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

Hassen Nigatu, Li Jihao, Keqi Zhu, Junhan Zhang, Haotian Guo, Guodong Lu, Doik Kim

TL;DR

This work analyzes the stiffness of the Sprint Z3 3-PRS parallel manipulator under parasitic motion, a previously underexplored factor in PKM performance. By deriving a velocity-level stiffness model from the inverse Jacobian and virtual-work principles, and by aggregating component elasticities through a structured stiffness matrix, the authors quantify how parasitic and independent motions affect load resistance. Numerical simulations reveal that stiffness in the parasitic space is shallower and smaller than in the orientation space, underscoring the need to consider parasitic motion in design optimization for improved rigidity. The findings have practical implications for redesign strategies aiming to bolster stiffness and stability during precision machining tasks.

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.

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

TL;DR

This work analyzes the stiffness of the Sprint Z3 3-PRS parallel manipulator under parasitic motion, a previously underexplored factor in PKM performance. By deriving a velocity-level stiffness model from the inverse Jacobian and virtual-work principles, and by aggregating component elasticities through a structured stiffness matrix, the authors quantify how parasitic and independent motions affect load resistance. Numerical simulations reveal that stiffness in the parasitic space is shallower and smaller than in the orientation space, underscoring the need to consider parasitic motion in design optimization for improved rigidity. The findings have practical implications for redesign strategies aiming to bolster stiffness and stability during precision machining tasks.

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.
Paper Structure (9 sections, 24 equations, 9 figures, 3 tables)

This paper contains 9 sections, 24 equations, 9 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Kinematic description of Sprint Z3
  3. Velocity Level Parasitic Motion
  4. Parasitic Motion and the Stiffness Relation
  5. Stiffness Formulation
  6. Stiffness modeling and analysis
  7. Formulation of stiffness matrix
  8. Numerical Simulation
  9. Conclusions

Figures (9)

  • Figure 1: Sprint Z3 parallel manipulator: CAD model (left) Schematic (right)
  • Figure 2: Sprint Z3 Limb
  • Figure 3: The parasitic motion of the manipulator. (a) $x$ and (b) $y$ axes translation
  • Figure 4: The x-axis axial stiffness distribution. (a) Across orientation space. (b) Across parasitic space
  • Figure 5: The y-axis axial stiffness distribution. (a) Across orientation space. (b) Across parasitic space
  • ...and 4 more figures