## 1 Introduction
The authors noticed that both the linear and nonlinear least squares techniques can retrieve synthesized (simulated) measurements but fail to provide physically feasible estimates when real, noisy measurements are used. For that reason, constrained optimization is used in this work to obtain a physically feasible solution. A similar approach has been used by [PERSON] et al. [2] and [PERSON] et al. [3], who respectively used a constrained optimization algorithm and a direct search to identify the dynamic parameters of a parallel kinematics mechanism (PKM). Moreover, [PERSON] et al. [4] used interval analysis to identify the dynamic parameters of an H4 manipulator, which is a three-translational and one-rotational (3T1R) PKM. Furthermore, this work considered a PKM with significant friction due to the presence of sliding (prismatic) joints subject to a significant load. This load was comprised of a constant gravity load and varying reaction forces. Different from a system having sliding joints with constant normal forces, such as in [PERSON] et al. [5], in this work, the total load resulted in varying normal forces, and therefore, varying friction forces. In fact, the normal forces varied because of the changing posture of the PKM. This behavior applies to all types of PKMs, regardless of the magnitude of the variation. However, to the authors' knowledge, there has been no published work on the dynamic parameter identification of PKMs that considers the variation of the friction forces. Moreover, most of the works, including References [3; 4; 6; 7; 8; 9; 10; 11; 12; 13], have also used a linear friction model to enable the use of linear least squares algorithms, including the unweighted linear least squares, weighted linear least squares, and total linear least squares algorithms, as the identification tool. Recently, [PERSON] et al. [2] used a nonlinear friction model to identify the dynamic parameters of a 3 RPS (3 Revolute-Prismatic-Spherical joint topology) PKM. Furthermore, [PERSON] and [PERSON] [13] identified not only the inertial and friction parameters of an Orthoglide PKM but also its drive gains. All of the mentioned works considered the friction in the PKMs constant. This study investigated the identification of the dynamic parameters of a PKM by considering nonlinear, varying friction. In short, this work proposed an approach for the identification of a PKMwith noisy measurements, as well as nonlinear and varying friction. In this work, the dynamics were derived by using a Lagrange approach. A set of constraint equations corresponding to the required Lagrange multipliers were formulated. These Lagrange multipliers corresponded to the reaction forces at all joints, including the active and passive ones. Since the friction on the active, prismatic joints were assumed to be much more significant than that on the passive joints, only the former was considered. To describe the approach, a non-symmetric planar 3 PRR (3 Prismatic-Revolute-Revolute joint topology) PKM [14; 15], as shown in Figure 1, was considered as the study case. This paper is organized as follows. First, the inverse dynamics of the mechanism at hand with and without friction are derived and the friction model is presented. Second, the identification technique is discussed, where the discussion includes the optimization of the exciting trajectory and the physical feasibility of the estimation. Finally, the identification results are discussed.