In this paper, a method to predict the precision of parallel microstructures made of carbon fibers, polyimide layers and piezoelectric materials is proposed. To this aim, we propose to combine the exponential representation of transformation matrix with intervals to bound the uncertainties in each flexure joint of the microstructures. Based on interval techniques and algorithms, the derived model permits to guarantee a bound on the precision value of the end effector. The method has been demonstrated with a numerical example of parallel microrobot devoted to orient the laser spot towards vocal fold during phonomicrosurgery. This example considers the uncertainties that occur in the compliant joints caused by the fabrication technique.