Dynamics analysis and characteristics of the 8-PSS flexible redundant
parallel manipulator
Yongjie Zhao
a,
n
, Feng Gao
b
, Xingjian Dong
b
, Xianchao Zhao
b
a
Department of Mechatronics Engineering, Shantou University, Shantou City, Guangdong 515063, PR China
b
State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, PR China
article info
Article history:
Received 28 September 2009
Received in revised form
19 February 2011
Accepted 7 March 2011
Available online 30 March 2011
Keywords:
Flexible redundant parallel manipulator
Kineto-elastodynamic
Dynamic characteristic
Finite element method
Substructure synthesis technique
abstract
The modeling methodology and the dynamic characteristics of the 8-PSS flexible redundant parallel
manipulator are investigated based on some basic assumptions. Firstly, the system description and the
rigid dynamic model are presented. The actuating forces with minimum norm and least quadratic sum
among the possible actuating forces are achieved. Then, the kineto-elastodynamic model of the
manipulator is developed by virtue of the finite element method and the substructure synthesis
technique. Finally, the dynamic characteristics represented by the natural frequency, the sensitivity
analysis, the energy ratios and the displacement responses of the moving platform are investigated
through simulation. It is shown that the second order natural frequency is a little higher than the first
order natural frequency for the 8-
PSS flexible redundant parallel manipulator. The first order natural
frequency is much more sensitive to the radius of the lead-screws than to the radius of the struts. From
the computation of the energy ratio distribution, the mass of the moving platform should be reduced or
the stiffness of the strut should be increased in order to improve the dynamic characteristic of the
manipulator. For the investigated trajectory, the displacement response of the moving platform along
the x direction is slightly larger than these displacement responses along the y direction and along the
z direction. The angular displacement response of the moving platform rotating about the x axis is
slightly larger than those angular displacement responses rotating about the y axis and about the z axis.
& 2011 Elsevier Ltd. All rights reserved.
1. Introduction
Required to handle large and variable loads, seismic simulators
are usually developed with redundant parallel manipulators [1,2].
Redundancy can usually improve the ability and performance
of the parallel manipulator [3–12]. It is usually believed that
redundancy can bring some advantages for the parallel manip-
ulators such as avoiding kinematic singularities, increasing work-
space, improving dexterity and enlarging load capability. There
are mainly two different types of redundancy for the parallel
manipulators: (a) kinematic redundancy and (b) actuation redun-
dancy. A parallel manipulator is said to be kinematically redun-
dant when its mobility is greater than the required degrees of
freedom of the moving platform. On the other hand, a parallel
manipulator is redundantly actuated when the number of actua-
tors is greater than the mobility of the mechanism. Redundant
actuation in parallel manipulator can be implemented by the
following approaches. The first one is to actuate some of the
passive joints within the branches of the parallel manipulator.
The second one is to add some additional branches beyond the
minimum necessary to actuate the parallel manipulator. The last
one can be the hybrid of the above two approaches. The 8-
PSS
parallel manipulator under consideration in this paper is a
redundantly actuated manipulator implemented by adding two
additional branches to the 6-
PSS parallel manipulator.
The respective requirement such as heavy loads, high speed and
lightweight structures from industry makes it necessary to con-
sider the deformation, stiffness and other dynamic characteristics
for the parallel manipulator [13–36]. For the 8-
PSS redundant
parallel manipulator, which is usually developed for seismic
simulation with large and variable loads, the dynamic model
considering the structure flexibility is fundamental for perfor-
mance prediction, optimization design, control strategy develop-
ment, prototype building and seismic wave simulation. Compared
with the vast body of literature covering the kinematics and rigid
dynamics [37–39], there is little work on the flexible dynamics
of the parallel manipulator [37,40] due to: (i) computational cost;
(ii) geometrical complexity; and (iii) unidentified mechanics
property. There is no closed-form solution to the inverse kinematic
model for the flexible parallel manipulator. Setting up the math-
ematical model of a general flexible parallel manipulator is
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journal homepage: www.elsevier.com/locate/rcim
Robotics and Computer-Integrated Manufacturing
0736-5845/$ - see front matter & 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.rcim.2011.03.003
n
Corresponding author.
E-mail addresses: meyjzhao@yahoo.com.cn (Y. Zhao),
fengg@sjtu.edu.cn (F. Gao), donxij@sjtu.edu.cn (X. Dong),
xczhao@sjtu.edu.cn (X. Zhao).
Robotics and Computer-Integrated Manufacturing 27 (2011) 918–928