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Geometric stiffness analysis of wire robots: A mechanical approach

: Krüger, J.


Tobias Bruckmann (Ed.); Pott, Andreas (Ed.) ; International Federation for the Promotion of Mechanism and Machine Science:
Cable-driven parallel robots : First International Conference on Cable-Driven Parallel Robots in Stuttgart, Germany
Berlin: Springer, 2013 (Mechanisms and Machine Science 12)
ISBN: 978-3-642-31987-7
ISBN: 978-3-642-31988-4
DOI: 10.1007/978-3-642-31988-4
International Conference on Cable-Driven Parallel Robots <1, 2012, Stuttgart>
Fraunhofer IPK ()

This paper presents a mechanical approach for the modelling of wire robots dynamics considering the effects of structural elasticity. The mechanical wires represent critical flexible elements of a wire robot that are responsible for elastic deformations and vibrations of the entire structure. A comprehensive elastodynamic analysis plays a crucial role in wire-robot synthesis and control. Especially in the large-span systems, the elastic deformations and vibrations may be characterized by relatively low frequencies and high amplitudes causing undesirable behaviour. The paper considers coupled 6D deformations of the common wire-robot platform in both over- and under-constrained wire robot structures. Special emphasis is on the geometric stiffness matrix that is dependent on wire tension and which has been derived following a rigorous mechanical approach analysing the motion of the entire system and specific components. The geometric stiffness matrix in wire robots plays a crucial role in stabilization of the wire robot, such as in active stiffening and damping of unacceptable vibration effects. The decomposition of both spatial elastic wire and geometric stiffness matrices on virtual elemental springs has been applied to provide a physical insight and better understanding of the wire robot elastic behaviour. Several examples illustrate the theoretical analysis.