Increasing the Structural Rigidity of the Manipulator

A research and development project focused on optimizing the structural rigidity of a robotic manipulator through topology optimization using the SIMP algorithm.

Project Overview

This project addresses the challenge of improving the stiffness of a manipulator arm while maintaining mass constraints. The goal was to reduce tip deflection to ≤0.3mm under various loading conditions while limiting mass increase to no more than 15%.

Key Objectives

• Reduce manipulator tip deflection to ≤0.3mm
• Maintain mass increase within 15% of original design
• Preserve existing joint angles (270° per joint)
• Minimize unique custom-manufactured parts

Components Optimized

1. Aluminum Bracket - Main structural element
2. Steel U-shaped Bracket - Connection component
3. Steel "Fin" Bracket - Support structure

Aluminum Bracket	Steel U-shaped Bracket	Steel "Fin" Bracket

Results Summary

Parameter	Original Design	Optimized Design	Improvement
Mass	1.937 kg	2.376 kg	+22.7%
Max Stress	93 MPa	25 MPa	-73%
Vertical Deflection (Fy)	1.05 mm	0.41 mm	-61%
Horizontal Deflection (Fx)	1.03 mm	0.31 mm	-70%
Longitudinal Deflection (Fz)	0.62 mm	0.21 mm	-66%

Note: While significant improvements were achieved (57-76% reduction in deflections), the target of ≤0.3mm was not fully met. The final maximum deflection of 0.41mm exceeds the specification.

Methodology

Finite Element Modeling (FEM)

• Shell Elements (QUAD4): Used for U-bracket and fin bracket (thin-walled structures)
• Solid Elements (HEX8): Used for aluminum bracket and bearings
• RBE2 Elements: Used for bolt connections and servo motor modeling
• Contact Modeling: Slide-type contact between bearings and brackets

Topology Optimization (SIMP Method)

The Solid Isotropic Material with Penalization (SIMP) method was employed to find optimal material distribution within design spaces. Key features:

• Minimization of weighted compliance (maximizing stiffness)
• Mass fraction constraints
• Manufacturing constraints (draw direction, minimum member size)
• Stress constraints (≤150 MPa)

Project Structure

├── README.md                                              # This file
├── Increasing the structural rigidity of the manipulator ru.md  # Russian report
├── Increasing the structural rigidity of the manipulator en.md  # English report
└── media/                                                 # Images and animations
    ├── manipulator_*.jpg                                  # Manipulator views
    ├── FEM_*.jpg                                          # FEM model images
    ├── optimization_*.jpg/png/gif                         # Optimization results
    └── *.avi/*.mp4                                        # Video files

Key Findings

1. Topology optimization effectiveness confirmed: The method successfully identified loaded and unloaded zones, enabling targeted geometry modifications.

2. Design recommendations:

   • Steel U-bracket: Expand base, increase wall thickness to 6mm
   • Aluminum bracket: Distribute mass along walls (I-beam profile tendency)
   • Steel fin bracket: Increase vertical wall thickness to 6mm

3. Future improvements suggested:

   • Consider replacing aluminum brackets with steel (E: 70 GPa → 200 GPa)
   • Explore alternative materials with higher elastic modulus
   • Relocate center of mass closer to the base
   • Allow greater mass increase if stricter deflection requirements must be met

Optimization Results

Steel Fin Bracket	Steel U-shaped Bracket	Aluminum Bracket

Optimized Structure Analysis

FEM of Optimized Design	Results

Software Used

• Altair OptiStruct: FEM analysis and topology optimization
• CAD Software: 3D modeling and design space creation

Author

Arkhipov N.A.
Engineer

License

This is a proprietary research report. All rights reserved.