# Displacement Analysis of Under-Constrained Cable-Driven Parallel Robots

Abbasnejad Matikolaei, Ghasem (2014) Displacement Analysis of Under-Constrained Cable-Driven Parallel Robots , [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Meccanica e scienze avanzate dell'ingegneria, 26 Ciclo. DOI 10.6092/unibo/amsdottorato/6627.
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## Abstract

This dissertation studies the geometric static problem of under-constrained cable-driven parallel robots (CDPRs) supported by n cables, with n ≤ 6. The task consists of determining the overall robot conﬁguration when a set of n variables is assigned. When variables relating to the platform posture are assigned, an inverse geometric static problem (IGP) must be solved; whereas, when cable lengths are given, a direct geometric static problem (DGP) must be considered. Both problems are challenging, as the robot continues to preserve some degrees of freedom even after n variables are assigned, with the ﬁnal conﬁguration determined by the applied forces. Hence, kinematics and statics are coupled and must be resolved simultaneously. In this dissertation, a general methodology is presented for modelling the aforementioned scenario with a set of algebraic equations. An elimination procedure is provided, aimed at solving the governing equations analytically and obtaining a least-degree univariate polynomial in the corresponding ideal for any value of n. Although an analytical procedure based on elimination is important from a mathematical point of view, providing an upper bound on the number of solutions in the complex ﬁeld, it is not practical to compute these solutions as it would be very time-consuming. Thus, for the efﬁcient computation of the solution set, a numerical procedure based on homotopy continuation is implemented. A continuation algorithm is also applied to ﬁnd a set of robot parameters with the maximum number of real assembly modes for a given DGP. Finally, the end-effector pose depends on the applied load and may change due to external disturbances. An investigation into equilibrium stability is therefore performed.

Abstract
Tipologia del documento
Tesi di dottorato
Autore
Supervisore
Dottorato di ricerca
Scuola di dottorato
Ingegneria industriale
Ciclo
26
Coordinatore
Settore disciplinare
Settore concorsuale
Parole chiave
Cable-driven parallel robots, underactuated robots, kinematic analysis, static analysis.
URN:NBN
DOI
10.6092/unibo/amsdottorato/6627
Data di discussione
15 Aprile 2014
URI