Stiffness Evaluation of a Decoupled Cartesian Parallel Manipulator

Abstract This article proposes a new approach to evaluate the stiffness of a three degrees-of-freedom decoupled Cartesian parallel manipulator which uses revolute joints. Prior to the discussion on the new approach, the stiffness of an individual limb is discussed. This discussion focuses on the influence of kinematic parameters on the limb's stiffness. Taking advantage of the decoupled behavior of the Cartesian parallel manipulator, the stiffness evaluation is initially performed in multiple analyses at the individual limb level. Subsequently, the end-effector deformation is obtained by summing the individual limbs' deformations. This approach does not require the assembly of the complete manipulator. Accordingly, it offers a simpler and more intuitive way to analyze the stiffness of the manipulator. The approach was demonstrated in a 3PRRR decoupled parallel manipulator. The result of the proposed approach was compared with that of a standard approach that considers a completely assembled manipulator. The comparison shows an acceptable agreement, suggesting that the proposed approach can quickly estimate the stiffness of the entire manipulator. The stiffness evaluations in the article employed several methods, including analytical approximation, matrix structural analysis, and finite element analysis.