Abstract

The flexure joints are proposed to replace the rigid assembly between the cross-arm and the moving carriages of dual-drive H-type gantry (DHG) for higher reliability and fine rotational alignments. In the literature, the flexure joint of the DHG is modeled as an ideal linear torsional spring, resulting in an inaccurate estimation of the cross-arm’s angle. In this study, a generalized analytical kinetostatic model of flexure-linked DHG is built by considering the geometric nonlinearities. The expressions of beam coefficients in the model are obtained from either beam constraint model (BCM) or Timoshenko BCM (TBCM) according to the given criterion of length-to-thickness ratio. The model is capable to accurately estimate any two variables among the rotation angle of the cross-arm, the misalignment of two carriages, and the net driving force, as long as the other is known. Simulations and experiments on the testbed validate the accuracy and show practical appeals of the proposed model.

References

1.
Li
,
D.
, and
Yoon
,
S. W.
,
2016
, “
PCB Assembly Optimization in a Single Gantry High-speed Rotary-Head Collect-and-Place Machine
,”
Int. J. Adv. Manuf. Technol.
,
88
(
9–12
), pp.
2819
2834
.
2.
Kuriyama
,
K.
,
Onishi
,
H.
,
Sano
,
N.
,
Komiyama
,
T.
,
Aikawa
,
Y.
,
Tateda
,
Y.
,
Araki
,
T.
, and
Uematsu
,
M.
,
2003
, “
A New Irradiation Unit Constructed of Self-Moving Gantry-CT and Linac
,”
Int. J. Radiat. Oncol. Biol. Phys.
,
55
(
2
), pp.
428
35
.
3.
Farjood
,
E.
,
Vojdani
,
M.
,
Torabi
,
K.
, and
Khaledi
,
A. A.
,
2017
, “
Marginal and Internal Fit of Metal Copings Fabricated With Rapid Prototyping and Conventional Waxing
,”
J. Prosthetic Dent.
,
117
(
1
), pp.
164
170
.
4.
Li
,
C.
,
Chen
,
Z.
, and
Yao
,
B.
,
2018
, “
Adaptive Robust Synchronization Control of a Dual-Linear-Motor-Driven Gantry With Rotational Dynamics and Accurate Online Parameter Estimation
,”
IEEE Trans. Ind. Inform.
,
14
(
7
), pp.
3013
3022
.
5.
Hu
,
C.
,
Hu
,
Z.
, and
Wang
,
Z.
,
2017
, “
Advanced GTCF-LARC Contouring Motion Controller Design for an Industrial X-Y Linear Motor Stage With Experimental Investigation
,”
IEEE. Trans. Ind. Electron.
,
64
(
4
), pp.
3308
3318
.
6.
Chen
,
Z.
,
Yao
,
B.
, and
Wang
,
Q.
,
2015
, “
μ-Synthesis-Based Adaptive Robust Control of Linear Motor Driven Stages With High-Frequency Dynamics: A Case Study
,”
IEEE/ASME Trans. Mechatron.
,
20
(
3
), pp.
1482
1490
.
7.
Garcá-Herreros
,
I.
,
Kestelyn
,
X.
,
Gomand
,
J.
,
Coleman
,
R.
, and
Barre
,
P.-J.
,
2013
, “
Model-Based Decoupling Control Method for Dual-Drive Gantry Stages: A Case Study With Experimental Validations
,”
Control. Eng. Pract.
,
21
(
3
), pp.
298
307
.
8.
Ma
,
J.
,
Chen
,
S.-L.
,
Kamaldin
,
N.
,
Teo
,
C. S.
,
Tay
,
A.
,
Al Mamun
,
A.
, and
Tan
,
K. K.
,
2018
, “
Integrated Mechatronic Design in the Flexure-Linked Dual-Drive Gantry by Constrained Linear-Quadratic Optimization
,”
IEEE. Trans. Ind. Electron.
,
65
(
3
), pp.
2408
2418
.
9.
Zhao
,
Y.
,
Zhao
,
H.
,
Guo
,
J.
,
Tu
,
H.
, and
Yin
,
S.
,
2020
, “
Quality Inspection of Satellite Imagery Block Adjustment Without GCP
,”
Int. Arch. Photogram Rem Sens. Spatial Inform. Sci.
,
43
(
8
), pp.
1411
1416
.
10.
Xu
,
Q.
,
2013
, “
Design and Development of a Compact Flexure-Based XY Precision Positioning System With Centimeter Range
,”
IEEE. Trans. Ind. Electron.
,
61
(
2
), pp.
893
903
.
11.
Kamaldin
,
N.
,
Chen
,
S.-L.
,
Teo
,
C. S.
,
Lin
,
W.
, and
Tan
,
K. K.
,
2018
, “
A Novel Adaptive Jerk Control With Application to Large Workspace Tracking on a Flexure-Linked Dual-Drive Gantry
,”
IEEE. Trans. Ind. Electron.
,
66
(
7
), pp.
5353
5363
.
12.
Ma
,
J.
,
Chen
,
S.-L.
,
Liang
,
W.
,
Teo
,
C. S.
,
Tay
,
A.
,
Al Mamun
,
A.
, and
Tan
,
K. K.
,
2019
, “
Robust Decentralized Controller Synthesis in Flexure-Linked H-Gantry by Iterative Linear Programming
,”
IEEE Trans. Ind. Inform.
,
15
(
3
), pp.
1698
1708
.
13.
Turkkan
,
O. A.
, and
Su
,
H. -J.
,
2017
, “
A General and Efficient Multiple Segment Method for Kinetostatic Analysis of Planar Compliant Mechanisms
,”
Mech. Mach. Theory.
,
112
(
6
), pp.
205
217
.
14.
Kahrobaiyan
,
M.
,
Rahaeifard
,
M.
,
Tajalli
,
S.
, and
Ahmadian
,
M.
,
2012
, “
A Strain Gradient Functionally Graded Euler–Bernoulli Beam Formulation
,”
Int. J. Eng. Sci.
,
52
(
3
), pp.
65
76
.
15.
Zhang
,
A.
, and
Chen
,
G.
,
2013
, “
A Comprehensive Elliptic Integral Solution to the Large Deflection Problems of Thin Beams in Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
5
(
2
), p.
021006
.
16.
Holst
,
G. L.
,
Teichert
,
G. H.
, and
Jensen
,
B. D.
,
2011
, “
Modeling and Experiments of Buckling Modes and Deflection of Fixed-Guided Beams in Compliant Mechanisms
,”
ASME J. Mech. Des.
,
133
(
5
), p.
051002
.
17.
Awtar
,
S.
,
Slocum
,
A. H.
, and
Sevincer
,
E.
,
2007
, “
Characteristics of Beam-Based Flexure Modules
,”
ASME J. Mech. Des.
,
129
(
6
), pp.
625
639
.
18.
Hao
,
G.
, and
Li
,
H.
,
2016
, “
Extended Static Modeling and Analysis of Compliant Compound Parallelogram Mechanisms Considering the Initial Internal Axial Force
,”
ASME J. Mech. Rob.
,
8
(
4
), p.
041008
.
19.
Sen
,
S.
,
2013
, “
Beam Constraint Model: Generalized Nonlinear Closed-Form Modeling of Beam Flexures for Flexure Mechanism Design
,”
PhD thesis
,
University of Michigan and State of Michigan
.
20.
Awtar
,
S.
,
Shimotsu
,
K.
, and
Sen
,
S.
,
2010
, “
Elastic Averaging in Flexure Mechanisms: A Three-Beam Parallelogram Flexure Case Study
,”
ASME J. Mech. Rob.
,
2
(
4
), p.
041006
.
21.
Chen
,
G.
,
Ma
,
F.
,
Hao
,
G.
, and
Zhu
,
W.
,
2019
, “
Modeling Large Deflections of Initially Curved Beams in Compliant Mechanisms Using Chained Beam Constraint Model
,”
ASME J. Mech. Rob.
,
11
(
1
), p.
011002
.
22.
Kong
,
K.
,
Chen
,
G.
, and
Hao
,
G.
,
2019
, “
Kinetostatic Modeling and Optimization of a Novel Horizontal-Displacement Compliant Mechanism
,”
ASME J. Mech. Rob.
,
11
(
6
), p.
064502
.
23.
Liu
,
P.
, and
Yan
,
P.
,
2018
, “
Kinetostatic Modeling of Bridge-Type Amplifiers Based on Timoshenko Beam Constraint Model
,”
Int. J. Precis. Eng. Manuf.
,
19
(
9
), pp.
1339
1345
.
24.
Chen
,
G.
, and
Ma
,
F.
,
2015
, “
Kinetostatic Modeling of Fully Compliant Bistable Mechanisms Using Timoshenko Beam Constraint Model
,”
ASME J. Mech. Des.
,
137
(
2
), p.
022301
.
25.
Ma
,
F.
, and
Chen
,
G.
,
2017
, “
Bi-BCM: A Closed-form Solution for Fixed-Guided Beams in Compliant Mechanisms
,”
ASME J. Mech. Rob.
,
9
(
1
), p.
014501
.
26.
Merriam
,
E. G.
, and
Howell
,
L. L.
,
2016
, “
Lattice Flexures: Geometries for Stiffness Reduction of Blade Flexures
,”
Precis. Eng.
,
45
(
7
), pp.
160
167
.
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