Fundamentals of manipulator stiffness modeling using matrix structural analysis


The work generalizes existing contributions to the stiffness modeling of robotic manipulators using Matrix Structural
Analysis. It presents a unified and systematic approach that is suitable for serial, parallel and hybrid architectures con-
taining closed-loops, flexible links, and rigid connections, passive and elastic joints, flexible and rigid platforms, taking
into account external loadings and preloadings. The proposed approach can be applied to both under-constrained, fully-
constrained and over-constrained manipulators in generic and singular configurations, it is able to produce either non-
singular or rank-deficient Cartesian stiffness matrices in a semi-analytical manner. It is based on a unified mathematical
formulation that presents the manipulator stiffness model as a set of two groups of matrix equations describing elasticity
of separate links and connections between the links in the form of constraints. Its principal advantage is the simplicity
of the model generation that includes straightforward aggregation of link/joint equations without conventional merging
of rows and columns in the global stiffness matrix. The advantages of this method and its application are illustrated by
an example that deals with the stiffness analysis of NaVaRo parallel manipulator where the efficiency of the proposed
technique was confirmed by the FEA modeling. For this example, the computational expenses for stiffness modeling
were estimated on the level of 10 ms per a manipulator configuration (in Matlab environment on the conventional lap-
Dr. Alexandr Klimchik received the Engineering and Master degree in automation control from Belarusian State Uni-
versity of Informatics and Radioelectronics (Belarus) in 2006 and 2007, respectively, Ph.D degrees in mechanical engi-
neering (robotics) from the Ecole Centrale de Nantes (France) in 2011. From 2011 to 2015 he was a Postdoctoral Fellow
with the Ecole des Mines de Nantes (France) and was a member of the robotic team in the Research Institute in Com-
munications and Cybernetics of Nantes (IRCCyN, France).
In 2015 Dr. Klimchik joined Innopolis University as an Assistant Professor, was promoted to the head of the lab in 2016,
head of the Robotic Center in 2017. He is the Head of Robotic Institute and Master on Robotics Program at Innopolis
University. Alexandr Klimchik is a leader of 7 national projects with a budget from 100K € to 13.5M €. He was a leader
of the team developed national strategy for Robotic and Censors development in Russian Federation. His research in-
terests include stiffness modeling of serial, quasi-serial and parallel manipulators, identification robot geometrical and
elasto-static parameters, design of calibration experiments, optimization of technological process based on the kineto-
static modeling, compensation positioning errors using indirect measurements, modeling and control SEA and VSA and
corresponding mechanism, modeling and control cable-driven robots.
Dr. Klimchik is the author of more than 100 research papers, he has an h-index of 15 and over 880 citations. His paper
published in “Mechanisms and Machine Theory” (2011, 46 (5), 662-679) is Top-2 sited papers in this journal. Now he
is a head of National Center of Competence in Robotics and Mechatronics and leading a team of 60 researchers and
Eingeladen von: Prof. Dr. Sergej Fatikow


26. August 2019, 14:00


Prof. Dr. Alexandr Klimchik Innopolis University, Russia


A1 3-330

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