Dynamic Models of Spherical Parallel Robots for Model-Based Control Schemes
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In this paper, derivation of different forms of dynamic formulation of spherical parallel robots (SPRs) is investigated. These formulations include the explicit dynamic forms, linear regressor, and Slotine-Li (SL) regressor, which are required for the design and implementation of the vast majority of model-based controllers and dynamic parameters identification schemes. To this end, the implicit dynamic of SPRs is first formulated using the principle of virtual work in task-space, and then by using an extension, their explicit dynamic formulation is derived. The dynamic equation is then analytically reformulated into linear and S-L regression form with respect to the inertial parameters, and by using the Gauss-Jordan procedure, it is reduced to a unique and closed-form structure. Finally, to illustrate the effectiveness of the proposed method, two different SPRs, namely, the ARAS-Diamond, and the 3-RRR, are examined as the case studies. The obtained results are verified by using the MSC-ADAMS software, and are shared to interested audience for public access.
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