On the stiffness analysis of robotic manipulators and calculation of stiffness indices

This paper aims at introducing new performance indices for robotic manipulators in order to evaluate the robot stiffness at the design embodiment stage. In this regard, the calculation of the Cartesian stiffness matrix of a manipulator is elaborated based on a matrix structural analysis methodology. Then, by resorting to linear algebra, four stiffness indices, two for translational and two for rotational deformation of the end-effector, are extracted from a Cartesian stiffness matrix. It is proved that the indices represent the maximum and the minimum value of the resistance forces or moments of a manipulator against an exerted deflection, on the end-effector. As a case study, the foregoing stiffness analysis will be applied on a Delta parallel robot and the corresponding stiffness indices will be derived.