  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.
