Differential Geometry and Geometric Structures
Main Page | Research Areas | Singularity Closeness of Stewart-Gough Platforms


FWF logo Linear pentapod of SG type
Given is a non-singular pose (green) of a pentapod with linear platform and non-planar base (black anchor points).
The closest singular configuration in the position/orientation workspace is illustrated in blue/magenta.
The closest singular pose under Euclidean/equiform motions of the linear platform is displayed in red/yellow.

Singularity Closeness of Stewart-Gough Platforms

This project is devoted to evaluating the closeness of Stewart-Gough platforms to singularities.

This project is funded by the Austrian Science Fund (FWF).

FWF grant no. P 30855-N32

Duration: 2018-2022

FWF-Funding: € 192 774.76

Project leader: Georg Nawratil

Aims and Scope

A parallel manipulator of Stewart-Gough (SG) type consists of a moving platform, which is connected via spherical-prismatic-spherical legs with the base, where only the prismatic joints are active. The number of applications of SG manipulators, ranging from medical surgery to astronomy, has increased enormously during the last decades due to their advantages of high speed, stiffness, accuracy, load/weight ratio, etc.

One of the drawbacks of these parallel robots are their singular configurations, where the manipulator is shaky while all leg lengths are fixed. As a consequence the actuator forces can become very large, which may result in a breakdown of the mechanism. Therefore singularities have to be avoided. This reasons the high interest of the kinematic/robotic community in evaluating the singularity closeness of SG platforms, but geometric meaningful distance measures for this task are still missing. The research project closes this gap.

Project Publications

  1. G. Nawratil: Singularity Distance for Parallel Manipulators of Stewart Gough Type. 15th IFToMM World Congress 2019, accepted

Project Talks

  1. G. Nawratil: 15th IFToMM World Congress, Krakow June 30-July 4 2019, Poland, paper presentation.
  2. G. Nawratil: SIAM Conference on Applied Algebraic Geometry, Bern July 9-13 2019, Switzerland, Title: Singularity distance computation for parallel manipulators of Stewart Gough Type.

Related Publications

  1. G. Nawratil: Point-models for the set of oriented line-elements – a survey. Mechanism and Machine Theory 111, 118-134 (2017) DOI 10.1016/j.mechmachtheory.2017.01.008
  2. A. Rasoulzadeh and G. Nawratil: Rational Parametrization of Linear Pentapod's Singularity Variety and the Distance to it. Computational Kinematics (S. Zeghloul et al. eds.), pages 516-524, Springer, 2017, ISBN 978-3-319-60866-2, DOI 978-3-319-60867-9_59 [Extended version on arXiv:1701.09107]
  3. A. Rasoulzadeh and G. Nawratil: Linear Pentapods with a Simple Singularity Variety – Part II: Computation of Singularity-Free Balls. 15th IFToMM World Congress 2019, accepted [Part of arXiv:1712.06952]

Related Talks

  1. A. Rasoulzadeh : 7th IFToMM International Workshop on Computational Kinematics (CK), Futuroscope-Poitiers May 22-24 2017, France, paper presentation.
  2. G. Nawratil: Conference on Geometry: Theory and Applications, Pilsen June 26-30 2017, Czech Republic, Title: On the set of oriented line-elements: point-models, metrics and applications. [Abstract, Slides]

Quick Links

Georg Nawratil
Arvin Rasoulzadeh
Flexible Structures
Geometry of Mechanisms
Stewart-Gough Platforms with Self-Motions

External Links

Austrian Science Fund (FWF)

Copyright © 1996-2019 by Differential Geometry and Geometric Structures. All rights reserved.
Last modified on January 30th, 2019.