Geometric Stiffness Analysis of Wire Robots: A Mechanical Approach
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 a
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Abstract 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. Keywords Wire-robots elastic deformations decomposition · Screw-analysis
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Geometric stiffness
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Stiffness
D. Surdilovic (B) · J. Radojicic · J. Krüger Department of Robotics and Automation, Fraunhofer Institute for Production Systems and Design Technology IPK-Berlin, Pascalstr. 8-9, 10587 Berlin, Germany e-mail: [email protected] T. Bruckmann and A. Pott (eds.), Cable-Driven Parallel Robots, Mechanisms and Machine Science 12, DOI: 10.1007/978-3-642-31988-4_24, © Springer-Verlag Berlin Heidelberg 2013
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1 Introduction The wire-robots (the term also used: cable driven parallel robots) have been recently addressed in numerous researches focusing on their advantages for implementing large spans, fast moving, lightweight and heavy-duty active spatial mechanisms. In comparison to a more general class of cable robots (e.g. spatial advanced robotized crane systems), the wire robots, especially the so called over-constrained structures, offer benefits to apply and control wire over-tension by wire pulling forces and thus to perform more precise and robust pose and motion control in spite of the external dynamic perturbations and excitations (e.g. wind, inertia etc.). However, due to the relatively large dimensions and inevitable elasticity inherent in robot cables, the wire robots are prone to vibrations. Thereby the common platform can perform complex coupled 6D oscillations, particularly in case of abrupt motion changes. The motion planning of wire-robots cannot be similar to that of the convenient industrial robots performed separately from system dynamic i.e. quasi-static analysis considerations, suc
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