This paper presents a finite element method (FEM) for the kinematic solution of parallel manipulators (PMs), and this approach is applied to analyze the kinematics of a parallel hip joint manipulator (PHJM). The analysis and simulation results indicate that FEM can get accurate results of the kinematics of the PHJM, and the solution process shows that using FEM can solve nonlinear and linear kinematic problems in the same mathematical framework, which provides a theory base for establishing integrated model among different parameter models of the PHJM.

References

1.
Özgür
,
E.
,
Nicolas
,
A.
, and
Philippe
,
M.
,
2013
, “
Linear Dynamic Modeling of Parallel Kinematic Manipulators From Observable Kinematic Elements
,”
Mech. Mach. Theory
,
69
, pp.
73
89
.10.1016/j.mechmachtheory.2013.05.002
2.
Lu
,
Y.
, and
Hu
,
B.
,
2007
, “
Analyzing Kinematics and Solving Active/Constrained Forces of a 3SPU + UPR Parallel Manipulator
,”
Mech. Mach. Theory
,
42
(
10
), pp.
1298
1313
.10.1016/j.mechmachtheory.2006.11.002
3.
Zhang
,
D.
, and
Gao
,
Z.
,
2012
, “
Forward Kinematics, Performance Analysis, and Multi-Objective Optimization of a Bio-Inspired Parallel Manipulator
,”
Rob. Comput.-Integr. Manuf.
,
28
(
4
), pp.
484
492
.10.1016/j.rcim.2012.01.003
4.
Abbasnejad
,
G.
,
Daniali
,
H. M.
, and
Fathi
,
A.
,
2012
, “
Closed Form Solution for Direct Kinematics of a 4PUS + 1PS Parallel Manipulator
,”
Sci. Iran.
,
19
(
2
), pp.
320
326
.10.1016/j.scient.2012.02.015
5.
Cheng
,
G.
,
Yu
,
J. L.
, and
Gu
,
W.
,
2012
, “
Kinematic Analysis of 3SPS + 1PS Bionic Parallel Test Platform for Hip Joint Manipulator Based on Unit Quaternion
,”
Rob. Comput.-Integr. Manuf.
,
28
(
2
), pp.
257
264
.10.1016/j.rcim.2011.09.007
6.
Gan
,
D. M.
,
Liao
,
Q. Z.
,
Dai
,
J. S.
, and
Wei
,
S. M.
,
2010
, “
Design and Kinematics Analysis of a New 3CCC Parallel Mechanism
,”
Robotica
,
28
(
7
), pp.
1065
1072
.10.1017/S0263574709990555
7.
Jaime
,
G.
,
Raúl
,
L.
,
José
,
M. R.
, and
Gürsel
,
A.
,
2011
, “
The Kinematics of Modular Spatial Hyper-Redundant Manipulators Formed From RPS-Type Limbs
,”
Rob. Auton. Syst.
,
59
(
1
), pp.
12
21
.10.1016/j.robot.2010.09.005
8.
Javad
,
E.
, and
Alireza
,
A. T.
,
2010
, “
A Novel Approach for Forward Position Analysis of a Double-Triangle Spherical Parallel Manipulator
,”
Eur. J. Mech.-A/Solids
,
29
(
3
), pp.
348
355
.10.1016/j.euromechsol.2009.12.001
9.
Sandipan
,
B.
, and
Ashitava
,
G.
,
2008
, “
An Algebraic Formulation of Kinematic Isotropy and Design of Isotropic 6-6 Stewart Platform Manipulators
,”
Mech. Mach. Theory
,
43
(
5
), pp.
591
616
.10.1016/j.mechmachtheory.2007.05.003
10.
Dhingra
,
A. K.
,
Almadi
,
A. N.
, and
Kohli
,
D.
,
2001
, “
Closed-Form Displacement and Coupler Curve Analysis of Planar Multi-Loop Mechanisms Using Gröbner Bases
,”
Mech. Mach. Theory
,
36
(
2
), pp.
273
298
.10.1016/S0094-114X(00)00043-4
11.
Gan
,
D. M.
,
Liao
,
Q. Z.
,
Dai
,
J. S.
,
Wei
,
S. M.
, and
Seneviratne
,
L. D.
,
2009
, “
Forward Displacement Analysis of the General 6-6 Stewart Mechanism Using Grobner Bases
,”
Mech. Mach. Theory
,
44
(
9
), pp.
1640
1647
.10.1016/j.mechmachtheory.2009.01.008
12.
Ramachandran
,
S.
,
Nagarajan
,
T.
, and
Prasad
,
N. S.
,
1992
, “
A Finite Element Approach to the Design and Dynamic Analysis of Platform Type Robot Manipulators
,”
Finite Elem. Anal. Des.
,
10
(
4
), pp.
335
350
.10.1016/0168-874X(92)90020-D
13.
Rout
,
B. K.
, and
Mittal
,
R. K.
,
2008
, “
Optimal Manipulator Parameter Tolerance Selection Using Evolutionary Optimization Technique
,”
Eng. Appl. Artif. Intell.
,
21
(
4
), pp.
509
524
.10.1016/j.engappai.2007.05.011
14.
Nie
,
S. H.
,
Li
,
B.
,
Qiu
,
A. H.
, and
Gong
,
S. G.
,
2011
, “
Kinematic Configuration Analysis of Planar Mechanisms Based on Basic Kinematic Chains
,”
Mech. Mach. Theory
,
46
(
10
), pp.
1327
1334
.10.1016/j.mechmachtheory.2011.05.014
15.
Werff
,
K. V.
,
1977
, “
Kinematic and Dynamic Analysis of Mechanisms, A Finite Element Approach
,” Ph.D. thesis, Delft University, Delft, Netherlands.
16.
Avile's
,
R.
,
Goizalde
,
A.
,
Enrique
,
A.
, and
Vicente
,
G. H.
,
2000
, “
A Finite Element Approach to the Position Problems in Open-Loop Variable Geometry Trusses
,”
Finite Elem. Anal. Des.
,
34
(
3–4
), pp.
233
255
.10.1016/S0168-874X(99)00041-4
17.
Zarate
,
I. O.
,
Aguirrebeitia
,
J.
,
Avile
,
R.
, and
Fernandez
,
I.
,
2011
, “
A Finite Element Approach to the Inverse Dynamics and Vibrations of Variable Geometry Trusses
,”
Finite Elem. Anal. Des.
,
47
(
3
), pp.
220
228
.10.1016/j.finel.2010.10.009
18.
Aviles
,
R.
,
Hernandez
,
A.
,
Amezua
,
E.
, and
Altuzarra
,
O.
,
2008
, “
Kinematic Analysis of Linkages Based in Finite Elements and the Geometric Stiffness Matrix
,”
Mech. Mach. Theory
,
43
(
8
), pp.
964
983
.10.1016/j.mechmachtheory.2007.07.007
19.
Fernández-Bustos
,
I.
,
Agirrebeitia
,
J.
,
Ajuria
,
G.
, and
Angulo
,
C.
,
2006
, “
A New Finite Element to Represent Prismatic Joint Constraints in Mechanisms
,”
Finite Elem. Anal. Des.
,
43
(
1
), pp.
36
50
.10.1016/j.finel.2006.06.010
20.
Hernandez
,
A.
,
Altuzarra
,
O.
,
Aviles
,
R.
, and
Petuya
,
V.
,
2003
, “
Kinematic Analysis of Mechanisms Via a Velocity Equation Based in a Geometric Matrix
,”
Mech. Mach. Theory
,
38
(
12
), pp.
1413
1429
.10.1016/S0094-114X(03)00095-8
21.
Aviles
,
R.
,
Ajuria
,
M. B. G.
,
Hormaza
,
M. V.
, and
Hernandez
,
A.
,
1996
, “
A Procedure Based on Finite Elements for the Solution of Nonlinear Problems in the Kinematic Analysis of Mechanisms
,”
Finite Elem. Anal. Des.
,
22
(
4
), pp.
305
327
.10.1016/0168-874X(95)00017-N
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