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
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.
Singularity Distance for Parallel Manipulators of Stewart Gough Type.
Advances in Mechanism and Machine Science –
Proc. of the 15th IFToMM World Congress on Mechanism and Machine Science (T. Uhl ed.), pages 259-268, Springer Nature, 2019, ISBN 978-3-030-20131-9,
A. Rasoulzadeh and G. Nawratil:
Variational Path Optimization of Linear Pentapods with a Simple Singularity Variety.
see homepage of Arvin Rasoulzadeh
Evaluating the snappability of bar-joint frameworks.
Advances in Robot Kinematics (J. Lenarcic, B. Siciliano eds.), Springer Nature (accepted)
[Extended version on arXiv:2001.04430]
Animations of the snapping deformation of Fig. 2:
A. Kapilavai and G. Nawratil: On homotopy continuation based singularity distance computations for 3-RPR manipulators.
New Trends in Mechanism Science (D. Pisla, B. Corves eds.), Springer (accepted)
[Extended version on arXiv:2004.08359]
On the snappability and singularity-distance of frameworks with bars and triangular plates.
In Springer's Proceedings in Advanced Robotics of the
IMA Conference on Mathematics of Robotics (accepted)
[Corresponding arXiv paper]
15th IFToMM World Congress,
Krakow June 30-July 4 2019, Poland, paper presentation.
SIAM Conference on Applied Algebraic Geometry,
Bern July 9-13 2019, Switzerland, Invited Talk (Mini-symposium: Algebraic geometry for kinematics, mechanism science, and rigidity),
Title: Singularity distance computation for parallel manipulators of Stewart Gough Type.
17th International Symposium on Advances in Robot Kinematics (ARK'20), Lubljana December 6-10 2020, Slovenia, paper presentation.
IMA Conference on Mathematics of Robotics, Manchester September 8-10 2021, England, paper presentation.