Comprehensive Stiffness Modeling and Evaluation of an Orthopedic Surgical Robot for Enhanced Cutting Operation Performance

Abstract

This study presents an integrated stiffness modeling and evaluation framework for an orthopedic surgical robot, aiming to enhance cutting accuracy and operational stability. A comprehensive stiffness model is developed, incorporating the stiffness of the end-effector, cutting tool, and force sensor. End-effector stiffness is computed using the virtual joint method based on the Jacobian matrix, enabling accurate analysis of stiffness distribution within the robot's workspace. Joint stiffness is experimentally identified through laser tracker-based displacement measurements under controlled loads and calculated using a least-squares method. The results show displacement errors below 0.3 mm and joint stiffness estimation errors under 1.5%, with values more consistent and stable than those reported for typical surgical robots. Simulation studies reveal spatial variations in operational stiffness, identifying zones of low stiffness and excessive stiffness. Compared to prior studies where stiffness varied over 50%, the proposed model exhibits superior uniformity. Experimental validation confirms model fidelity, with prediction errors generally below 5%. Cutting experiments on porcine femurs demonstrate real-world applicability, achieving average stiffness prediction errors below 3%, and under 1% in key directions. The model supports stiffness-aware trajectory planning and control, reducing cutting deviation by up to 10% and improving workspace stiffness stability by 30%. This research offers a validated, high-accuracy approach to stiffness modeling for surgical robots, bridging the gap between simulation and clinical application, and providing a foundation for safer, more precise robotic orthopedic procedures.

Keywords: joint stiffness identification; orthopedic surgical robot; stiffness distribution; stiffness modeling; virtual joint method.

Figure 1

Joint dimensions and connecting rod coordinate systems of robotic cutting system for orthopedic surgery.

Figure 2

Cutting tool compositions and their corresponding stiffness model.

Figure 3

Joint stiffness identification experiment setup of robotic cutting system for orthopedic surgery.

Figure 4

Errors between measured displacement values and calculated displacement values.

Figure 5

(a–c) Stiffness change in the robot end in the x-axis direction by changing the angle of joints 1–3.

Figure 6

(a–c) Three-dimensional stiffness distribution heatmaps for joint angle variations.

Figure 7

(a,b) Stiffness change in the robot end along the line trajectory AB.

Figure 8

(a,b) Stiffness change in the robot end along the line trajectory CD.

Figure 9

Stiffness change in the robot end in z-axis direction by changing the angle of joints 2–3.

Figure 10

Stiffness changes in the robot end in the x-axis direction from measurement values.

Figure 11

Stiffness changes in the robot end in the z-axis direction from measurement values.

Figure 12

Stiffness change in the robot end in the x-direction from measurement values.

Figure 13

Robotic bone cutting experimental platform.

Figure 14

Experimental stiffness variation curves in x-, y-, and z-directions.