Safe trajectory of a piece moved by a robot

TL;DR

This paper develops a mathematical model for the movement of a metal piece manipulated by a robot, analyzing stresses and deformations using Kirchhoff plate theory, and provides a numerical approach and a simplified solution.

Contribution

It introduces a new mathematical framework for modeling robotic manipulation of metal pieces based on Kirchhoff plate theory, including numerical methods and a simplified solution.

Findings

Derived equations for stresses and deformations during robotic manipulation.

Presented a numerical treatment for the equations.

Provided a solution to the one-dimensional analog of the problem.

Abstract

In this work, we propose a mathematical model for a physical problem based on the movement of a metal piece held by a robot. Using the principles of Kirchoff plate theory, a set of equations determining stresses and deformations caused during the motion, have been provided. We also discuss possible numerical treatment of these equations and finally, a solution to the one-dimensional analog of the problem has been presented.