Given is a nonsingular pose (green) of a pentapod with linear platform and nonplanar 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 StewartGough Platforms
This project is devoted to evaluating the closeness of StewartGough platforms to singularities.
This project is funded by the Austrian Science Fund (FWF).
FWF grant no. P 30855N32
Duration: 20182022
FWFFunding: € 192 774.76
Project leader: Georg Nawratil
Aims and Scope
A parallel manipulator of StewartGough (SG) type consists of a moving platform, which is connected via sphericalprismaticspherical 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

G. Nawratil:
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 259268, Springer Nature, 2019, ISBN 9783030201319,
DOI 10.1007/9783030201319_26
[Preprint]

A. Rasoulzadeh and G. Nawratil:
Variational Path Optimization of Linear Pentapods with a Simple Singularity Variety.
arXiv:1910.04810 (2019)
Supplementary data:
see homepage of Arvin Rasoulzadeh

G. Nawratil:
Evaluating the snappability of barjoint frameworks.
Advances in Robot Kinematics (J. Lenarcic, B. Siciliano eds.), Springer Nature (accepted)
[Extended version on arXiv:2001.04430]
Supplementary data:
Animations of the snapping deformation of Fig. 2:
left,
center,
right

A. Kapilavai and G. Nawratil: On homotopy continuation based singularity distance computations for 3RPR manipulators.
New Trends in Mechanism Science (D. Pisla, B. Corves eds.), Springer (accepted)
[Extended version on arXiv:2004.08359]

G. Nawratil:
On the snappability and singularitydistance of frameworks with bars and triangular plates.
In Springer's Proceedings in Advanced Robotics of the
2nd
IMA Conference on Mathematics of Robotics (accepted)
[Corresponding arXiv paper]
Project Talks

G. Nawratil:
15th IFToMM World Congress,
Krakow June 30July 4 2019, Poland, paper presentation.
[Slides]

G. Nawratil:
SIAM Conference on Applied Algebraic Geometry,
Bern July 913 2019, Switzerland, Invited Talk (Minisymposium: Algebraic geometry for kinematics, mechanism science, and rigidity),
Title: Singularity distance computation for parallel manipulators of Stewart Gough Type.
[Slides]

G. Nawratil:
17th International Symposium on Advances in Robot Kinematics (ARK'20), Lubljana December 610 2020, Slovenia, paper presentation.

G. Nawratil:
2nd
IMA Conference on Mathematics of Robotics, Manchester September 810 2021, England, paper presentation.
