Geometry and Direct Kinematics to MP3R with 4×4 Operators

Journal of Mechatronics and Robotics,Volume 1, Issue 2, Pages 38-46, 2017; DOI: 10.3844/jmrsp.2017.38.46

9 Pages Posted: 6 Jan 2018

See all articles by Relly Victoria Petrescu

Relly Victoria Petrescu

Polytechnic University of Bucharest - ARoTMM-IFToMM

Raffaella Aversa

Advanced Material Lab - Department of Architecture and Industrial Design

B. Akash

American University of Ras Al Khaimah

Filippo Berto

Norwegian University of Science and Technology (NTNU) - Department of Engineering Design and Materials

Antonio Apicella

Advanced Material Lab - Department of Architecture and Industrial Design

Florian Ion Petrescu

Polytechnic University of Bucharest - ARoTMM-IFToMM

Date Written: November 25, 2017

Abstract

Anthropomorphic mechatronic systems are the most widely used robotics systems worldwide today in industry and in all automated environments. These systems are best suited to the modern automation and mechatronisation needs of the modern world, being mobile, dynamic, light, robust, complex, technologically simple, easy to design and manufactured, implemented, maintained and used in almost any industrial site, both in machine building and in special environments, such as chemical, toxic, dyeing, underwater, nuclear, in space.... Anthropomorphic robots are flexible, dynamic, stable, lightweight, fast, fast, inexpensive, easy-to-install, mechanical, mechanical, mechanical and mechanical systems with a pleasant appearance, modern industrial design and easy to design and implement in any workplace, imposed. In this study we will present the 4×4 operators and the way they can be implemented and used in the complex matrix calculations in order to simplify the complex matrix algebraic numerical methods. 4×4 operators are designed to simplify algebraic matrix calculations by making difficult matrix operations simpler and easier to approach. The method of using 4×4 operators is meant to introduce a degree in addition to the matrices to facilitate algebraic operations. The kinematics of serial manipulators and robots will be exemplified for the 3R kinematic model. The fixed coordinate system was denoted by x0O0y0z0. The mobile systems (rigid) of the three mobile elements (1, 2, 3) have indices 1, 2 and 3. Their orientation has been chosen conveniently. Known kinematic parameters in the direct kinematics are the absolute rotation angles of the three moving elements: φ10, φ20, φ30, angles related to the rotation of the three actuators (electric motors) mounted in the kinematic rotation couplers. The output parameters are the three absolute coordinates xM, yM, zM of point M, i.e., the kinematic parameters (coordinates) of the endeffector (the actuator element (the final), which can be a grasping hand, a solder tip, painted , cut, etc ...). The 3×3 matrix is transformed into 4×4 (it is a mathematical operator) by adding two zero vectors (formed from three elements 0), one line and the other column, and adding one element 1 to the main diagonal (the last element). The matched T01 matrix becomes T014. The column vector matrix (consisting of three elements) undergoes a minimal transformation receiving a fourth fixed value 1 if it is only used for matrix products. The convenient form of matrix A12 is A12c.

Note: Copyright © 2017 Relly Victoria Petrescu, Raffaella Aversa, Bilal Akash, Filippo Berto, Antonio Apicella and Florian Ion Tiberiu Petrescu. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Suggested Citation

Petrescu, Relly Victoria and Aversa, Raffaella and Akash, B. and Berto, Filippo and Apicella, Antonio and Petrescu, Florian Ion, Geometry and Direct Kinematics to MP3R with 4×4 Operators (November 25, 2017). Journal of Mechatronics and Robotics,Volume 1, Issue 2, Pages 38-46, 2017; DOI: 10.3844/jmrsp.2017.38.46. Available at SSRN: https://ssrn.com/abstract=3096478 or http://dx.doi.org/10.2139/ssrn.3096478

Relly Victoria Petrescu

Polytechnic University of Bucharest - ARoTMM-IFToMM ( email )

Romania

Raffaella Aversa

Advanced Material Lab - Department of Architecture and Industrial Design ( email )

81031 Aversa (CE)
Italy

B. Akash

American University of Ras Al Khaimah ( email )

American University of Ras Al Khaimah
School of Graduate Studies and Research
Ras Al Khaimah, RAK 10021
United Arab Emirates

HOME PAGE: http://www.aurak.ac.ae

Filippo Berto

Norwegian University of Science and Technology (NTNU) - Department of Engineering Design and Materials ( email )

Trondheim
Norway

Antonio Apicella

Advanced Material Lab - Department of Architecture and Industrial Design ( email )

81031 Aversa (CE)
Italy

Florian Ion Petrescu (Contact Author)

Polytechnic University of Bucharest - ARoTMM-IFToMM ( email )

Romania

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