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

Mohamed Aboelnasr; Hussein M Bahaa; Ossama Mokhiamar

doi:10.15282/jmes.15.2.2021.02.0627

Authors

M.I.M. Abo Elnasr Department of Electro-Mechanical Engineering, Faculty of Engineering, Alexandria University, El-Chatby, Alexandria 21544, Egypt
Hussein M Bahaa Department of Electro-Mechanical Engineering, Faculty of Engineering, Alexandria University, El-Chatby, Alexandria 21544, Egypt
Ossama Mokhiamar Mechanical Engineering Department, Faculty of Engineering, Alexandria University, El-Chatby, Alexandria 21544, Egypt

DOI:

https://doi.org/10.15282/jmes.15.2.2021.02.0627

Keywords:

singularity analysis, Kinematic modeling, Monte-Carlo methods, 6 DOF Serial robotic arm, Forward Kinematics

Abstract

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.

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