Cartesian stiffness matrix of manipulators with passive joints: analytical approach

TL;DR

This paper presents an analytical and recursive method for computing the stiffness matrix of manipulators with passive joints, applicable to general cases and capable of handling singularities, demonstrated through Stewart-Gough platform examples.

Contribution

It introduces a novel analytical and recursive approach for stiffness matrix computation in manipulators with passive joints, including singular cases.

Findings

Effective in both analytical and numerical forms

Applicable to general manipulator configurations

Successfully demonstrated on Stewart-Gough platforms

Abstract

The paper focuses on stiffness matrix computation for manipulators with passive joints. It proposes both explicit analytical expressions and an efficient recursive procedure that are applicable in general case and allow obtaining the desired matrix either in analytical or numerical form. Advantages of the developed technique and its ability to produce both singular and non-singular stiffness matrices are illustrated by application examples that deal with stiffness modeling of two Stewart-Gough platforms.