Stiffness Distribution of 3-RPS Parallel Manipulator Based on the Base-and-platform Configuration

Abstract

Rehabilitation of ankle injuries must be under supervision of a therapist to prevent severe injuries. However, relying on a therapist is not consistent and accurate. In the present days, parallel manipulators play a key role as an ankle rehabilitation device to overcome the problem imposed by a therapist. The ankle rehabilitation device should be able to sustain the external forces and moments exerted from the patient’s feet. The external forces and moments applied to the platform can cause deflections, either translation or rotational deflections. These deflections depend mostly upon the stiffness properties of the device. The stiffness property is one of crucial factors to be considered in designing the ankle rehabilitation device. Therefore, this paper aims to analyse and establish the static and stiffness model of the 3-RPS parallel manipulator which is employed as an ankle rehabilitation device. Each RPS leg applies one constraint force and one actuation force intersecting the centre of spherical joint. By collecting all constraint forces and actuation forces, the Jacobian matrix can be formulated according to the Screw theory and Quaternion parameters. Influences of actuators and base-and-platform configuration are identified by using stiffness index, namely eigenvalues of the stiffness matrix. The base-and-platform configuration is described by the distance of each joint to the origin of coordinate frame and the angle among three legs. For given external wrenches, numerical simulations have been performed to determine the optimal distributions of actuators and base-and-platform configuration by taking into account the stiffness.