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Research Papers

On the Dynamic Modeling of a Bevel-Geared Surgical Robotic Mechanism

[+] Author and Article Information
Xiaoli Zhang

Division of Engineering and Physics, Wilkes University, Wilkes-Barre, PA 18766xiaoli.zhang@wilkes.edu

Carl A. Nelson1

Department of Mechanical Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588; Department of Surgery, Center for Advanced Surgical Technology, University of Nebraska Medical Center, Omaha, NE 68198cnelson5@unl.edu

1

Corresponding author.

J. Med. Devices 4(4), 041002 (Oct 12, 2010) (11 pages) doi:10.1115/1.4002549 History: Received September 05, 2009; Revised August 26, 2010; Published October 12, 2010; Online October 12, 2010

The use of robotics to enhance visualization and tissue manipulation capabilities contributes to the advancement of minimally invasive surgery. For the development of surgical robot manipulators, the use of advanced dynamic control is an important aspect at the design stage to determine the driving forces and/or torques, which must be exerted by the actuators in order to produce a desirable trajectory of the end effector. Therefore, this study focuses on the generation of inverse dynamic models for a spherical bevel-geared mechanism called Compact Bevel-geared Robot for Advanced Surgery (CoBRASurge), which is used as a surgical tool manipulator. For given typical trajectories of end effectors in clinical experiments, the motion of each element in the mechanism can be derived using the inverse kinematic equations. The driving torques exerted by actuators can be determined according to the presented inverse dynamic formulations. The simulation results of CoBRASurge reveal the nature of the driving torques in spherical bevel-geared mechanisms. In addition, sensitivity analysis of mass contribution has been performed to evaluate the effect of individual elements on the peak driving torques. Dynamic models, such as the one presented, can be used for the design of advanced dynamic control systems, including gravity compensation and haptic interfaces for enhanced surgical functionality. The accompanying sensitivity analysis also provides a solid guideline for the design of the next generation CoBRASurge prototype. The present dynamic modeling methodology also gives a general dynamic analysis approach for other spherical articulated linkage mechanisms.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 14

Driving torque of link 2 with different external load

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Figure 15

Driving torque of link 5 with different external load

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Figure 16

Driving torque of link 6 with different external load

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Figure 17

Velocity profiles of the end effector within a 3 s period

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Figure 18

Driving torques of link 5 under different motion types in 3 s

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Figure 19

Driving torques of link 5 under different motion types in 1 s

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Figure 1

Functional schematic of the spherical bevel-geared mechanism

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Figure 2

Equivalent open-loop chain of the spherical bevel-geared mechanism

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Figure 3

Reaction force and exerted point for an ideal revolute bearing joint

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Figure 4

Computer-aided design (CAD) model of CoBRASurge in conjunction with a robot arm

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Figure 5

Schematic drawing of link 4 with payload

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Figure 6

The selected trajectory of the end effector

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Figure 7

The motion procedure of CoBRASurge

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Figure 8

Joint displacement of θ21 in a constant-speed motion within 3 s

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Figure 9

Joint displacement of θ32 in a constant-speed motion within 3 s

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Figure 10

Joint displacement of θ43 in a constant-speed motion within 3 s

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Figure 11

Driving torque of link 2 for a given trajectory

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Figure 12

Driving torque of link 5 for a given trajectory

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Figure 13

Driving torque of link 6 for a given trajectory

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