
Kinematic and Dynamic
Simulation of 6 DOF PUS Type Manipulators 

A
parallel manipulator typically
consists of a moving platform and a fixed base that are connected together by
several limbs. Because of the closedloop architecture, not all of the joints
can be independently actuated and usually the number of actuated joints is
selected to be equal to the number of degrees of freedom of the manipulator.
Parallel manipulators for which the number of chains is strictly equal to the
number of d.o.f. of the endeffector
are called fully parallel kinematic
manipulators (FPKMs). Architecturally,
there are many choices for type of legs, joints and numbers of attached legs
to the platform which can be significant factors for determining the
workspace and actuation requirements. Considerable efforts have focused on
enumerating and classifying various types of parallel architecture
manipulators. Further significant efforts have also been expended for
dimensional optimization to enhance kinematic, kinetostatic and dynamic
performance of such systems. It has been studied
earlier that it is advantageous to locate the actuations adjacent to the
fixed base (rather than attaching it midway in an articulated leg like the
traditional StewartGough platform). Such architectures proved to be
beneficial based on the following factors: (1) absorption of major portion of
reaction forces by the ground resulting in almost vibrationfree operation
with lightweight mobile components, (2) reduced effect of inertia due to the
elimination of actuator’s weight, (3) absence of interference of actuators
and routing cables due to base location of actuators. Further, by selecting
the base actuated joint to be prismatic, the proximal links are not subjected
to the bending moments and the corresponding stresses. The resulting class of
6DOF PUS (active prismatic– universal– spherical, shortly referred
to as 6PUS hereafter) FPKMs is generally composed of six sliding
actuators, six fixed length links and a mobile platform (as in Figure 1). The
sliders are active prismatics that move along linear motion guides and are
fixed on the ground. Hence, such systems are also referred to as “HexaSlides”
or “Hexaglides” in the past. The axes of the prismatic joints along which the
centers of the universal joints are being translated will be referred to as
the rail axes. The links are of constant length and are connected to the
sliders through universal joints (U). Finally, the links are connected to the
mobile platform through spherical joints (S). Nevertheless, there are many challenges to successful deployment of such a method. Two facets contribute to the increased computation cost and complexity engendered in workspace design and analysis. First, while the process is conceptually simple and that can be trivially implemented for planar manipulators, the complexity increases considerably when spatial manipulators are considered. Further, effective visualization is a key to workspacedesign and analysis and can be difficult for 6DOF workspaces. To overcome this issue, such workspaces are classified into various groups out of which two types are commonly considered important and studied: (i) a constant orientation workspace, taken to be the 3D space of points where the manipulator can reach while keeping its orientation fixed; (ii) a constant position workspace –set of orientations possible for the manipulator while keeping the position of the platform center fixed. The efficient geometricbased workspace calculation techniques were proposed for this purpose. The efficiency and performance of this improvised method was compared against the conventional (parametric sweeping) method. Finally, this scheme was extended to reap the benefits of automatic volume calculation and a subsequent kinematic design optimization using a commercial CAD package. While our focus is the 6PUS manipulator, the method is benchmarked against published results for the StewartGough platform as well.
A
Gaussian divergence theorem based framework was also implemented that could
be used to compute exact workspaces for parallel manipulators. Presently, we
have implemented it to compute the entire workspace of a 3PRR planar
manipulator using a 2D Gaussian divergence theorem. In the near future, we
also intend to extend this work to spatial class of parallel manipulators
especially to 6PUS to enable 3D volume computation. Despite advances in stateoftheart and
considerable efforts over past few decades, the unified method to develop
dynamic models of parallel architecture systems still remains a challenge.
The applicability of many standard approaches including Lagrangian modeling,
principle of virtual work etc has been restricted to standard manipulators
due to the complexities and nonlinearities— introduced mainly by the
multiplicity of chains of such systems under consideration. This is
particularly the case in spatial robots, whose nature as systems requires
integration of physical and information infrastructures and systembased
thinking. Our guiding vision however is to create an overall framework for
simulation of inverse dynamic analysis and implement simultaneous force and
trajectory control on this complicated manipulator. We also intend to explore
the advantage and effectiveness of a modelbased control performance using
symbolic computation available in commercial packages like Maple, MapleSim
etc. *This project
is funded by the National Science Foundation CAREER Award under Grant
IIS0347653 and CNS0751132. 



Students Involved: 

 Madusudanan Sathia Narayanan, PhD Candidate, University at Buffalo  Xiaobo Zhou, PhD Candidate, University at Buffalo  Luca Carbonari, Visiting Scholar
 LengFeng Lee, PhD Candidate,
University at Buffalo  Hrishi L Shah, M. S., University
at Buffalo [Graduated]  Srikanth Kannan, M. S., University at Buffalo [Graduated]  Yao Wang, M. S., University at Buffalo [Graduated] 


Related Publications  Conference Proceedings: 


[02] 
H., Shah, M.S., Narayanan, and V.N., Krovi, “CADEnhanced Workspace Optimization for Parallel Manipulators: A Case Study”, IEEE 2010 Conference on Automation Science and Engineering, Toronto, Ontario, Canada, August 2124, 2010. (Best Conference Poster Award) [IEEEXplore] 
[PDF] [PPS] 

[01] 
M.S. Narayanan, Sourish Chakravarty, Hrishi Shah, and V.N. Krovi, "Kinematic Static and Workspace Analysis of a 6 PUS Parallel Manipulator", Proceedings of ASME 2010 International Design Engineering Technical Conferences, Montreal, Quebec, Canada, August 1518, 2010. 
[PDF] [PPS] 





Related Publications  Theses: 

[04] 
Hrishi
L Shah,
"Role of
Automated Symbolic Generation of Plant Models in Robotics Education", M.S.
Thesis, Dept. of Mechanical & Aerospace Engineering, SUNY at Buffalo,
Sep. 2010. 
[PDF] 

[03] 
Madusudanan
Sathia Narayanan, "Analysis of Parallel Manipulator Architectures for Use
in Masticatory Studies", M.S. Thesis, Dept. of Mechanical &
Aerospace Engineering, SUNY at Buffalo, Sep. 2008. 
[PDF] 

[02] 
Srikanth
Kannan, "Quantitative Analysis Of Masticatory Performance in
Vertebrates", M.S. Thesis, Dept. of Mechanical & Aerospace
Engineering, SUNY at Buffalo, Sep. 2008. 
[PDF] 

[01] 
Yao
Wang, "Symbolic Kinematics and Dynamics Analysis and Control of a
General Stewart Parallel Manipulator", M.S. Thesis, Dept. of Mechanical
& Aerospace Engineering, SUNY at Buffalo, Sep. 2008. 
[PDF] 

by Automation,
Robotics & Mechatronics Laboratory, Mechanical and Aerospace Engineering, University at
Buffalo
Last
Updated: March 07, 2011