Abstract

Robot-assisted bone reduction surgery consists in using robots to reposition the bone fragments into their original place prior to fracture healing. This study presents the application of a 3-RRPS augmented tripod mechanism with six degrees-of-freedom for longitudinal bone reduction surgery. First, the inverse and forward kinematic models of the mechanism are investigated. Particularly, the forward kinematic is solved by applying Sylvester's dialytic method. Second, the velocity model is studied and its singular configurations are identified. The workspace of the 3-RRPS mechanism is then outlined and compared with the Stewart platform, which is a classical mechanism for the targeted application. The results show that this mechanism provides a larger workspace, especially its rotation angle about the vertical axis, which is an important aspect in the bone reduction. A series of simulations on the numerical and graphic software is performed to verify the entire analysis of the parallel mechanism. A physiguide and mscadams software are used to carry out a simulation of a real case of femur fracture reduction using the proposed mechanism to validate its suitability. Finally, a robotic prototype based on the mechanism is manufactured and experimented using an artificial bone model to evaluate the feasibility of the mechanism.

References

1.
Bowman
,
E. N.
,
Mehlman
,
C. T.
,
Lindsell
,
C. J.
, and
Tamai
,
J.
,
2011
, “
Non-Operative Treatment of Both-Bone Forearm Shaft Fractures in Children: Predictors of Early Radiographic Failure
,”
J. Pediatr. Orthop.
,
31
(
1
), pp.
23
32
.10.1097/BPO.0b013e318203205b
2.
Arneson
,
T. L.
,
Melton
,
L. J.
,
Lewallen
,
D. G.
, and
O'Fallon
,
W. N.
,
1998
, “
Epidemiology of Diaphyseal and Distal Femoral Fractures in Rochester, Minnesota, 1965-1984
,”
Clin. Orthop. Relat. Res.
,
234
, pp.
188
194
.https://journals.lww.com/clinorthop/Abstract/1988/09000/Epidemiology_of_Diaphyseal_and_Distal_Femoral.33.aspx
3.
Zlowodzki
,
M.
,
Bhandari
,
M.
,
Marek
,
D. J.
,
Cole
,
P. A.
, and
Kregor
,
P. J.
,
2006
, “
Operative Treatment of Acute Distal Femur Fractures: Systematic Review of 2 Comparative Studies and 45 Case Series (1989 to 2005)
,”
J. Orthop. Trauma
,
20
(
5
), pp.
366
371
.10.1097/00005131-200605000-00013
4.
Zhang
,
Y.-Z.
,
2016
, “
Minimally Invasive Reduction and Fixation in Orthopedic Trauma
,”
Chin. Med. J.
,
129
(
21
), pp.
2521
2523
.10.4103/0366-6999.192773
5.
Xie
,
L.
,
Wu
,
W.-J.
, and
Liang
,
Y.
,
2016
, “
Comparison Between Minimally Invasive Transforaminal Lumbar Interbody Fusion and Conventional Open Transforaminal Lumbar Interbody Fusion: An Updated Meta-Analysis
,”
Chin. Med. J.
,
129
(
16
), pp.
1969
1986
.10.4103/0366-6999.187847
6.
Seide
,
K.
,
Wolter
,
D.
, and
Kortmann
,
H.-R.
,
1999
, “
Fracture Reduction and Deformity Correction With the Hexapod Ilizarov Fixator
,”
Clin. Orthop. Related Res.
, (
363
), pp.
186
195
.https://europepmc.org/article/med/10379322
7.
Seide
,
K.
,
Faschingbauer
,
M.
,
Wenzl
,
M. E.
,
Weinrich
,
N.
, and
Juergens
,
C.
,
2004
, “
A Hexapod Robot External Fixator for Computer Assisted Fracture Reduction and Deformity Correction
,”
Int. J. Med. Rob. Comput. Assisted Surg.
,
1
(
1
), pp.
64
69
.10.1002/rcs.6
8.
Tang
,
P.
,
Hu
,
L.
,
Du
,
H.
,
Gong
,
M.
, and
Zhang
,
L.
,
2012
, “
Novel 3D Hexapod Computer-Assisted Orthopaedic Surgery System for Closed Diaphyseal Fracture Reduction
,”
Int. J. Med. Rob. Comput. Assisted Surg.
,
8
(
1
), pp.
17
24
.10.1002/rcs.417
9.
Mohammad
,
H. A.
,
Gallardo-Alvarado
,
J.
, and
Farahmand
,
F.
,
2017
, “
A Wide-Open 3-Legged Parallel Robot for Long Bone Fracture Reduction
,”
ASME J. Mech. Rob.
,
9
(
1
), p.
015001
.10.1115/1.4035495
10.
Füchtmeier
,
B.
,
Egersdoerfer
,
S.
,
Mai
,
R.
,
Hente
,
R.
,
Dragoi
,
D.
,
Monkman
,
G.
, and
Nerlich
,
M.
,
2004
, “
Reduction of Femoral Shaft Fractures In Vitro by a New Developed Reduction Robot System ‘RepoRobo’
,”
Int. J. Care Injured
,
35
(
1
), pp.
113
119
.10.1016/j.injury.2004.05.019
11.
Westphal
,
R.
,
Gösling
,
T.
,
Oszwald
,
M.
,
Bredow
,
J.
,
Klepzig
,
D.
,
Winkelbach
,
S.
,
Hüfner
,
T.
,
Krettek
,
C.
, and
Wahl
,
F.
,
2008
, “
Robot Assisted Fracture Reduction
,”
Exp. Rob.
,
39
, pp.
153
163
.10.1007/978-3-540-77457-0
12.
Oszwald
,
M.
,
Westphal
,
R.
,
Bredow
,
J.
,
Calafi
,
A.
,
Hufner
,
T.
,
Wahl
,
F.
,
Krettek
,
C.
, and
Gosling
,
T.
,
2010
, “
Robot-Assisted Fracture Reduction Using Three-Dimensional Intraoperative Fracture Visualization: An Experimental Study on Human Cadaver Femora
,”
J. Orthop. Res.
,
28
(
9
), pp.
1240
1244
.10.1002/jor.21118
13.
Oszwald
,
M.
,
Ruan
,
J.
,
Westphal
,
R.
,
O'Loughlin
,
P. F.
,
Kendoff
,
D.
,
Hufner
,
T.
,
Wahl
,
F.
,
Krettek
,
C.
, and
Gosling
,
T.
,
2008
, “
A Rat Model for Evaluating Physiological Responses to Femoral Shaft Fracture Reduction Using a Surgical Robot
,”
J. Orthop. Res.
,
26
(
12
), pp.
1656
1659
.10.1002/jor.20698
14.
Westphal
,
R.
,
Winkelbach
,
S.
,
Wah
,
F.
,
Gösling
,
T.
,
Oszwald
,
M.
,
Hüfner
,
T.
, and
Krettek
,
C.
,
2009
, “
Robot-Assisted Long Bone Fracture Reduction
,”
Int. J. Rob. Res.
,
28
(
10
), pp.
1259
1278
.10.1177/0278364909101189
15.
Gosling
,
T.
,
Westphal
,
R.
,
Hufner
,
T.
,
Faulstich
,
J.
,
Kfuri
,
M.
, Jr.
Wahl
,
F.
, and
Krettek
,
C.
,
2005
, “
Robot-Assisted Fracture Reduction: A Preliminary Study in the Femur Shaft
,”
Med. Biol. Eng. Comput.
,
43
(
1
), pp.
115
120
.10.1007/BF02345131
16.
Hung
,
S.-S.
, and
Lee
,
M.-Y.
,
2010
, “
Functional Assessment of a Surgical Robot for Reduction of Lower Limb Fractures
,”
Int. J. Med. Rob. Comput. Assist Surg.
,
6
(
4
), pp.
413
421
.10.1002/rcs.351
17.
Wang
,
J.
,
Han
,
W.
, and
Lin
,
H.
,
2013
, “
Femoral Fracture Reduction With a Parallel Manipulator Robot on a Traction Table
,”
Int J Med Rob. Comput. Assist Surg.
,
9
(
4
), pp.
464
471
.10.1002/rcs.1550
18.
Du
,
H.
,
Hu
,
L.
,
Li
,
C.
,
Wang
,
T.
,
Zhao
,
L.
,
Li
,
Y.
,
Mao
,
Z.
,
Liu
,
D.
,
Zhang
,
L.
,
He
,
C.
,
Zhang
,
L.
,
Hou
,
H.
,
Zhang
,
L.
, and
Tang
,
P.
,
2015
, “
Advancing Computer-Assisted Orthopaedic Surgery Using a Hexapod Device for Closed Diaphyseal Fracture Reduction
,”
Int. J. Med. Rob. Comput. Assist Surg
,
11
(
3
), pp.
348
359
.10.1002/rcs.1614
19.
Nguyen Phu
,
S.
,
Essomba
,
T.
,
Idram
,
I.
, and
Lai
,
J. Y.
,
2019
, “
Kinematic Analysis and Evaluation of a Hybrid Mechanism for Computer Assisted Bone Reduction Surgery
,”
Mech. Sci.
,
10
(
2
), pp.
589
604
.10.5194/ms-10-589-2019
20.
Hunt
,
K. H.
,
1983
, “
Structural Kinematics of In-Parallel-Actuated Robot-Arms
,”
J. Mech., Trans., Autom. Des.
,
105
(
4
), pp.
705
712
.10.1115/1.3258540
21.
Carretero
,
J. A.
,
Podhorodeski
,
R. P.
,
Nahon
,
M. A.
, and
Gosselin
,
C. M.
,
2000
, “
Kinematic Analysis and Optimization of a New Three Degree-of-Freedom Spatial Parallel Manipulator
,”
ASME J. Mech. Des.
,
122
(
1
), pp.
17
24
.10.1115/1.533542
22.
Li
,
B.
,
Li
,
Y.
, and
Zhao
,
X.
,
2016
, “
Kinematics Analysis of a Novel Over-Constrained Three Degree-of-Freedom Spatial Parallel Manipulator
,”
Mech. Mach. Theory
,
104
, pp.
222
233
.10.1016/j.mechmachtheory.2016.06.003
23.
Zhang
,
D.
,
Xu
,
Y.
,
Ya
,
J.
, and
Zhao
,
Y.
,
2018
, “
Design of a Novel 5-DOF Hybrid Serial-Parallel Manipulator and Theoretical Analysis of Its Parallel Part
,”
Rob. Comput. Integr. Manuf.
,
53
, pp.
228
239
.10.1016/j.rcim.2018.04.004
24.
Beji
,
L.
, and
Pascal
,
M.
,
1999
, “
The Kinematics and the Full Minimal Dynamic Model of a 6-DOF Parallel Robot Manipulator
,”
Nonlinear Dyn.
,
18
(
4
), pp.
339
356
.10.1023/A:1026440021125
25.
Behi
,
F.
,
1988
, “
Kinematic Analysis for a Six-Degree-of-Freedom 3-PRPS Parallel Mechanism
,”
IEEE J. Rob. Autom.
,
4
(
5
), pp.
561
565
.10.1109/56.20442
26.
Shim
,
J. H.
,
Kwon
,
D. S.
, and
Cho
,
H. S.
,
1999
, “
Kinematic Analysis and Design of a Six D.O.F. 3-PRPS in-Parallel Manipulator
,”
Robotica
,
17
(
3
), pp.
269
281
.10.1017/S0263574799001368
27.
Tahmasebi
,
F.
, and
Tsai
,
L.-W.
,
1995
, “
On the Stiffness of a Novel Six-Degree-of-Freedom Parallel Minimanipulator
,”
J. Rob. Syst.
,
12
(
12
), pp.
845
856
.10.1002/rob.4620121208
28.
Kim
,
J.
,
Park
,
F. C.
,
Ryu
,
S. J.
,
Kim
,
J.
,
Hwang
,
J. C.
,
Park
,
C.
, and
Iurascu
,
C. C.
,
2001
, “
Design and Analysis of a Redundantly Actuated Parallel Mechanism for Rapid Machining
,”
IEEE Trans. Rob. Autom.
,
17
(
4
), pp.
423
424
.10.1109/70.954755
29.
Azulay
,
H.
,
Mahmoodi
,
M.
,
Zhao
,
R.
,
Mills
,
J. K.
, and
Benhabib
,
B.
,
2014
, “
Comparative Analysis of a New 3-PPRS Parallel Kinematic Mechanism
,”
Rob. Comput.-Integr. Manuf.
,
30
(
4
), pp.
369
378
.10.1016/j.rcim.2013.12.003
30.
Nag
,
A.
,
Mohan
,
S.
, and
Bandyopadhyay
,
S.
,
2017
, “
Forward Kinematic Analysis of the 3-RPRS Parallel Manipulator
,”
Mech. Mach. Theory
,
116
, pp.
262
272
.10.1016/j.mechmachtheory.2017.05.009
31.
Mohan
,
S.
, and
Corves
,
B.
,
2017
, “
Inverse Dynamics and Trajectory Tracking Control of a New Six Degrees of Freedom Spatial 3-RPRS Parallel Manipulator
,”
Mech. Sci.
,
8
(
2
), pp.
235
248
.10.5194/ms-8-235-2017
32.
Lu
,
Y.
, and
Li
,
X. P.
,
2014
, “
Dynamics Analysis for a Novel 6-DoF Parallel Manipulator I with Three Planar Limbs
,”
Adv. Rob.
,
28
(
16
), pp.
1121
1132
.10.1080/01691864.2014.908743
33.
Nguyen
,
A. V.
,
Bouzgarrou
,
B. C.
,
Charlet
,
K.
, and
Béakou
,
A.
,
2015
, “
Static and Dynamic Characterization of the 6-Dofs Parallel Robot 3CRS
,”
Mech. Mach. Theory
,
93
, pp.
65
82
.10.1016/j.mechmachtheory.2015.07.002
34.
Li
,
W.
, and
Angeles
,
J.
,
2017
, “
A Novel Three-Loop Parallel Robot With Full Mobility: Kinematics, Singularity, Workspace, and Dexterity Analysis
,”
ASME J. Mech. Rob.
,
9
(
5
), p.
051003
.10.1115/1.4037112
35.
Alizade
,
R. I.
,
Tagiyev
,
N. R.
, and
Duffy
,
J.
,
1994
, “
A Forward and Reverse Displacement Analysis of a 6-DOF in-Parallel Manipulator
,”
Mech. Mach. Theory
,
29
(
1
), pp.
115
124
.10.1016/0094-114X(94)90024-8
36.
Huang
,
X.
,
Liao
,
Q.
, and
Wei
,
S.
,
2010
, “
Closed-Form Forward Kinematics for a Symmetrical 6-6 Stewart Platform Using Algebraic Elimination
,”
Mech. Mach. Theory
,
45
(
2
), pp.
327
334
.10.1016/j.mechmachtheory.2009.09.008
37.
Guo
,
W.
,
Li
,
R.
,
Cao
,
C.
, and
Gao
,
Y.
,
2016
, “
Kinematics, Dynamics, and Control System of a New 5-Degree-of-Freedom Hybrid Robot Manipulator
,”
Adv. Mech. Eng.
,
8
(
11
), pp.
1
19
.https://journals.sagepub.com/doi/10.1177/1687814016680309
38.
Lee
,
P. Y.
,
Lai
,
J. Y.
,
Huang
,
C. Y.
,
Hu
,
Y. S.
, and
Feng
,
C. L.
,
2014
, “
Computer Assisted Fracture Reduction and Fixation Simulation for Pelvic Fractures
,”
J. Med. Biol. Eng.
,
34
(
4
), pp.
368
376
.10.5405/jmbe.1605
39.
Irwansyah
,
I.
,
Lai
,
J. Y.
, and
Lee
,
P. Y.
,
2019
, “
Repositioning Bone Fragments Using Registration of Pairs-Points and Assisted Constraints in Virtual Bone Reduction Surgery
,”
Biomed. Eng. Appl., Basis Commun.
,
31
(
3
), p.
1950021
.10.4015/S1016237219500212
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