Article
Optimization of the 2PRU-1PRS Parallel Manipulator Based on
Workspace and Power Consumption Criteria
Saioa Herrero
1,
* , Charles Pinto
1
, Mikel Diez
1
and Asier Zubizarreta
2
Citation: Herrero, S.; Pinto, C.; Diez,
M.; Zubizarreta, A. Optimization of
the 2PRU-1PRS Parallel Manipulator
Based on Workspace and Power
Consumption Criteria. Appl. Sci. 2021,
11, 7770. https://doi.org/10.3390/
app11177770
Academic Editor: Giovanni Boschetti
Received: 7 July 2021
Accepted: 17 August 2021
Published: 24 August 2021
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4.0/).
1
Department of Mechanical Engineering, University of the Basque Country (UPV/EHU), 48013 Bilbao, Spain;
charles.pinto@ehu.eus (C.P.); mikel.diez@ehu.eus (M.D.)
2
Department of Systems Engineering and Automation, University of the Basque Country (UPV/EHU),
48013 Bilbao, Spain; asier.zubizarreta@ehu.eus
* Correspondence: saioa.herrero@ehu.eus; Tel.: +34-94-601-4014
Abstract:
In the last few years, parallel manipulators are being increasingly studied and used for
different applications. The performance of parallel manipulators is very sensitive to the geometric
parameters, so it is essential to optimize them in order to obtain the desired function. We propose two
optimization algorithms that consider the size and regularity of the workspace. The first one obtains
the geometric parameters combination that results in the biggest and most regular workspace. The
second method analyzes the geometric parameters combinations that result in an acceptable size of
the workspace—even if it is not the biggest one—and finds out which ones result in the lowest power
consumption. Even if the results vary depending on the application and trajectories studied, the
proposed methodology can be followed to any type of parallel manipulator, application or trajectory.
In this work we focus on the dimension optimization of the geometric parameters of the 2PRU-1PRS
Multi-Axial Shaking Table (MAST) for automobile pieces testing purposes.
Keywords: parallel manipulators; robotics; optimization; workspace; power consumption
1. Introduction
If we compare parallel manipulators (PM) with serial manipulators, we observe that
parallel manipulators have some interesting advantages, such as a higher stiffness all over
the workspace (WS), better load/weight ratio and lower inertia. Nevertheless, parallel
manipulators have also some disadvantages—more complex kinematics and dynamics
and also more complex and smaller workspace.
In the last few years, parallel manipulators have been studied and used for applica-
tions where high stiffness, high speed and/or very good accuracy are required. Geometric
parameters have a pronounced effect on these performance criteria of the parallel manipu-
lators. Thus, the geometrical optimization of parallel manipulators is essential in order to
obtain the desired performance in a particular application.
Some of the possible performance criteria include design for best position accuracy,
design to obtain the biggest possible workspace and design for optimum velocity, stiffness,
force, dexterity or manipulability all over the workspace. As Hüsing et al. [
1
] explained,
depending on the application, certain performance criteria are more important than others.
Thus, one of the first steps is to define the application of the parallel manipulator we want to
design and identify how the different parameters of the manipulator affect the performance
for that specific application. Performance requirements of parallel manipulators may be
antagonistic to one another, as Modungwa et al. [
2
] highlighted. If so, we can define an
appropriate design
that does not optimize a single function but ensures that the manipulator
satisfies all the desired requirements.
Since small workspace is one of the biggest drawbacks of parallel manipulators, many
authors have optimized different parallel manipulators to obtain a desired workspace.
Merlet [
3
,
4
] presented a numerical method to obtain the geometries of a Gough-type PM
Appl. Sci. 2021, 11, 7770. https://doi.org/10.3390/app11177770 https://www.mdpi.com/journal/applsci
