SUMMARYThis paper presents a new configuration for ankle rehabilitation using a 9-DOF (degree of freedom) hybrid parallel robot. The robot contains nine linear actuators serially connecting two movable platforms and one stationary platform. The optimization is based on the singularity and dynamic analysis of the robot. The obtained data of the ankle motions from a series of experiments were applied to the model in order to investigate the motion of the end-effector and the force required for each actuator in a particular path. The end-effector tracking simulation results validated the proposed theoretical analysis of the required rehabilitation path of the foot.
Stiffness is one of the important parameters for estimating the performance of hybrid parallel robots as it is not constant throughout its workspace. The aim of this study is to provide an optimum path based on maximum stiffness within the workspace of a 9-degree-of-freedom hybrid parallel mechanism configuration, which includes nine linear actuators connecting one stationary and two moving platforms in series. The proposed robot is designed for ankle rehabilitation, where accurate and precise movement of lower extremities is required. The design takes advantage of two important characteristics of parallel robots: stiffness and workspace. The proposed methodology to determine the stiffness of hybrid robot in three single axes is based on calculation of position vector of each actuator in any particular pose, by considering the inverse kinematics of the system, in order to obtain the magnitude and direction of the applied forces. The results obtained from the workspace calculations have been compared with those of two standard parallel mechanisms including a 6-degree-of-freedom hexapod and a tripod with 3 degrees of freedom. The stiffness of the robot has been calculated in simulation and then compared with those of a developed prototype hybrid model in two different case studies.
This paper addresses the path planning of a hybrid parallel robot for ankle rehabilitation. The robot contains 3-DOF parallel mechanism that is attached on top of the 6-DOF hexapod. The 6-UPU-3-UPR parallel robot is developed to simulate ankle motions for the rehabilitation of post-stroke patients with an affected ankle. The inverse kinematic of hybrid parallel robot is developed in order to track the end-effector’s position through Matlab software. The calculated stroke size of each actuator is imported to apply the forward kinematic for determining the position of end-effector. The experimental and simulation values of the hexapod are compared with those of the hybrid structure through a number of exercise motion paths. The results reveal that, in general, the simulation values follow well the experimental values, although with different degrees of variation for each of the structures considered.
In this paper, a new methodology for the development of the dynamic formulation for a hybrid parallel robot is introduced. The robot includes a tripod that is serially connected on top of a hexapod in order to increase its overall workspace, while maintaining sufficient accuracy and stiffness in motion. The robot will have applications involving gripping and manipulation of large aerospace components such as a wingbox structures and panels. The dynamic formulation of the system, based on Newton-Euler and inverse kinematic equations, is presented by identifying the position vector of the actuators during motion when the system follows certain point and orientation in space. Based on the velocity and acceleration, calculated by taking derivative of the motion equation, the force on the actuator is identified. Since the position vectors of all tripod joints can change through motion, the above methodology offers less complex calculations compared with the existing methods such as using forward dynamics. A MATLAB software was developed to create a set of comprehensive dynamic equations for the overall control system design. An experimental physical hybrid robot was built in order to verify the theoretical formulations. Force sensors, connected at each actuator joint, were used to obtain the applied force on each actuator through a number of given motions. The applied forces subsequently assist to calculate the acceleration of the moving platform. The experimental actuators’ force results compare well with the proposed theoretical formulation.
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