◽  
Mahboubeh Ghalandari ◽  
Bahman Babayar Razlighi
Keyword(s):  
Monte Carlo ◽  
Numerical Methods ◽  
Physical Properties ◽  
Maximum Intensity ◽  
Step Method ◽  
Saturation Parameter ◽  
Potential Depth ◽  
Fractional System ◽  
Nonlinear Fractional Schrödinger Equation ◽  
Good Agreement

Abstract In the current research, the propagation of solitons in a saturable PT-symmetric fractional system is studied by solving nonlinear fractional Schrödinger equation. Three numerical methods are employed for this purpose, namely Monte Carlo based Euler-Lagrange variational schema, split-step method, and extrapolation approach. The results show good agreement and accuracy. The effect of different parameters such as potential depth, Levy indices, and saturation parameter, on the physical properties of the systems such as maximum intensity and soliton width oscillations are considered.

Domains of Interference Between Working Bodies in Mechanisms and Manipulators

1995 ◽  
Author(s):  
Edward J. Haug ◽  
Frederick A. Adkins ◽  
Chi-Mei Luh ◽  
Jia-Yi Wang
Keyword(s):  
Numerical Methods ◽  
Jacobian Matrix ◽  
Underlying Mechanism ◽  
Rank Deficiency ◽  
Ground Vehicle ◽  
Complementary Problems ◽  
Stewart Platforms ◽  
Working Bodies ◽  
Set Of Points

Abstract Criteria for the set of all points in a pair of working bodies in a mechanism or manipulator that can coincide for any kinematically admissible configuration of the underlying mechanism, called the domain of interference between the bodies, are formulated. Kinematic equations for the mechanism and parameterizations of the domains of the working bodies are used to derive analytical criteria for domains of interference. Three complementary problems are formulated and analyzed to characterize (1) the set of points in one of the interfering bodies that are occupied by any point in the second body, (2) the set of points in one of the interfering bodies that are occupied by any point on the boundary of the second body, and (3) the set of all points in space that are simultaneously occupied by points in the interfering bodies; each condition occurring for any kinematically admissible configuration of the mechanism. Analytical criteria for the boundaries of domains of interference for each of the three problems arc derived, based on row-rank deficiency of a sub-Jacobian matrix associated with the kinematic equations for each of the problems. Numerical methods for mapping boundaries of domains of interference are presented and illustrated for planar Stewart platforms with domes attached that are characteristic of flight or ground vehicle simulators.

Numerical Methods in Coupled Monte Carlo and Thermal-Hydraulic Calculations

2017 ◽  
Vol 185 (1) ◽  
pp. 194-205 ◽  
Author(s):  
Daniel F. Gill ◽  
David P. Griesheimer ◽  
David L. Aumiller
Keyword(s):  
Monte Carlo ◽  
Numerical Methods

scholarly journals Forward kinematic analysis of Dobot using closed-loop method

2020 ◽  
Vol 9 (3) ◽  
pp. 153
Author(s):  
Javier Dario Sanjuan De Caro ◽  
Mohammad Rahman ◽  
Ivan Rulik
Keyword(s):  
Analytical Solution ◽  
Kinematic Analysis ◽  
Closed Loop ◽  
Dynamical Model ◽  
Forward Kinematics ◽  
Loop Method ◽  
Serial Robots ◽  
Forward Kinematic

Dobot is a hybrid robot that combines features from parallel and serial robots. Because of this characteristic, the robot excels for is reliability, allowing its implementation in diverse applications. Therefore, researchers have studied its kinematics to improve its capabilities. However, to the extent of our knowledge, no analysis has been reported taking into consideration the closed-loop configuration of Dobot. Thus, this article presents the complete analytical solution for the forward kinematics of Dobot, considering each link. The results are expected to be utilized in the development of a dynamical model that contemplates the dynamics of each element of the robot.

Optimal Design via Curve Fitting of Monte Carlo Experiments

1995 ◽  
Vol 90 (432) ◽  
pp. 1322 ◽  
Author(s):  
Peter Muller ◽  
Giovanni Parmigiani
Keyword(s):  
Monte Carlo ◽  
Optimal Design ◽  
Curve Fitting ◽  
Monte Carlo Experiments

scholarly journals High Performance Numerical Computing for High Energy Physics: A New Challenge for Big Data Science

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Florin Pop
Keyword(s):  
Monte Carlo ◽  
Big Data ◽  
Numerical Methods ◽  
High Performance ◽  
Data Science ◽  
Experimental Validation ◽  
High Energy Physics ◽  
High Energy ◽  
Performance Computing ◽  
Energy Physics

Modern physics is based on both theoretical analysis and experimental validation. Complex scenarios like subatomic dimensions, high energy, and lower absolute temperature are frontiers for many theoretical models. Simulation with stable numerical methods represents an excellent instrument for high accuracy analysis, experimental validation, and visualization. High performance computing support offers possibility to make simulations at large scale, in parallel, but the volume of data generated by these experiments creates a new challenge for Big Data Science. This paper presents existing computational methods for high energy physics (HEP) analyzed from two perspectives: numerical methods and high performance computing. The computational methods presented are Monte Carlo methods and simulations of HEP processes, Markovian Monte Carlo, unfolding methods in particle physics, kernel estimation in HEP, and Random Matrix Theory used in analysis of particles spectrum. All of these methods produce data-intensive applications, which introduce new challenges and requirements for ICT systems architecture, programming paradigms, and storage capabilities.

Simulation and analysis on the ship energy efficiency operational indicator for bulk carriers by Monte Carlo simulation method

2020 ◽  
Vol 11 (04) ◽  
pp. 2050036
Author(s):  
Tien Anh Tran
Keyword(s):  
Energy Efficiency ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Curve Fitting ◽  
Simulation Method ◽  
Monte Carlo Simulation Method ◽  
Bulk Carrier ◽  
Parametric Curve ◽  
Parametric Curve Fitting ◽  
Operational Data

The ship energy efficiency management is an important topic in the field of the energy management onboard and the exhaust gases emission nowadays. The advanced model plays a vital role to improve the ship energy efficiency management when considering the variable factors. The establishment of the ship energy efficiency model through energy efficiency operational indicator (EEOI) index has been conducted through Monte Carlo simulation method along with using the operation data of a bulk carrier. A bulk carrier is chosen, namely, M/V NSU JUSTICE 250,000 DWT of VINIC Shipping Transportation Company in Vietnam. This research uses the real operational data to perform a statistical methodology which calculates the various factors used to calculate EEOI. This method is supported by Matlab program through the curve fitting tool. The normal distribution estimation and the kernel density estimation method are used for the parametric curve fitting and non-parametric curve fitting, respectively. The average weather condition (wind speed and wave height) and the fouling condition of hull have been investigated and compared with the research results. The validation of the proposed methods has been conducted through the study of the external factors influencing the research results. The research result shows the optimal operational data for the fuel consumption at each certain voyage. This paper is useful for the ship-owners and the ship-operators in the field of the ship energy efficiency management.

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