Design, Construction and Implementation in Simulation of a Parallel Spherical 3RRR Robot for Therapeutic Assistance in the Rehabilitation of Ankle Injuries in Infants with Cerebral Palsy

Abstract

This research work presents the biomechanical analysis of the ankle joint, as well as the study of the movements in the rehabilitation task of two basic movements commonly used in this process such as dorsi/plantarflexion and eversion/inversion of this joint, in order to propose an adequate design of a prototype that satisfactorily performs the task of rehabilitation assistant in infants with cerebral palsy. The mechanical design of the robot was performed in the SolidWorks © design program together with the most suitable actuators for the application. Based on the above, the analysis of a parallel coaxial 3-RRR robot for ankle rehabilitation is presented. This way, a mathematical analysis of the robot was made , which consists of inverse and forward kinematic using geometric and numerical methods, respectively using Matlab © environment. In adition eight possible working and assembly modes are presented. To obtain the mathematical model, the velocity state and screw-coordinate Jacobian matrix was developed based on Screw theory for a trajectory obtained through the polynomial result of a system of acquisition in the sagittal and frontal planes using a goniometer. Furthermore, manipulability, dexterity and rotational sensitivity indices are calculated with representation of tilt and torsion angles. Likewise, the workspace and reciprocal index as a measure of the robot’s sensibility, were calculated for the trajectory, by track with the end-effector. In the same way, a dynamical model of one of the legs and the mobile platform was made. This model was obtained by the method of Lagrange and as a result showed the necessary torques from the above mentioned trajectories. The results provides that, for the path planning created, the inverse and forward kinematics are good in agreement. The robot remains in the workspace with high accuracy, with errors not exceeding 10−4 rad. Therefore, the sensibility analysis computed with the reciprocal index shown that this type of parallel robots are efficient inside their workspace, even at points close to the singularity. For future researches the designed robot will develop a control algorithm by combining the fuzzy aproach with PID sliding mode control method. The proposed method combines the adaptive fuzzy algorithm and robust control technique to guarantee a robust tracking performance for robotic system. In addition, motor selection will be carried out according to the torques previously found. Finally the necessary tests will be performed on infants in the age range 8 to 12 years old.