Enhanced stiffness modeling of manipulators with passive joints

TL;DR

This paper introduces a non-linear stiffness model for manipulators with passive joints, accounting for load effects on configuration and stability, and provides a numerical method for analysis of their elastic behavior.

Contribution

It presents a novel non-linear stiffness model and a linearization technique for manipulators with passive joints, enabling accurate analysis of their elastic and stability properties.

Findings

The methodology accurately models non-linear behavior and buckling phenomena.

Simulation results demonstrate the effectiveness of the approach on Ortholide manipulators.

The approach captures load-dependent stiffness variations and elastic instability.

Abstract

The paper presents a methodology to enhance the stiffness analysis of serial and parallel manipulators with passive joints. It directly takes into account the loading influence on the manipulator configuration and, consequently, on its Jacobians and Hessians. The main contributions of this paper are the introduction of a non-linear stiffness model for the manipulators with passive joints, a relevant numerical technique for its linearization and computing of the Cartesian stiffness matrix which allows rank-deficiency. Within the developed technique, the manipulator elements are presented as pseudo-rigid bodies separated by multidimensional virtual springs and perfect passive joints. Simulation examples are presented that deal with parallel manipulators of the Ortholide family and demonstrate the ability of the developed methodology to describe non-linear behavior of the manipulator structure such as a sudden change of the elastic instability properties (buckling).