Mathematical modeling of the interaction of elements of an electromechanical multilink system using the example of a rehabilitation exoskeleton of the lower extremities

The purpose of the research is to develop a mathematical model, analyze the interaction of the elements of a three- link electromechanical system of a rehabilitation exoskeleton of the lower extremities and predict the driving forces.  
Methods. The presented article discusses an electromechanical multi-link system of a rehabilitation exoskeleton of the lower extremities. The analysis was performed using the decomposition method, which is the dismemberment of the system  into  its component parts and  the study of  the  functioning of each part separately. Based on  the developed mathematical model of a multi-link system, a computational experiment was conducted. The animation method is used, which creates a virtual trajectory of the ankle joint movement of a human-machine system. The proposed approach makes it possible to predict the behavior of the system, determine its configuration and, importantly, evaluate the values of control actions in the form of torque of electric drives that ensure the functioning of the system as part of rehabilitation measures.  
Results. A mathematical model of the functioning of the rehabilitation skeleton system of the  lower extremities has been obtained, which makes it possible to predict the interaction of elements of an electromechanical multilink system. Based on  the data  from  the computational experiment,  it was  found  that  the control of  the hybrid drive affects  the functioning of the links of the system under consideration. An animation method has been developed that creates a virtual trajectory of the ankle  joint based on video motion capture and anthropomorphic parameters. The simulation results demonstrate that the gravity compensator of the hybrid drive creates an auxiliary torque that compensates for part of the gravitational forces from the elements of the electromechanical system. The effect of using a hybrid drive in the femoral joint on the functioning of the remaining links of the electromechanical system is shown, manifested in the exclusion of high-frequency vibrations of the knee and ankle links.  
Conclusion. The results of mathematical modeling make it possible to predict the interaction of the elements of the electromechanical system and to effectively control the robot's drive system over time. The discovered effect of the use of a hybrid drive in the femoral sphere on the functioning of the remaining links of the electromechanical system will make it possible to create a device capable of performing its functions in various operating conditions and providing motion parameters close to anthropomorphic. 

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