The Stiffness of 3-PRS PM Across Parasitic and Orientational Workspace

TL;DR

This paper develops a stiffness model for 3-PRS parallel manipulators that includes parasitic motion effects, revealing that stiffness is lower in parasitic motion space than in the regular workspace, which impacts precision and design.

Contribution

The study introduces the first stiffness model accounting for parasitic motion space in 3-PRS manipulators, highlighting its influence on stiffness performance.

Findings

Stiffness is lower in parasitic motion space compared to the regular workspace.

Stiffness profile in parasitic space is shallower and has smaller values.

Assessing stiffness during parasitic motion is crucial for manipulator performance.

Abstract

This study investigates the stiffness characteristics of the Sprint Z3 head, also known as 3-PRS Parallel Kinematics Machines, which are among the most extensively researched and viably successful manipulators for precision machining applications. Despite the wealth of research on these robotic manipulators, no previous work has demonstrated their stiffness performance within the parasitic motion space. Such an undesired motion influences their stiffness properties, as stiffness is configuration-dependent. Addressing this gap, this paper develops a stiffness model that accounts for both the velocity-level parasitic motion space and the regular workspace. Numerical simulations are provided to illustrate the stiffness characteristics of the manipulator across all considered spaces. The results indicate that the stiffness profile within the parasitic motion space is both shallower and the values are smaller when compared to the stiffness distribution across the orientation workspace. This implies that evaluating a manipulator's performance adequately requires assessing its ability to resist external loads during parasitic motion. Therefore, comprehending this aspect is crucial for redesigning components to enhance overall stiffness.