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]
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]
