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Nanomachines such as nanorobots working either in vacuum or in a fluid as mobile machines themselves become the size of the order of the Brownian particle, a nanoparticle free floating in the fluid. For nanomachines working in fluids, the thermal agitation around the machine influences its movement to a greater degree. The nanomachine itself is modeled as a sphere of radius r and proof mass m, which is thermally agitated by fluid particles in a time continuum. The thermal impact equals white noise. A model of the nanoparticle, considering it as an elastic body instead of assuming it as rigid, has been developed by considering the impact process in different ways. The stochastic motion indexes, mean, and variances, were obtained for different models using a correlation technique, with a validity constraint that variance cannot be negative. A probable model has been found that survived universally the constraint test accounting for the Brownian and non-Brownian motion, simultaneously. The model predictions have been verified and were found in good agreement with published experimental results.