This paper deals with a 2-DOF (degrees-of-freedom) 3-4R parallel manipulator (PM) with planar base and platform—a novel PM with multiple operation modes (or disassembly free reconfigurable PM) that can use the minimum number of actuated joints. At first, a set of constraint equations of the 3-4R PM are derived with the orientation of the moving platform represented using a Euler parameter quaternion (also Euler–Rodrigues quaternion) and then solved using the algebraic geometry method. It is found that this 3-4R PM has six 2-DOF operation modes, including the two expected spherical translation mode and sphere-on-sphere rolling mode when the PM was synthesized. The motion characteristics of the moving platform are obtained using the kinematic interpretation of Euler parameter quaternions with certain number of constant zero components, which was presented in a recent paper by the first author of this paper, instead of the eigenspace-based approach in the literature. The transition configurations, which are constraint singular configurations, among different operation modes are also presented. This work provides a solid foundation to the development and control of the 2-DOF 3-4R PM with both 2-DOF spherical translation mode and 2-DOF sphere-on-sphere rolling mode.

References

References
1.
Kong
,
X.
,
Gosselin
,
C.
, and
Richard
,
P. L.
,
2007
, “
Type Synthesis of Parallel Mechanisms With Multiple Operation Modes
,”
ASME J. Mech. Des.
,
129
(
6
), pp.
595
601
.
2.
Kong
,
X.
,
2013
, “
Type Synthesis of 3-DOF Parallel Manipulators With Both a Planar Operation Mode and a Spatial Translational Operation Mode
,”
ASME J. Mech. Rob.
,
5
(
4
), p.
041015
.
3.
Kong
,
X.
, and
Yu
,
J.
,
2015
, “
Type Synthesis of 2-DOF 3-4R Parallel Mechanisms With Both Spherical Translation Mode and Sphere-on-Sphere Rolling Mode
,”
ASME J. Mech. Rob.
,
7
(
4
), p.
041018
.
4.
Fanghella
,
P.
,
Galletti
,
C.
, and
Gianotti
,
E.
,
2006
, “
Parallel Robots That Change Their Group of Motion
,”
Advances in Robot Kinematics
,
J.
Lenarčič
and
B.
Roth
, eds.,
Springer
,
Dordrecht, The Netherlands
, pp.
49
56
.
5.
Refaat
,
S.
,
Hervé
,
J. M.
,
Nahavandi
,
S.
, and
Trinh
,
H.
,
2007
, “
Two-Mode OverConstrained Three-DOFs Rotational–Translational Linear-Motor-Based Parallel Kinematics Mechanism for Machine Tool Applications
,”
Robotica
,
25
(4), pp.
461
466
.
6.
Li
,
Q.
, and
Hervé
,
J. M.
,
2009
, “
Parallel Mechanisms With Bifurcation of Schoenflies Motion
,”
IEEE Trans. Rob.
,
25
(
1
), pp.
158
164
.
7.
Gogu
,
G.
,
2011
, “
Maximally Regular T2R1-Type Parallel Manipulators With Bifurcated Spatial Motion
,”
ASME J. Mech. Rob.
,
3
(
1
), p.
011010
.
8.
Wu
,
K.
,
Yu
,
J.
,
Zong
,
G.
, and
Kong
,
X.
,
2014
, “
A Family of Rotational Parallel Manipulators With Equal-Diameter Spherical Pure Rotation
,”
ASME J. Mech. Rob.
,
6
(
1
), p.
011008
.
9.
Gan
,
D.
,
Dai
,
J. S.
, and
Liao
,
Q.
,
2009
, “
Mobility Change in Two Types of Metamorphic Parallel Mechanisms
,”
ASME J. Mech. Rob.
,
1
(
4
), p.
041007
.
10.
Zhang
,
K. T.
,
Dai
,
J. S.
, and
Fang
,
Y. F.
,
2012
, “
Geometric Constraint and Mobility Variation of Two 3SvPSv Metamorphic Parallel Mechanisms
,”
ASME J. Mech. Des.
,
135
(
1
), p.
011001
.
11.
Cox
,
D. A.
,
Little
,
J. B.
, and
O'Shea
,
D.
,
2007
,
Ideals, Varieties, and Algorithms
,
Springer
,
New York
.
12.
Walter
,
D. R.
,
Husty
,
M. L.
, and
Pfurner
,
M.
,
2009
, “
Chapter A: Complete Kinematic Analysis of the SNU 3-UPU Parallel Manipulator
,”
Contemporary Mathematics
, Vol.
496
,
American Mathematical Society
,
Providence, RI
, pp.
331
346
.
13.
Sommese
,
A. J.
, and
Wampler
,
C. W.
, II
,
2005
,
The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
,
World Scientific Press
,
Singapore
.
14.
Decker
,
W.
, and
Pfister
,
G.
,
2013
,
A First Course in Computational Algebraic Geometry
,
Cambridge University Press
,
New York
.
15.
Decker
,
W.
,
Greuel
,
G.-M.
,
Pfister
,
G.
, and
Schönemann
,
H.
,
2011
, “
Singular 3-1-3—A Computer Algebra System for Polynomial Computations
,” TU Kaiserslautern, Kaiserslautern, Germany, http://www.singular.uni-kl.de
16.
Kong
,
X.
,
2014
, “
Reconfiguration Analysis of a 3-DOF Parallel Mechanism Using Euler Parameter Quaternions and Algebraic Geometry Method
,”
Mech. Mach. Theory
,
74
, pp.
188
201
.
17.
Carbonari
,
L.
,
Callegari
,
M.
,
Palmieri
,
G.
, and
Palpacelli
,
M.-C.
,
2014
, “
A New Class of Reconfigurable Parallel Kinematic Machines
,”
Mech. Mach. Theory
,
79
, pp.
173
183
.
18.
Nurahmi
,
L.
,
Schadlbauer
,
J.
,
Caro
,
S.
,
Husty
,
M.
, and
Wenger
,
Ph.
,
2015
, “
Kinematic Analysis of the 3-RPS Cube Parallel Manipulator
,”
ASME J. Mech. Rob.
,
7
(
1
), p.
011008
.
19.
Arponen
,
T.
,
Piipponen
,
S.
, and
Tuomela
,
J.
,
2013
, “
Kinematical Analysis of Wunderlich Mechanism
,”
Mech. Mach. Theory
,
70
, pp.
16
31
.
20.
Spring
,
K. W.
,
1986
, “
Euler Parameters and the Use of Quaternion Algebra in the Manipulation of Finite Rotations: A Review
,”
Mech. Mach. Theory
,
21
(
5
), pp.
365
373
.
21.
Phillips
,
W. F.
, and
Hailey
,
C. E.
,
2001
, “
Review of Attitude Representations Used for Aircraft Kinematics
,”
J. Aircr.
,
38
(
4
), pp.
718
737
.
You do not currently have access to this content.