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.
| Identifer | oai:union.ndltd.org:unibo.it/oai:amsdottorato.cib.unibo.it:6627 |
| Date | 15 April 2014 |
| Creators | Abbasnejad Matikolaei, Ghasem <1984> |
| Contributors | Carricato, Marco |
| Publisher | Alma Mater Studiorum - Università di Bologna |
| Source Sets | Università di Bologna |
| Language | English |
| Detected Language | English |
| Type | Doctoral Thesis, PeerReviewed |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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