The workspace of hexapod robots is a key performance parameter which has attracted the attention of numerous researchers during the past decades. The selection of the hexapod parameters for a desired workspace generally employs the use of numerical methods. This paper presents a general methodology for solving the closed-form constant orientation workspace of radially symmetric hexapod robots. The closed-form solution facilitates hexapod robot design and minimizes numerical efforts with on-line determination of stability and workspace utilization. The methodology can be used for robots with nonsymmetric and nonidentical kinematic chains. In this paper, the methodology is used to derive the closed-form equations of the boundary of the constant-orientation workspace of axially symmetric hexapod robots. Several applications are provided to demonstrate the capability of the presented closed-form solution in design and optimization. An approach for workspace-based design optimization is presented using the provided analytical solution by applying an iterative optimization algorithm to the find optimized structural parameters and an optimized workspace.

References

References
1.
Iborra
,
A.
,
Alvarez
,
B.
,
Ortiz
,
F.
,
Marin
,
F.
,
Fernandez
,
C.
, and
Fernandez-Merono
,
J.
,
2001
, “
Service Robot for Hull-Blasting
,”
The 27th Annual Conference of the IEEE Industrial Electronics Society
, IECON, Vol. 3, pp.
2178
2183
.
2.
Oh
,
J.-K.
,
Lee
,
A.-Y.
,
Oh
,
S. M.
,
Choi
,
Y.
,
Yi
,
B.-J.
, and
Yang
,
H. W.
,
2007
, “
Design and Control of Bridge Inspection Robot System
,”
International Conference on Mechatronics and Automation
, pp.
3634
3639
.
3.
Choi
,
C.
,
Park
,
B.
, and
Jung
,
S.
,
2010
, “
The Design and Analysis of a Feeder Pipe Inspection Robot With an Automatic Pipe Tracking System
,”
IEEE/ASME Trans. Mechatronics
,
15
(
5
), pp.
736
745
.10.1109/TMECH.2009.2032541
4.
Schempf
,
H.
,
1994
, “
Neptune: Above-Ground Storage Tank Inspection Robot System
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, pp.
1403
1408
.
5.
Nassiraei
,
A.
,
Kawamura
,
Y.
,
Ahrary
,
A.
,
Mikuriya
,
Y.
, and
Ishii
,
K.
,
2007
, “
Concept and Design of A Fully Autonomous Sewer Pipe Inspection Mobile Robot ‘KANTARO
,”
IEEE International Conference on Robotics and Automation
, pp.
136
143
.
6.
Billah
,
M. M.
,
Ahmed
,
M.
, and
Farhana
,
S.
,
2008
, “
Walking Hexapod Robot in Disaster Recovery: Developing Algorithm for Terrain Negotiation and Navigation
,”
Proceedings of World Academy of Science, Engineering and Technology
, Vol.
42
, pp.
328
333
.
7.
Karalarli
,
E.
,
Erkmen
,
A.
, and
Erkmen
,
I.
,
2004
, “
Intelligent Gait Synthesizer for Hexapod Walking Rescue Robots
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, Vol.
3
, pp.
2177
2182
.
8.
Massari
,
M.
,
Massioni
,
P.
,
Nebuloni
,
S.
,
Sangiovanni
,
G.
, and
Bernelli-Zazzera
,
F.
,
2005
, “
Realization and Control of a Prototype of Legged Rover for Planetary Exploration
,” Proceedings of the
IEEE/ASME International Conference on Advanced Intelligent Mechatronics
, pp.
863
868
10.1109/AIM.2005.1511117.
9.
Wu
,
S.
,
Wu
,
L.
, and
Liu
,
T.
,
2011
, “
Design of a Sliding Wall Climbing Robot With a Novel Negative Adsorption Device
,”
The 8th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI)
, pp.
97
100
.
10.
Go
,
Y.
,
Yin
,
X.
, and
Bowling
,
A.
,
2004
, “
A Navigable Six-Legged Robot Platform
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, Vol.
5
, pp.
5105
5110
.
11.
Duan
,
X.
,
Chen
,
W.
,
Yu
,
S.
, and
Liu
,
J.
,
2009
, “
Tripod Gaits Planning and Kinematics Analysis of a Hexapod Robot
,”
Proceedings of the IEEE International Conference on Control and Automation
, pp.
1850
1855
.
12.
Netto
,
S.
,
Evsukoff
,
A.
, and
Dutra
,
M. S.
,
2000
, “
Fuzzy Systems to Solve Inverse Kinematics Problem in Robots Control: Application to an Hexapod Robots' Leg
,”
Proceedings of the IEEE 6th Brazilian Symposium on Neural Networks
, pp.
150
155
.
13.
Jianhua
,
G.
,
2006
, “
Design and Kinematic Simulation for Six-DOF Leg Mechanism of Hexapod Robot
,”
Proceedings of the IEEE International Conference on Robotics and Biomimetics
, Vol.
2
, pp.
625
629
.
14.
Fujii
,
S.
,
Inoue
,
K.
,
takubo
,
T.
, and
Arai
,
T.
,
2006
, “
Climbing up onto Steps for limb Mechanism ROBOT ASTERISK
,”
23rd International Symposium on Automation and Robotics in Construction
, pp.
225
230
.
15.
Gosselin
,
C.
,
1990
, “
Determination of the Workspace of 6-DOF Parallel Manipulators
,”
ASME J. Mech. Des.
,
112
(
3
), pp.
331
336
.10.1115/1.2912612
16.
Jiang
,
Q.
, and
Gosselin
,
C.
,
2008
, “
The Maximal Singularity-Free Workspace of the Gough-Stewart Platform for a Given Orientation
,”
ASME J. Mech. Des.
,
130
(
11
), p.
112304
.10.1115/1.2976452
17.
Majid
,
M.
,
Huang
,
Z.
, and
Yao
,
Y.
,
2000
, “
Workspace Analysis of a Six-Degrees of Freedom, Three-Prismatic-Prismatic-Spheric-Revolute Parallel Manipulator
,”
Int. J. Adv. Manuf. Technol.
,
16
, pp.
441
449
.10.1007/s001700050176
18.
Bonev
,
I. A.
, and
Ryu
,
J.
,
2001
, “
A Geometrical Method for Computing the Constant-Orientation Workspace of 6-PRRS Parallel Manipulators
,”
Mech. Mach. Theory
,
36
, pp.
1
13
.10.1016/S0094-114X(00)00031-8
19.
Pusey
,
J.
,
Fattah
,
A.
,
Agrawal
,
S.
, and
Messina
,
E.
,
2004
, “
Design and Workspace Analysis of a 66 Cable-Suspended Parallel Robot
,”
Mech. Mach. Theory
,
39
, pp.
761
778
.10.1016/j.mechmachtheory.2004.02.010
20.
Merlet
,
J.
,
1999
, “
Determination of 6D Workspace of Gough-Type Parallel Manipulator and Comparison Between Different Geometries
,”
Int. J. Rob. Res.
,
18
(
9
), pp.
902
916
.10.1177/02783649922066646
21.
Jiang
,
Q.
, and
Gosselin
,
C.
,
2009
, “
Determination of the Maximal Singularity-Free Orientation Workspace for the Gough-Stewart Platform
,”
Mech. Mach. Theory
,
44
, pp.
1281
1293
.10.1016/j.mechmachtheory.2008.07.005
22.
Bonev
,
I. A.
, and
Ryu
,
J.
,
2001
, “
A New Approach to Orientation Workspace Analysis of 6-DOF Parallel Manipulators
,”
Mech. Mach. Theory
,
36
, pp.
15
28
.10.1016/S0094-114X(00)00032-X
23.
Tsai
,
K.
, and
Lin
,
J.
,
2006
, “
Determining the Compatible Orientation Workspace of Stewart-Gough Parallel Manipulators
,”
Mech. Mach. Theory
,
41
, pp.
1168
1184
.10.1016/j.mechmachtheory.2005.12.002
24.
Portman
,
V. T.
, and
Sandler
,
B.-Z.
,
2002
, “
Tripod Robot With Cylindrically Actuated Limbs: Structure and Kinematics
,”
Mech. Mach. Theory
,
37
, pp.
1447
1463
.10.1016/S0094-114X(02)00073-3
25.
Affi
,
Z.
,
Romdhane
,
L.
, and
Maalej
,
A.
,
2004
, “
Dimensional synthesis of a 3-Translational-DOF in-Parallel Manipulator for a Desired Workspace
,”
Eur. J. Mech. A/Solids
,
23
, pp.
311
324
.10.1016/j.euromechsol.2004.01.003
26.
Szep
,
C.
,
Stan
,
S.-D.
, and
Csibi
,
V.
,
2011
, “
Design, Workspace analysis, and Inverse Kinematics Problem of Delta Parallel Robot
,”
Mechanika
,
17
(
3
), pp.
296
299
.10.5755/j01.mech.17.3.506
27.
Bonev
,
I. A.
, and
Gosselin
,
C. M.
,
2006
, “
Analytical Determination of the Workspace of Symmetrical Spherical Parallel Mechanisms
,”
IEEE Trans. Rob.
,
22
(
5
), pp.
1011
1017
.10.1109/TRO.2006.878983
28.
Lee
,
T.
, and
Perng
,
M.
,
2007
, “
Analysis of Simplified Position and 5-DOF Total Orientation Workspaces of a Hexapod Mechanism
,”
Mech. Mach. Theory
,
42
, pp.
1577
1600
.10.1016/j.mechmachtheory.2007.01.007
29.
Zhao
,
J.-S.
,
Chen
,
M.
,
Zhou
,
K.
,
Dong
,
J.-X.
, and
Feng
,
Z.-J.
,
2006
, “
Workspace of Parallel Manipulators With Symmetric Identical Kinematic Chains
,”
Mech. Mach. Theory
,
41
(
6
), pp.
632
645
.10.1016/j.mechmachtheory.2005.09.007
30.
Merlet
,
J.-P.
,
Gosselin
,
C. M.
, and
Mouly
,
N.
,
1998
, “
Workspaces of Planar Parallel Manipulators
,”
Mech. Mach. Theory
,
33
(
1–2
), pp.
7
20
.10.1016/S0094-114X(97)00025-6
31.
Toz
,
M.
, and
Kucuk
,
S.
,
2013
, “
Dexterous Workspace Optimization of an Asymmetric Six-Degree of Freedom Stewart–Gough Platform Type Manipulator
,”
Rob. Auton. Syst.
,
61
(
12
), pp.
1516
1528
.10.1016/j.robot.2013.07.004
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