Complete kinematic analysis of the Stewart-Gough platform by unit quaternions

• Autorzy: Serrano F. E. , Rossell J. M.

Identyfikatory

DOI

10.7494/mech.2015.34.4.59

Warianty tytułu

PL

Analiza kinematyczna platformy Stewarta-Gougfla z zastosowaniem kwaternionów

• Języki publikacji: EN

Abstrakty

EN

In this paper, a complete analysis of Stewart-Gough platform kinematics by unit quaternions is proposed. Even when unit quaternions have been implemented in different applications (including a kinematic analysis of the Stewart platform mechanism), the research regarding the application of this approach is limited only to the analysis of some issues related to the kinematic properties of this parallel mechanism. For this reason, a complete analysis of the Stewart-Gough platform is shown. The derivation of the inverse and forward kinematics of the Stewart platform using unit quaternions shows that they are suitable to represent the orientation of the upper platform due to their simplicity, equivalence, and compact representation as compared to rotation matrices. Then, the leg velocities are derived to compute these values under different conditions.

PL

W niniejszym artykule zaproponowano analizę kinematyki platformy Stewarta-Gougha z zastosowaniem kwaternionów. Mimo ze kwaterniony znalazły zastosowanie w różnych aplikacjach (w tym w analizie kinematycznej mechanizmu platformy Stewarta), to ich zastosowanie ogranicza się jedynie do analizy własności kinematycznych mechanizmów równoległych. Z tego powodu przedstawiono pełną analizę kinematyczną platformy Stewarta-Gougha. Uzyskanie kinematyki prostej i odwrotnej platformy Stewarta z zastosowaniem kwaternionów pokazuje, ze są one odpowiednie do reprezentowania orientacji górnej platformy. Przede wszystkim cechują się prostotą oraz zwartą reprezentacją w porównaniu do macierzy obrotów. Następnie wyznacza się prędkości podpor, w celu obliczenia wartości w różnych warunkach.

Słowa kluczowe

EN

Stewart platform; parallel kinematics; unit quaternions; robotics

PL

platforma Stewarta; kinematyka równoległa; kwaternion; robotyka

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Mechanics and Control
• Rocznik: 2015
• Tom: Vol, 34, no. 4
• Strony: 59--69
• Opis fizyczny: Bibliogr. 34 poz., rys., tab.

Twórcy

autor

Serrano F. E.

• Universidad Tecnologica Centroamericana (UNITEC) Tegucigalpa, Honduras

autor

Rossell J. M.

• Universitat Politecnica de Catalunya, Department of Mathematics, Spain
• [e-mail]

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