## 1 Introduction  
The dynamic parameters of a rigid body system typically consist of the inertial and friction parameters. In a system where its inertial parameters are very dominant and its friction parameters are relatively very small, the friction parameters can be neglected in the identification. However, when the friction is significant, one should incorporate it in the dynamics, and accordingly include the friction parameters in the identification. Otherwise, the corresponding dynamic model is not adequate to capture the real dynamics. An identification usually estimates the inertial parameters as the so-called barycentric parameters, which consist of the masses, the first moments of inertia, and the moments of inertia relative to the origin of the component frames. Upon obtaining the masses and the first moments of inertia, one can easily obtain the centers of masses (COMs). The moments of inertia relative to the COM can be obtained from the moments of inertia relative to the component frame by utilizing the Huygens-Steiner theorem, which is commonly called the parallel axis theorem. The dynamics of a mechanism can typically be modeled as a linear system in terms of the dynamic parameters. As a result, linear least squares can be conveniently used to identify the dynamic parameters [1]. Based on measurements along a certain exciting trajectory, an overdetermined linear system can be composed, and subsequently, the dynamic parameters can be estimated by usingthe closed-form linear least squares solution, which involves the evaluation of the pseudo-inverse of the observation matrix. In this case, accurate estimates of the dynamic parameters can only be obtained if the observation matrix has a full rank. In fact, the observation matrix is often rank-deficient. In such a case, a numerical or symbolic mathematical treatment is commonly performed to transform the rank-deficient observation matrix into a full-rank one. This results in a new full-ranked linear system with a reduced size. As the rank-deficiency implies a linear dependency among some dynamic parameters, the reduced linear system can only present the dynamic parameters as linear combinations of the parameters, commonly known as the base parameters. When friction is included, the linear least squares technique can only incorporate a linear friction model. The use of nonlinear optimization techniques can overcome this issue. There are at least three main advantages of this approach. First, one can directly utilize the nonlinear dynamic model, including a nonlinear friction model, to identify the dynamic parameters instead of transforming the nonlinear dynamic model into a linear model, as described earlier. In other words, one can directly use the nonlinear inverse dynamics for identification. The second advantage is the capability of this approach to provide the dynamic parameters as lonely parameters, i.e., not as linear combinations. The third advantage of this approach is the flexibility to identify the dynamic parameters as either the standard parameters or the barycentric parameters. One of the commonly used nonlinear optimization techniques is the nonlinear least squares, in which the Jacobian of the system with respect to the dynamic parameters should be evaluated. While in the linear identification method, the observation matrix should be full-rank to obtain a trustworthy solution from the linear least squares, in a similar fashion, the system Jacobian matrix should be full-rank to get a trustworthy solution from the nonlinear least squares. Although the linear least squares methods applied to a full-rank reduced linear system or the nonlinear least squares applied to a nonlinear system with a full-rank system Jacobian matrix can theoretically give a trustworthy solution, in practice, it is very likely that it cannot give a physically feasible solution due to the presence of measurement noise and/or the inadequacy of the dynamic model.