Geometric Design and Tolerancing (GD&T) is the language that specifies several design features and, in this paper, is used to deal with the tolerances of Translational Parallel Manipulators (TPMs). TPMs intend to make a platform have only translational motion with respect to the frame (base), but, in practice, TPMs’ platforms present undesirable rotation motions due to unavoidable geometric errors in links’ sizes. During the machine-element design, geometric errors can be limited by imposing given tolerances on links’ sizes and the tighter tolerances are the higher manufacturing costs are. Therefore, dealing with tolerances is the key for designing a TPM with assigned requirements in terms of platform’s rotation limits. In this context, this paper moves from the fact that machining processes generate link sizes with values distributed according to Gaussian distributions, whose mean values are the nominal sizes and whose standard deviations depend on the machining process accuracy, to build a novel method that makes a designer able to satisfy an assigned maximum orientation error on the TPM platform. The proposed method consists of two main phases: (a) identification of the geometric parameters that affect platform’s position and orientation, and (b) an analysis, based on numerical simulations, that relates the tolerances assigned to the identified parameters and the positioning precision of the platform. The method can be adapted to other types of lower-mobility robots (LMRs). A case study is also discussed to better illustrate the method.