## 1 Introduction
This is due to the same approximation that considers each segment as rigid and characterized by a specific marker cluster that should be, at the same time, rigid and not subjected to any relative motion. Functional techniques do not require any a priori definition of the joint center or rotation axis; therefore, they are quite effective in providing information regarding the actual DoFs and motion patterns allowed by a specific human joint [21; 22]. This paper focuses on the application of functional techniques aimed at the estimation of the axis of rotation (AoR) of a human joint. In particular, two of the most widely adopted methodologies are considered, that is, the instantaneous helical axis (IHA) [23; 24; 25] and the symmetrical axis of rotation approach (SARA) [26]. These techniques allow, starting from a motion capture dataset, to calculate the functional joint axes that describe in detail the kinematics under investigation [27; 28; 29; 30]. Similarly, the symmetrical center of rotation estimation (SCoRe) algorithm [31] deals with the estimation of the joint center of rotation, which can be useful for several applications as the improvement of the accuracy of biomechanical dynamic models [32; 33]. However, it was not considered in the current work due to the latter being focused on AoR estimation. Helical axis and SARA approaches have different performance and mathematical formulations; however, several similarities in the definitions of both algorithms have been already discussed in the literature [34]. Both methodologies have already been used for in vitro and in vivo analyses [27; 28; 29; 30; 34; 35; 36]; however, an extensive discussion and comparison of their performance with respect to diverse motion configurations and experimentation parameters have not been already performed to the best of our knowledge. To ease the testing of both algorithms in multiple scenarios, as well as to achieve an objective estimation of their accuracy, a modeling rather than an experimental approach was chosen. Actual experimentation can surely provide the most realistic results regarding the study of natural joint kinematics; however, it does not enable the easy and full customization of aspects that affect the accuracy of the analysis, such as measurement noise, range of motion, DoFs, sampling rate, and so on, that have to be investigated to assess the reliability of each algorithm. Moreover, real in vivo experimentation could be not appropriate to fulfill the objective of this work. Indeed, to quantitatively assess the accuracy in the determining of the AoR, expensive and/or invasive techniques could be required to assess the true functional axis in vivo. For this reason, a multi-body model, resembling a lower limb (only the shank-foot complex), was developed. Due to the model formulation, most of the discussion is focused on the ankle joint. However, similar considerations can be done for any other human or artificial joint. Based on the modeling approach, the aim of this paper is to objectively evaluate the performance of IHA and SARA algorithms in such a controlled environment so as to provide an indication for other researchers in the selection of one methodology rather than the other, depending on different conditions that could be manipulated through simulations.