We present and validate a computationally efficient lower limb musculoskeletal model for the control of a rehabilitation robot. It is a parametric model that allows the customization of joint kinematics, and it is able to operate in real time. Methods: Since the rehabilitation exercises corresponds to low-speed movements, a quasi-static model can be assumed, and then muscle force coefficients are position dependent. This enables their calculation in an offline stage. In addition, the concept of a single functional degree of freedom is used to minimize drastically the workspace of the stored coefficients. Finally, we have developed a force calculation process based on Lagrange multipliers that provides a closed-form solution; in this way, the problem of dynamic indeterminacy is solved without the need to use an iterative process. Results: The model has been validated by comparing muscle forces estimated by the model with the corresponding electromyography (EMG) values using squat exercise, in which the Spearman’s correlation coefficient is higher than 0.93. Its computational time is lower than 2.5 ms in a conventional computer using MATLAB. Conclusions: This procedure presents a good agreement with the experimental values of the forces, and it can be integrated into real time control systems.

There is growing interest in analyzing human movement data for clinical, sport, and ergonomic applications. Functional Data Analysis (FDA) has emerged as an advanced statistical method for overcoming the shortcomings of traditional analytic methods, because the information about continuous signals can be assessed over time. This paper takes the current literature a step further by presenting a new time scale normalization method, based on the Hilbert transform, for the analysis of functional data and the assessment of the effect on the variability of human movement waveforms. Furthermore, a quantitative comparison of well-known methods for normalizing datasets of temporal biomechanical waveforms using functional data is carried out, including the linear normalization method and nonlinear registration methods of functional data. This is done using an exhaustive database of human neck flexion-extension movements, which encompasses 423 complete cycles of 31 healthy subjects measured in two trials of the experiment on different days. The results show the advantages of the novel method compared to existing techniques in terms of computational cost and the effectiveness of time-scale normalization on the phase differences of curves and on the amplitude of means, which are assessed by Root Mean Square (RMS) values of functional means of angles, angular velocities, and angular accelerations. Additionally, the confidence intervals are obtained through a bootstrapping process.

Although parallel manipulators (PMs) started with the introduction of architectures with 6 Degrees of Freedom (DoF), a vast number of applications require less than 6 DoF. Consequently, scholars have proposed architectures with 3 DoF and 4 DoF, but relatively few 4 DoF PMs have become prototypes, especially of the two rotation (2R) and two translation (2T) motion types. In this paper, we explain the mechatronics design, prototype and control architecture design of a 4 DoF PM with 2R2T motions. We chose to design a 4 DoF manipulator based on the motion needed to complete the tasks of lower limb rehabilitation. To the author's best knowledge, PMs between 3 and 6 DoF for rehabilitation of lower limbs have not been proposed to date. The developed architecture enhances the three minimum DoF required by adding a 4 DoF which allows combinations of normal or tangential efforts in the joints, or torque acting on the knee. We put forward the inverse and forward displacement equations, describe the prototype, perform the experimental setup, and develop the hardware and control architecture. The tracking accuracy experiments from the proposed controller show that the manipulator can accomplish the required application.