# Calculation of industrial robot trajectory in frame composite production

• Programs and Algorithms of Numerical Mathematics, Publisher: Institute of Mathematics CAS(Prague), page 81-88

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## Abstract

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This article is focused on calculating the trajectory of an industrial robot in the production of composites for the automotive industry. The production technology is based on the winding of carbon fibres on a polyurethane frame. The frame is fastened to the end-effector of the robot arm (i.e. robot-end-effector, REE). The passage of the frame through the fibre processing head is determined by the REE trajectory. The position of the fibre processing head is fixed and is composed of three fibre guide wheels with coils of carbon fibres. The fibre processing head winds three layers of filaments onto the frame. The polyurethane frame is determined by the local Euclidean coordinate system ${E}_{3}$, which has its origin in the REE. We use a mathematical model and matrix calculus to compute the trajectory of the REE to guarantee the desired passage of the frame through the fibre processing head. The translation and rotation matrices of the local coordinate system (of the REE) are calculated with respect to the base coordinate system of the robot.

## How to cite

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Mlýnek, Jaroslav, Martinec, Tomáš, and Petrů, Michal. "Calculation of industrial robot trajectory in frame composite production." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics CAS, 2017. 81-88. <http://eudml.org/doc/288153>.

@inProceedings{Mlýnek2017,
abstract = {This article is focused on calculating the trajectory of an industrial robot in the production of composites for the automotive industry. The production technology is based on the winding of carbon fibres on a polyurethane frame. The frame is fastened to the end-effector of the robot arm (i.e. robot-end-effector, REE). The passage of the frame through the fibre processing head is determined by the REE trajectory. The position of the fibre processing head is fixed and is composed of three fibre guide wheels with coils of carbon fibres. The fibre processing head winds three layers of filaments onto the frame. The polyurethane frame is determined by the local Euclidean coordinate system $E_\{3\}$, which has its origin in the REE. We use a mathematical model and matrix calculus to compute the trajectory of the REE to guarantee the desired passage of the frame through the fibre processing head. The translation and rotation matrices of the local coordinate system (of the REE) are calculated with respect to the base coordinate system of the robot.},
author = {Mlýnek, Jaroslav, Martinec, Tomáš, Petrů, Michal},
booktitle = {Programs and Algorithms of Numerical Mathematics},
keywords = {robot trajectory; transformation matrix; Euler angle of rotation; orthogonal group},
location = {Prague},
pages = {81-88},
publisher = {Institute of Mathematics CAS},
title = {Calculation of industrial robot trajectory in frame composite production},
url = {http://eudml.org/doc/288153},
year = {2017},
}

TY - CLSWK
AU - Mlýnek, Jaroslav
AU - Martinec, Tomáš
AU - Petrů, Michal
TI - Calculation of industrial robot trajectory in frame composite production
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2017
CY - Prague
PB - Institute of Mathematics CAS
SP - 81
EP - 88
AB - This article is focused on calculating the trajectory of an industrial robot in the production of composites for the automotive industry. The production technology is based on the winding of carbon fibres on a polyurethane frame. The frame is fastened to the end-effector of the robot arm (i.e. robot-end-effector, REE). The passage of the frame through the fibre processing head is determined by the REE trajectory. The position of the fibre processing head is fixed and is composed of three fibre guide wheels with coils of carbon fibres. The fibre processing head winds three layers of filaments onto the frame. The polyurethane frame is determined by the local Euclidean coordinate system $E_{3}$, which has its origin in the REE. We use a mathematical model and matrix calculus to compute the trajectory of the REE to guarantee the desired passage of the frame through the fibre processing head. The translation and rotation matrices of the local coordinate system (of the REE) are calculated with respect to the base coordinate system of the robot.
KW - robot trajectory; transformation matrix; Euler angle of rotation; orthogonal group
UR - http://eudml.org/doc/288153
ER -

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