ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζῴων τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν

**Seminar
MECHANICS OF MACHINES AND MECHANISMS - MODELS AND MATHEMATICAL METHODS**

**PROGRAM**

**Plan rada Seminara Mehanika mašina i mehanizama - modeli i matematičke metode za DECEMBAR 2019.**

**UTORAK, 03.12.2019. u 17:00, Sala 301f, MI SANU, Kneza Mihaila 36**

*Ana Đurić, Wayne State University, Detroit, MI, U.S.A.*

**MODELING AND SOLVING ROBOTICS SYSTEMS USING RECONFIGURABLE TECHNIQUES**

Automated model generation and solutions for motion planning and re-planning of automated systems will play an important role in future of reconfigurable manufacturing systems. An n-DOF Global Kinematic Model (n-GKM) was developed for any combination of either rotational or translational type of joints. The automatic generation of the dynamic equations for the n-GKM is presented. For the symbolic calculation of the n-GKM dynamic equations, the recursive Newton-Euler algorithm is employed using the symbolic algebra package MAPLE 18. The dynamic model is named Global Dynamic Model (n-GDM).

The significance of the n-GDM is that it automatically generates each element of the inertia matrix A, Coriolis torque matrix B, centrifugal torque matrix C, and the gravity torque vector G, using the Automatic Separation Method (ASM). Several examples are used to demonstrate and validate the ASM equations.

The n-GDM is a dynamic solver for the n-GKM which includes predefined reconfigurable parameters. These parameters are used to control the joint’s positive directions and its type (rotational and/or translational).

Instead of solving the dynamics of different kinematic structures, the n-GDM can be used to auto-generate the solution by only defining these reconfigurable parameters. Using n-DOF Global Dynamic Model equations, a 3-DOF Global Dynamic Model (GDM) is derived. The 3-GDM has been validated using five selected cases (RR, RT, TR, TT planar and SCARA configurations). The results proved the model validity.
The 2-DOF Global Kinematic Model (2-GKM) model with both rotational and/or translational types of joints has been selected to demonstrate how to control reconfigurable paths.

Experimentally obtained velocity and pressure fields behind the CRM (common research model) wing are studied. CRM is designed by NASA and Boeing. Measurements have been performed in the windtunnel at 50 m/s and Reynolds number at wing tip chord Re

Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia

The project has produced original scientific results in the following themes:

- Elements of mathematical phenomenology and applications (in Mechanics, in nonlinear dynamics in general, in integration of scientific knowledge in reduction of number of models of dynamical systems).
- Analytical mechanics of discrete fractional order systems; Derived a series of theorems.
- Nonlinear and rare phenomena in dynamics of hybrid systems with coupled structures of rigid and deformable bodies; Transfer of energy through a system and subsystems; Synchronization of subsystems.
- Models of biodynamical oscillators; Phenomenon of transfer of signals, information and energy through their complex structures; Oscillations of DNA helix chains and discrete continuum models of Zone Pelucida, a biomechanical oscillatory model of the mitotic spindle.
- Mechanics of discrete continuum models. Dynamics of coupled structures of deformable bodies and discrete continuum layers with different constitutive relations: Linear elastic, nonlinear elastic, visco-elastic, hereditary and fractional order properties.
- Phenomenon of dynamics of systems with friction and vibro-impact system; Theory of collision of rolling bodies; Dynamics of billiards.
- Mechanics of damage and fracture.
- Control of systems with delay and theorems of stability.
- Continuation of doctoral research in accordance with scientific based themes by younger PhD students. 13 PhD students, younger than 30 years of age, are included in the project team and its scientific research. All of them were participants of the two year seminar. So far, 13 PhD students completed all courses at doctoral study programs; 11 candidates defender their doctoral dissertations.

Seminar Mehanika mašina i mehanizama - modeli i matematičke metode započeo je sa radom u junu 2018.god. Seminar se održava do dva puta mesečno, utorkom u periodu od 17.00 - 19.00 u Matematičkom institutu SANU.

dr Ivana Atanasovska

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