The performance evaluation is one of most important issues in the analysis and design of parallel manipulators. Characteristics such as manipulability and minimum singular value are used to determine the performance of the manipulators. The performance indices are used to eliminate the singularity and it’s near configurations. In this paper 6-UPS spatial parallel manipulator is considered and its performance indices such as condition number, manipulability and minimum singular value are determined for different structures.

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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 6, Issue 12, Dec 2015, pp. 01-08, Article ID: IJMET_06_12_001
Available online at
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=6&IType=12
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication
DEXTERITY INDICES OF 6-UPS PARALLEL
MANIPULATOR
Sri Rama Jayakrishna
Dept of Mechanical Engineering,
Holy Mary Institute of Technology and Science,
Kesar, R.R Dist, Telangana State, India
G. Satish Babu
Professor, Dept of Mechanical Engineering,
JNTUH College of Engineering Hyderabad, Telangana State, India
ABSTRACT
The performance evaluation is one of most important issues in the analysis
and design of parallel manipulators. Characteristics such as manipulability
and minimum singular value are used to determine the performance of the
manipulators. The performance indices are used to eliminate the singularity
and it’s near configurations. In this paper 6-UPS spatial parallel manipulator
is considered and its performance indices such as condition number,
manipulability and minimum singular value are determined for different
structures. Based on the performance indices, the optimum configuration of
the manipulator is determined. A MATLAB code is developed and used for the
analysis. The results are graphically presented.
Key words: Performance Index, Manipulability, Minimum Singular Value.
Cite this Article: Sri Rama Jayakrishna and G. Satish Babu. Dexterity Indices
of 6-UPS Parallel Manipulator, International Journal of Mechanical
Engineering and Technology, 6(12), 2015, pp. 01-08.
http://www.iaeme.com/currentissue.asp?JType=IJMET&VType=6&IType=12
INTRODUCTION
Paredis and Khosla (1) proposed a way to deal with illuminate the kinematic outline
of a non repetitive controller with joint confines that can achieve an arrangement of
determined focuses with required introductions. The issue was initially detailed by
them numerically by utilizing the idea of the kinematic hyper surface. They have
utilized a worldwide improvement system to minimize the punishment of a controller
outline which results in an ideal kinematic arrangement.
Ro and Lee (2) proposed a get together way calculation for male and female parts
utilizing just vertices of the male and female parts when their starting and objective
position are known. A calculation for the ideal position for two-arm fixtureless get
together in the workspace is proposed by them. Stance enhancement of two-arm

2. Sri Rama Jayakrishna And G. Satish Babu
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controller for fixtureless using so as to gather was concentrated on by them the
execution files, manipulability and calculability file.
Singh and Rastegar (3) presented the new idea, the worldwide speed ellipsoid,
which speaks to the worldwide movement manipulability or the speed transmission
qualities of a controller. The worldwide speed ellipsoid is acquired by considering a
weighted dispersion of the end-effector position over the workspace of the controller.
Parameters speaking to the worldwide isotropy and the worldwide size of the speed
transmission of controllers are utilized for breaking down and enhancing the
kinematic structure of controllers. The expansion of this idea to drive transmission
attributes and its usage for minimizing mistake engendering and improving precision,
assignment position and arranging are talked about by them.
Kircanski (4) amplified the system for typical SVD in view of Jacobian
deterioration is stretched out to straightforward excess controller. The Jacobian is
communicated in one of the moderate direction casings to get the least complex
typical expressions. General relations are built up by him between the SVD of
frameworks J and JJT that apply to any excess robot. He likewise examined the
utilization of the proposed strategy for taking care of the converse kinematic issue on
low-level position or constrain control calculations on undertaking directions.
Kircanski (5) decided all the isotropic designs of planar controllers with two, three
and four degrees of opportunity and 3 DOF spatial controller. The arrangements are
gotten as polynomials. The condition numbers are acquired as express investigative
elements of joint facilitates and connection length proportions.
Gosselin, Lemieux and Merlet (6) proposed and broke down a novel structural
planning of planar 3-DOF parallel controller. They have determined the situating and
speed mathematical statements. The component examined by them can be utilized as
a part of superior automated applications, for example, a planar situating and
introduction gadget or vehicle movement test systems.
Chablat and Wenger (7) characterized the movement of angle for parallel
controllers with different converse and direct kinematic arrangements. They have
discovered areas of the workspace and joint space without singularities. This strategy
can be utilized to study the moveability investigation in the workspace of the
controller and additionally way arranging and control.
Stucco, Salcudean and Sassani (8) exhibited another configuration grid
standardization strategy to handle the issue of non homogeneous physical units. The
undertaking space scale variables are utilized to set relative required quality or
velocity along any tomahawks of end-point movement while the joint space scale
elements are dealt with as free outline parameters to enhance isotropy through non
homogeneous activation.
Tanev and Stoyanov (9) connected the execution lists, the smoothness record,
manipulability, condition number and least solitary quality to a SCARA sort robot and
think about the lists. Xin-Jun Lin et al (10) proposed another spatial three-degrees-of-
opportunity parallel controller. The lists to assess the rotational capacity of the
moving stage of the controller are characterized and topology building design of the
controller is presented by them.
Xin-Jun Liu et al (11) utilized the assessment criteria, for example, the molding
record, the firmness to choose the connection lengths of 3-DOF circular parallel
controllers and broke down their operational execution. The chart books of the

3. Dexterity Indices of 6-UPS Parallel Manipulator
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worldwide molding file and the worldwide solidness record are acquired to improve
connection lengths of 3-DOF SPMS.
MEASURES OF KINEMATIC PERFORMANCE
Manipulability
The concept of manipulability of a manipulator was introduced by yoshikawa. The
manipulability is defined as the square root of the determinant of the product of the
manipulator jacobian by its transpose, i.e, det( )T
w JJ
The manipulability w is equal to the absolute value of the determinant of the
jacobian in case of a square jacobian. Using the singular value decomposition the
manipulability can be written as follows:
( )iw  
Where i are the singular values of the jacobian matrix J.
Minimum singular value
The minimum singular value changes more radically near singularities than the other
singular values. This suggests that the minimum singular value itself can be used as a
measure of dexterity. Thus the minimum singular value directly shows situations
where excessive joint velocities would be required, which is a characteristics of
nearness to singularities. The minimum singular value of the jacobian matrix of the
parallel manipulator is considered as a measure of performance.
6-UPS PARALLEL MANIPULATOR
Figure 1 Kinematic model of 6-UPS Parallel manipulator

4. Sri Rama Jayakrishna And G. Satish Babu
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The 6 UPS parallel manipulator shown in fig.1 consists of a fixed platform and
moving platform connected by six identical limbs. The reference frame attached to the
fixed platform is Os-xs,ys,zs.and the frame Op-xp,yp,zp is attached to the the moving
platform. The distances between the joints in moving and fixed platforms are:
Fixed Platform:
O1 O2=O3 O4=O5 O6= a1
O2 O3=O4 O5=O6 O1=a2
Moving Platform:
P1 P2=P3 P4=P5 P6= b1
P2 P3=P4 P5=P6 P1= b2
Optimal Design of 6-UPS Parallel Manipulator using Performance Indices
Jacobian Analysis
The instantaneous twist, $P , of the moving platform can be expressed as
for i= 1,2…………..6
where
^
1,
1,
1,
$
( )
i
i
i i i
s
b d s
 
     
^
2,
2,
2,
$
( )
i
i
i i i
s
b d s
 
     
^
3,
3,
0
$ i
is
 
  
 
^
4,
4,
4,
$
i
i
i i
s
b s
 
    
^
5,
5,
5,
$
i
i
i i
s
b s
 
    
^
6,
6,
6,
$
i
i
i i
s
b s
 
    
Where sj,i is a unit vector along the jth
joint axis of the ith
limb, iib PB and
3, 3,i i i ii
d AB d S 

5. Dexterity Indices of 6-UPS Parallel Manipulator
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The reciprocal screw, denoted as
^
,1,$r i is pointing in a direction perpendicular to
the joint axes of the universal joint.
^
,1,
0
$r i
in
 
  
 
^
,1,$ 0
T
r i 
$ 0C PJ 
Where
1 1 3
2 1 3
3 1 3
4 1 3
1 35
1 36
0
0
0
0
0
0
T
T
T
c T
T
T
n
n
n
J
n
n
n






 
 
 
 
 
 
 
 
 
 
Reciprocal to all passive joint screws of the ith limb can be identified as zero pitch
screw along the line passing through the two universal joints
Where
1 3,1 3,1
2 3,2 3,2
3 3,3 3,3
4 3,4 3,4
5 3,5 3,5
6 3,6 3,6
( )
( )
( )
( )
( )
( )
T T
T T
T T
x T T
T T
T T
b s s
b s s
b s s
J
b s s
b s s
b s s
 
 
 
 
 
  
 
 
 
  

6. Sri Rama Jayakrishna And G. Satish Babu
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Where
1 3,1 3,1
6 3,6 3,6
1 1 3
1 36
( )
( )
0
0
T T
T T
T
T
b s s
b s s
J
n
n


 
 
 
 
 
 
 
 
 
 
RESULTS
Using Matlab the following results have been obtained for 6 UPS spatial
manipulators. The results regarding optimum structures based on the performance
indices were identified have been presented in this section.
Figure 2 manipulability vs reach

7. Dexterity Indices of 6-UPS Parallel Manipulator
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Figure 3 minimum singular value Vs reach
CONCLUSION
The 6-UPS parallel manipulator has been analyzed for its performance indices. Based
on the performance indices, the optimum configurations are identified. All the
obtained results for the performance indices are graphically plotted.
REFERENCES
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Manipulators from Task Specifications,” The International Journal of Robotics
Research, Vol. 12, No. 3, pp 274-287, June 1993.
[2] Paul I. Ro and Byung R. Lee. “An Optimum Path and Posture Planning for
Fixtureless Assembly,” IEEE, Proc. Int. Conf. Adv. Robot., pp 808-813 (1993).
[3] J.R. Singh and J. Rastegar. “Optimal Synthesis of Robot Manipulators Based on
Global Kinematic Parameters,” Mechanism and Machine Theory, Vol. 30, No. 4,
pp 569-580 (1995).
[4] ManjaKircanski. “Symbolic Singular Value Decomposition for Simple
Redundant Manipulators and its Application to Robot Control,” The International
Journal of Robotics Research, Vol. 14, No. 4, pp 382-398, August 1995.
[5] ManjaKircanski. “Kinematic Isotropy and Optimal Kinematic Design of Planar
Manipulators and a 3-DOF Spatial Manipulator,” The International Journal of
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[6] Clement M. Gosselin et al. “ A new architecture of planar three-degree-of-
freedom parallel manipulator,” IEEE, proc. Int. Conf. Robotics and Automation,
pp 3738-3743, Minneapolis, Minnesota, April 1996.
[7] Damien Chablat and Philippe Wenger. “Working modes and aspects in fully
parallel manipulators,” IEEE Proc. Int. Conf. Adv. Robot., pp 1964-1969 (1998).
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[9] TanioTanev and BogdanStoyanov. “On the performance Indexes for Robot
Manipulators,” Journal of Bulgarian Academy of sciences, Problems of
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8. Sri Rama Jayakrishna And G. Satish Babu
http://www.iaeme.com/ijmet/index.asp 8 editor@iaeme.com
[10] Xin-Jun Liu et al. “On the Analysis of a New Spatial Three-Degrees-of-Freedom
Parallel Manipulator,” IEEE Trans. on Robotics and Automation, Vol. 17, No. 6,
pp 959-970, December 2001.
[11] A. Chandrashekhar and G. Satish Babu, Force Isotropy of Three-Limb Spatial
Parallel Manipulator. International Journal of Mechanical and Engineering
Technology 6(6), 2015, pp. 01-08.
[12] Xin-Jin Liu et al. “Optimum design of 3-dof spherical parallel manipulators with
respect to the conditioning and stiffness indices,” mechanism and machine theory
35, pp 1257-1267 (2000).