## 4 Discussion  
RPRs need to be assisted by MSMs that provide estimates of internal efforts, both for safety reasons and to ensure the effectiveness of rehabilitation exercises. Although there is extensive research activity in the field of MSMs, current approaches are directed towards greater complexity and levels of anatomical and physiological detail or the incorporation of information on muscle activity measured by EMG [15]. Despite their scientific interest, they are complex and expensive models in terms of time and equipment, which limits their applications in clinical practice and in the control of RPRs. MSMs used for controlling RPRs must be adaptable to the patient's characteristics, simple, and able to operate in real time, while also providing accurate estimates of the muscle forces and identifying overexertion in the body structures. In this paper, we present a model based on essential actions that attempt to solve some of the applicability problems of the current models. The level of detail used is like that of other previous models [15; 43]. However, some improvements were introduced to accomplish the aforementioned requirements. First, the kinematics of the knee joint is customized by adjusting a four-bar mechanism. This simplified model offers better results than those based on a fixed axis of rotation, without the need-to-know anatomical details, such as models that use the characteristics of the ligaments. The adjustment is carried out using a functional calibration process, which provides an advantage over parametric models obtained with specimens [10]. This aspect is relevant in the case of clinical applications, where it is important to be able to adapt the joint model to specific rehabilitation movements performed by people with medical disorders, and thus altered movement patterns [4; 5; 6; 7; 8; 9; 10; 11]. Secondly, simplifications have been made to the inverse dynamics model to reduce calculations and allow a real-time estimation of internal forces. This is necessary for effective control of the robot. For this, a quasistatic model is used, not considering the inertial forces compared to the segment weights and those directly applied. This simplification has two consequences. First, it makes the numerical calculation of velocities and accelerations unnecessary and, secondly, it transforms the relationships between forces and joint moments into geometric relationships that only depend on position. This allows the optimization process, used to solve muscle force indeterminacy problem, to have a direct analytical solution using Lagrange multipliers. As a result, muscle coefficients can be calculated in an offline calibration stage. The calculations of the muscle coefficients associated with an exercise can be reduced by assuming one functional degree of freedom [8; 41]. Then, the manifold combinations associated with fDOFs are much fewer than those corresponding to kinematic DOFs, which reduces the computational time and simplifies the application of the model. Another relevant aspect in the development of an MSM is its verification and validation. The verification and validation of the model have been carried out through the analysis of the squat movement, using a conventional biomechanical laboratory [2]. Regarding the movement used, it is an easily reproducible gesture that causes significant efforts at muscle and joint level. It has already been used previously in other works [5]. Although there are some guidelines on the MSM validation strategy, most of the published papers only verify the coherence between the estimated forces and the EMG signals. However, validation in a physical sense involves comparing estimated and measured forces directly. In this paper, we have followed this double strategy. First, the coherence between the EMG signals and the estimated forces was verified with calibration curves obtained in independent exercises. This strategy has been suggested previously [24], and ensuresthat the validation data are independent of those used in the calibration curves.