Non-linear stiffness behavior of planar serial robotic manipulators

TL;DR

This paper analyzes the nonlinear stiffness behavior of planar serial manipulators under compression, identifying buckling and quasi-buckling phenomena using eigenvalue and energy-based methods, with practical examples.

Contribution

It introduces a general eigenvalue-based method for critical force calculation and an energy-based approach for detecting quasi-buckling in manipulators.

Findings

Buckling occurs when compressive force exceeds a critical value.

Quasi-buckling involves rapid but not instant shape change.

Nonlinear stiffness behavior is demonstrated in three- and four-link manipulators.

Abstract

The paper focuses on the stiffness analysis of multi-link serial planar manipulators, which may demonstrate nonlinear stiffness behavior under the compressive loading. Two important cases are considered, where the manipulator has either a straight or non-straight initial configuration. It was proved that in the first case the loading may cause the buckling if it exceeds some critical value, and the manipulator suddenly changes its straight shape and stiffness properties. For computing this critical force, a general eigenvalue-based technique was proposed that can be applied to any multi-link serial manipulator. For the second case dealing with non-straight initial configurations, a universal energy-based technique was applied that allowed to detect quasi-buckling phenomenon when it is observed very fast but not instant change of the manipulator shape and its stiffness coefficient under the loading. These results are illustrated by numerous examples of non-linear stiffness behavior of three-and four-link manipulators that are subjected to compressive force.