key issues in studying parallel manipulators 2011

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Proceedings of the 011International Conference onAdvanced Mechatronic Systems, Zhengzhou, China, August 11-13 011

Key issues in studying parallel manipulatorsJianzheng Zhang! Hongnian Yu2, Feng Gao*! and Xianchao Zhao!

IState Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai, China. 200240.

2 Computing, Engineering and Tec nology, Staffordshire University, Stafford, ST 18 OD , UK

*Co esponding author

Abst act: This paper reviews several key issues on the

trends and open research problems of parallel

manipulators. The research of a parallel manipulator

str cture is an essential question. t includes two research

issues: design of a novel parallel robot mechanism and

performance indexes. This paper reviews the methods on

the two aspects and presents the research directions. The

paper discusses the nctions and roles of the k nematicsand dynamics in parallel manipulators. Especially, the

methods of developing dynamics are categorized and

summarized. The paper also proposes a method to set up

the control system, including the hardware and so are,

and evaluates the importance of a sensor with

multi-information. The paper introduces t o main new

applications of parallel manipulators: as heavy-dut

equipment and a micro-operation device, and highlights

several questions to be solved.

Keywo s: parallel manipulators; perfo ance index;

kinematics; dynamics; control system; applications.

1. I t o ct o

As the science and tec nology of robotics originated

with the sp rit of developing mechanical systems which

would carr out tasks no ally ascribed to human beings,

open-loop serial chains is used as robot manipulators

quite naturally. Like the human a , such robot

manipulators have the advantage of large workspaces and

dexterous maneuverabilit [I-2]. However their loadcapacit is rather poor due to the cantilever structure.

Consequently, the li ks become bulky on the one hand,

while on the other hand they tend to bend under heavy

load and vibrate at high speed. Serial manipulators

have an alte ative to conventional serial manipulators.

Based on enlighte ments om biological world: (1) the

bodies of load-ca ing animals are more stably suppor ed

on multiple in-parallel legs compared to the biped human,

(2) human beings also use both the arms in cooperation to

handle heavy loads and (3) for precise work like writing,

t ree ngers actuated n parallel are used[3], closed-loop

parallel manipulators are invented and developed. Sinceits proposal by Gough and Whitehall [4] in 1962 and

popularization by Stewart [5] in 1965, a parallel

manipulator has been used in many applications such as

tyre test machines [4], early-stage aircra simulators[5],

large spherical radio telescopes[6] and, more recently, in

micro manipulators[7]. However, with the constant

growth n development and application of parallel

manipulators, several new issues have emerged in

different research elds.

n this paper we review several key issues on the trends

and open research problems of parallel manipulators. n

Section 2, several issues of a parallel manipulator

structure are discussed om the two aspects, design of a

novel parallel robot mechanism and perfo ance indexes.

n section 3, the roles of k nematics and dynamics for

parallel manipulators are presented and the methods of

build ng dynamics are classi ed. Section 4 addresses the

control aspect of a parallel manipulator, includ ng the

control system, and sensors with multi-info ation.Several new applications of parallel manipulators are

discusses in section 5. Finally, the conclusions are given

in section 6.

. Des g o pa a eJ obots

possess a large workspace, their precision positioning n the design of parallel robots, i novation of the new

capabilit poor under heavy-load and high speed types of robotic mechanisms om applications is one of

enviro ments. the most important activities, because the mechanisms

Therefore, for applications where high load ca g dete ine the performance characteristics of the robots.

capacit , good dynamic perfo ance and prec se Here there are the two issues: design of the novel parallel

positioning are of paramount importance, it is desirable to robot mechanisms and perfo ance indexes, which can

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in uence the characteristics of a parallel manipulator.2.1 Design of the novel parallel robot mechanisms

Although many researchers[8-16] have paid attention to the design of the parallel robot mechanisms, and proposed several t pes of parallel mechanisms, forinstance, 2- and 3-DOF planar parallel

mechanisms[1 -13], Delta robots with 3 translationaldegrees of eedom[16], 3-DOF spherical robots[14-15]

and 6-0 F parallel mechanisms[8, 1 ], the several typesof parallel mechanisms are missing, such as 2-, 3-, 4- and5-DOF parallel robot mechanisms with desired

end-effector motions. The reason for this is that anef cient and general theor is not available for t pesynthesis of parallel mechanisms being given the number

and t pes of degrees of eedom.n the past several years, Feng Gao and his team have

done ndamental researches on the theor for i ovationand invention of new t pes of 2-, 3-, 4- and 5-DOF

parallel mechanisms[17-19]. Based on several t pes ofcomposite jo nts and kinds of sub-chains (limbs) with

speci c degrees of eedom as shown in gure I a new

principle for design of structures of parallel robotic mechanisms is presented for design of parallel robotic mechanisms with speci c kinematic characteristics. The

pr nciple can be represented as following. n a parallel mechanism, if the parallel mechanism has speci cdegrees of eedom ($), limbs I 2, ... , n by which the upper platform (moving end-effector) is co nected with

the lower platform ( xed me) have to satis thefollowing condition:$ = $1n $2 ... n $n (1)

where $ J denotes the degree of eedom of limb . IS

the special Pl cke coordinates and can be written

(2)

where v / vx J v Yv Z ) expresses the tra slation of the

ou ut li k of limb j, and O/O OP O denotes

the rotation of the output li k of limb with respect to t ree Euler's angles a, and . The special Pl cke

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taken as 1 or O For , it means that limb has that degree

of eedom; for , it means that limb has no that degreeof eedom. From Eq. (2), we obtain 2-, 3-, 4-, 5- a d6-DOF limbs with speci c kinematic characteristics andseveral new types of 2-, 3-,4- and 5-DOF parallel robotic

mechanisms can be developed accord ng to Eq. I

Figure I The limbs with composite s uctureThis principle is ef cient and general for synthesis of

parallel mechanisms being given the number and types ofdegrees of eedom. Several novel parallel robotic

mechanisms can be developed accord ng to this principle.2.2 Performance inde

Performance index is one of the key issues in designing

a new parallel robotic mechanism. Many researches have been done and some meaning l results are obta ned in the resent twenty years. n designing, it is unavoidable to take the relevant performance indexes nto account,

including str cture symmetr and isotropy[2 -22], bearing capacit [23-24], stif ess[25-28], precision[29-3 ], singularit [31], redundancy[32-34] and workspace[35-36], etc. These studies indicate most of performance indexes of a parallel manipulator involve its

Jacobian matrix.Because the performance of the robot is gradual and

continual n its solution space, the robot will have a better performance in its global workspace if it is decoupling orisotropous under a cer ain position and orientation.

Therefore, decoupling and isotropous are two importa t performance indexes.

To a parallel manipulator, there is always the mapping between the inputs and the outputs as followingy = Ax (3)



(5)

(6)

where A denotes the m Xn Jacobian matrix, Y denotes

m-dimension input vector and x denotes n-dimension

input vector. Eqs. (3)-(6) can be rewritten as

YFIY =lYJ )

{YF = A F x where YT= A Tx

(7)

(8)

9

(10)

The decoupling theorems can be obtained as

following:

Theorem I if A FAI =B is a diagonal matrix which

satis es Eq. (11), YF is decoupled

Theorem 2: if A TAJ =B Tis a diagonal matrix which

satis es Eq. (12), Y is decoupled

Theorem 3: if AA T= B is a diagonal matrix whichsatis es Eq. IS , i.e. Eqs. II , (12),(13) and (14) as well, Y is decoupled, meanwhile YFand Yrare orthogonal

to each other.

(13)

(14)

AA =B= diag(b F 11 b l 22 ... b )

IS

The isotropous theorems can be obtained as following:

Theorem 4: if A FAI is a diagonal matrix (Eq. (16))

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where the diagonal elements are equal, YF is isotropous

Theorem 5: if Ar is a diagonal matrix (Eq. (17))

where the diagonal elements are equal, YTis isotropous

Theorem 6: if AA l = B is a diagonal matrix (Eq. (20)) where the diagonal elements are equal, that also satis es

Eqs. (13), (14), (16) and (17),y is isotropous.

(18)

Generall speaking, a decoupled parallel robot not onl

simpli es the control s stem and e hances pa load, but

also possesses excellent kinematic perfo ance, which

will strengthen its operabilit . The decoupled and

isotropous parallel robotic mechanisms are appropriate

for the manipulator whose workspace is small, such as

micro-operation manipulator and multi-dimension force

sensors.

Others performance indexes are also mportant to

different parallel manipulators in different applications.

And, with some novel complex mechanisms being

invented, several new problems emerge n the research

area of performance indexes, which is an nteresting and

open research area. 3. kinematics and dynamics 3.1 Kinematics

Kinematics of parallel manipulators involves two

aspects, the inverse kinematics ( K), the forward

kinematics (FK).Inverse kinematics ( K) is one of the basic elements of

an robot controller. It is known that inverse kinematics is

usuall straightforward for an parallel robot. There is a

unique solution to the IK ( n some cases provided that

ph sical constraints are taken into account like for the

Delta robot[16]), which means each joint variable ma be

computed independentl being given the desired pose of

the robot.

The forward kinematics (FK) is to nd the possible

pose of the platform for the given joint coordinates. It



always is thought that FK is an academic question that

may be use l only off-line for simulation p poses as a

parallel robot will be position controlled using IK only.

But in the paper[37], it is considered to use in velocit

con l. The FK is a more complex problem than the IK

co terpart for a serial robot. Although this eld has been

recently investigated [38-41], many problems are still

unsolved. 3.2 Dynamics

Dynamics of a parallel manipulator also has two topics

like kinematics, inverse dynamics and for ard dynamics

(direct dynamic). The inverse dynamic model is

important for high-performance control algorit ms of

parallel robots, and the direct dynamic model is required

for their simulation. n our view, studying of parallel manipulator dynamics should be divided nto two elds,

building a dynamic model for a parallel manipulator and

applying dynamics in analysis and control design.

The dynamic modeling of parallel robots presents an

i herent complexit , due to their closed-loop s ucture

and k nematic constraints. Generally spea ing There are

four broadly adopted approaches for building dynamic

model of parallel manipulators: Newton Euler laws, the

pr nciple of virtual work , the Lagrangian formulation and

the Kane's mothed. The advantages and disadvantages of

the use of these four methods for the dynamic analysis of

parallel manipulators will be presented below.

The principle of virtual work ncluding the

D' Alember pr nciple of virtual work [ 42] and the

Jourdain's principle of virt al power[43], is an ef cient

approach to derive dynamic equations for the inverse

dynamics of the parallel manipulators[44-45]. This

pr nciple produces dynamic equations by relating the

virtual displacement of actuated jo nts to the vir ualdisplacement of a generalised end-effector. As the view

expressed in [46-47], the principle of virt al work

e hibits the following two advantages: F rstly, the derived

equations are computationally ef cient. Secondly, n the

case of closed-chain, the method leads to the least number

of equations which are just enough for the solutions of

actuator forces and torques. However, for the forward

dynamics, the method of v rtual work IS not

straightfor ard because of the complicated velocity

transform between the jo nt-space and task-space[48].

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The Kane's method implements the concept of

generalized speeds (quasi-velocit coordinates) as a way

to represent motion and allows one to focus on the motion

aspects of dynamic systems rather than only on the

con guration[ 49-50]. Therefore, it provides a suitable

amework for treating no holonomic constraints which

were a hurdle in the process of obtain ng equations of

motion for dynamic systems in the past. Several

researchers [51-54] present the dynamic Equations of

robotic based on this method. Liu[55] applies the method

for the dynamic analysis of parallel manipulators.

However, the choice of the generalized speeds is crucial

because they signi cantly affect the simplicit of the

resulting equations of motion[56]. The Kane's method

needs special experiences and skills.The Lagrangian formalism is a ver attractive method

for the derivation of manipulator's nverse dynamics,

because it allows the elimination of all reaction forces and

moments at the begi ning a d provides a well analytical

and orderly str cture which is ver use l for control

pu oses. Nevertheless due to the numerous constraints

imposed by the closed loops of a parallel manipulator it is

a dif cult task to derive the equations of motion in terms

of a set of ndependent generalized coordinates[ 1]. To

simpli the problem additional coordinates (for example

jo nt-space) with a set of Lagrangian multipliers must be

introduced. The application of this principle for general

robots was considered by different researchers [57-60].

The computations of Lagrange multipliers in the nverse

dynamics can be avoided by the method of Nakamura and

Ghodoussi [61], but it involves the so-called virt al

actuations (in lieu of Lagrange multipliers) which have to

be eliminated for developing the closed-form dynamic

equations. So the redundant generalized coordinatescomplex the problem and increase the computational

burden by using Lagrangian formulation. n practice it is

desirable to de ne the motion with regard to the

coordinates of the end-effector, namely task-space.

However, Newton Euler approach allows to obtain the

straightforward dynamic equations in task-space easily, so

it is extremely suitable for parallel and closed-loop

manipulators. Additionally, th ks to developing

equilibration equations of individual bodies, it is

convenient to consider how the actuation forces and



torques con ibute to the end-effector motion.

F thermore, the more evident bene ts of this approach

are because the forces of the actuators and the reactions in

the joints are dete ined om the relatively simple

equilibrium equations of the leg and the platform. In view

of these, Dasgupta and Chou ur address the question

of dynamic formulation of the parallel manipulator [62]

and present a general strategy based on the Newton Euler

approach. Another signi cative contribution is that

Dasgupta and Mruthyunjaya[63-64] solve the dynamic

equations in closed form, and they show the advantage of

its application n the case of parallel robots. The

Newton-Euler method has been recently applied to a few

speci c parallel manipulators[65-66] with signi cant

advantage. So far as the Newton-Euler method'sdrawback is conce ed, the only major dif culty in the

derivation of closed-form dynamic equations is in the

elimination of the joint reactions, as mentioned by Kane

and Levinson[51].

In a word, ever method has its advantages and

disadvantages. One ca select a suitable method to build

the dynamic model according to his research p pose and

aim. It should be noted that proposing some new and

effective ways to build the dynamic model for parallel

manipulator is a challenging research area.

One of p poses of building dynamic model for

parallel manipulator is applying it for control. But control

of such robots is a di cult task[37]. The reason is that it

takes a long time to solve the inverse dynamics because

of the complexit of the dynamic model, which means it

ca not meet the real-time requirement of the control

system. To apply the dynamic model to the con l system

of parallel manipulators, some approaches to improve the

computational ef ciency of inverse dynamics have been presented. These approaches can be approximately

divided into four t pes by the paper[66]: amending the

modeling method mentioned above, neglecting the

secondar factor of the dynamic model[67-68], parallel

algorit m[69-70] and linearization of the dynamic

model[71-72]. It should be ndicated that more effective

methods of simpli ing parallel manipulator dynamics are

expected.4. Control

Apart om the effective kinematics and dynamics,

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effectiveness of con lling a parallel manipulator is also

re ected in other two aspects, the control system,

includ ng its hardware and so ware, and the sensors.4.1 System

With the constant growth in development and

application of parallel robots, the demand for a parallel

robot system with position acc acy, stabilit , quick

responses and so on is growing. Furthermore, because of

the strong nonlinearit and coupling in the parallel

structure, compatibilit and real-time among axes is ver

important when the parallel robot is operating. Though

some researchers make progress in practicabilit [73-76],

they o en focus on one performance index only and are

not conce ed with the whole con guration of the control

system and the combination properties of the digitalcon ol system itself. So the method of establishing an

advanced digital control system for a multi-DOF parallel

robot is one of the most challenging issues in the parallel

robot research eld. Here, we propose a method to build a

digital control system for a multi-DOF parallel

manipulator.

As to the hardware mework of the control system,

the mode of IPC (industr PC) and multi- axis control

board is applied. In view of the system characteristics,

such as large data ansfer between the components,

precise sync ronization control and so on, we chose the

development platfo based on the PX bus. The PX bus

speci cation de nes a compact modular PC platform for

industrial instr mentation. This development platform has

not only the maximum bandwidth of on-board data buses

but also the lowest transmission delay n the indus . For

a six-axis parallel manipulator, its control system can be

built as shown in g e 2. The build of the hardware

system can ens e that the parallel robot achievesaccuracy control, real-time control and multi-axis

control[77].

So ware of control system of a parallel manipulator

should embody both its user- iendl ness a d its

practicability. According to the characteristics of the

hardware components mentioned above and system

nction of a parallel manipulator, we suggest to divide

the n erical control so are into t ee levels, namely

the application so ware level, the core so ware level and

the drive so are level. There are also many nctional



modules on each level according to the requirements of

the system. Fig e 3 shows the relation of the levels and

modules.

Figure 2. The structure of the ha dware system and the

relation of the components

Figure 3. The relationship between the levels and

modules of the so ware4.2 Sensor

n order to e hancing the sensor abilit of a parallel

robot, the novel sensors with multi-dimension

information, like 6-dimention force/torque sensor and6-dimention acceleration sensor, are supposed to be

created and applied in parallel manipulator.

Force/torque (F/T) sensors have widely been used In

measuring inertia force [78], monitoring forces of

variable directions and intensit [79] and as a component

of force feedback controller [80]. Feng Gao and his team

present a novel six-component force/torque sensor with

parallel structure[81-82] shown in Figure 4 and give the

method of designing it. nd based on the six-component

force/torque sensor, a novel 6-dimensional mouse shown

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I Figure 5 is investigated and applied in virt al

enviro ment to accomplish corresponding motions.

Figure 4 Small size F/T sensor

Figure 5 6-D mouse

Considering the requirement of measuring

6-dimensional acceleration during simulating earthquakes

using earthquake simulator with 6-DOF, a novel

integrative acceleration sensor is being studied at

Shanghai Jiao Tong Universit .

t should be ndicated that the research and application

of 6-dimensional F /T and acceleration sensors is

signi cative to accelerate the research process of parallel

manipulators.. Applications

Apart om using as machine tools and traditional

motion simulators, the application area of a parallel manipulator is extended widely and widely. The two most

outstanding elds are the heavy-duty equipment and the

micro-operation device..1 Heavy-duty equipment

Recent st dies [83-86] indicate that a parallel

manipulator with high stif ess and large payload will be

bene cial for industrial applications in heavy-dut

enviro ments. Many different approaches [87-94] have

been proposed in the past several years to achieve high

stif ess and large payload capabilities. Most of these



approaches are based on two tec niques, namely

hydraulic ive with large-scale energy storage [91-92, 95]

and redundant actuation with multi-motors [87, 90, 93-94]

tec niques. The huge servo hy aulic cylinder with a

large-scale energy storage has many disadvantages, such

as bulky installation, high manufacturing and

maintenance costs, poor energy e ciency, env ro mental

pollution and so on. Though a mechatronic system driven

by servo motors does not have the disadvantages

mentioned above, there is not a servo motor c rently

available that can meet the power demand, l ke simulating

earthquakes. The high research and development (R&D)

costs and tec ological ba riers are also a hindrance to

the development of high power servo motors. Therefore,

redundant actuation with multi-motors [93, 96] is becoming an emerging research area.

Generally speaking, redundant actuation m parallel

manipulators can be divided into t ree categories[89]: 1)

a parallel manipulator with redundant driving passive

joints; 2) additional (redundant) branches to actuate the

device, which is widely used in large-scale industrial

devices, for example, the earthquake simulator developed

by the NIED[95]; 3) a hybrid of the preceding two

categories. For categor 1), the redunda t driving jo nts

make the k nematics and dynamics of the parallel

manipulator complicated. For categor 2), the inte al

force and the over-constrained are avoidable because of

the out-sync among red dant branches caused by e ors.

Especially, when there is a halt or backward motion in

one of red dant branches because of faults or

misoperations, the inte al force among redundant

bra ches ncreases sharply, which may cause the

equipment damaged. Thus, the research on the redunda t

actuation with no-over-constraint capabilit IS

signi cance to the application of parallel manipulators in

the heavy dut enviro ment.

Sha ghai Jiao Tong Universit have been done many

substantive work [86, 93-94] about a heavy-dut forging

manipulator and a heavy-dut press machine, and

papers[96-97] present a earthquake simulator with

redundant and fault-tolerant act ator unit shown in

Figures 6.

5 2 Micro-operation manipulator

Using as micromanipulator is the other one of the

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important aspects of the manipulator with parallel

mechanism. Flexure hinges and monolithic str ctures of

micromanipulators achieves the fact that there is no error

acc ulation, no backlash, no iction, and no need for

lubrication, which makes micromanipulators have high

resolution and precision. Several different

micromanipulators[98-99] have been presented by

different institutions with different applications. Yue[ OO]

proposes a 6- F micromanipulator shown in Figure 7,

which will be used as a device to cut a c romosome.

Some others applications of micromanipulators, like

micro positioning and nano-imprint, are also the focuses

of research.

Figure 6 a earthquake simulator with redundant actuator

unit

Figure 8 6-D F parallel micromanipulator[ OO]6. Conclusions

This paper has reviewed and discussed several key

issues on the trends and open research problems of

parallel manipulators. Two essential questions of a

parallel manipulator str cture, design of the novel parallel

robot mechanisms and performance indexes have been

discussed. A novel theor of designing several new

mechanisms is given and two performance indexes,

decoupled and isotropous, have been presented. The roles

and nctions of the kinematics and dynamics of parallel



manipulators have been discussed. Especially, the

methods of building dynamics have been categorized, and

the advantages and the disadvantages of ever method

have been s u arized. The paper has proposed a method

to set up the control system for a parallel manipulator,

including the hardware and so ware. The importance of a

sensor with multi-information has been pointed out. Two

main new applications, as a heavy-dut equipment and a

micro-operation device, have been ntroduced, and some

unsolved questions in the t o application areas have been

indicated.

A knowledgment

This research is jointly sponsored by the Key Project of

Chinese National Programs for Fundamental Research

and Development (973 program) (Grant No:2006CB705402); Important National Science &

Tec nology Speci c Projects (Grant No:

2009ZX04002-061 and BQ020034); the National High

Tec nology Research and Development Program of

China (863 Program) ( Grant No: 2008A04XK1478950

and B3306B); National Natural Science Foundation of

China (Grant No: B 728B, B1405B, B 354B and

50821003). and the E-li k project.

Referen es

1. Tsai, L., Robot analysis: the mechanics of serial and

parallel manipulators 1999: Wi ey-Interscience.

2. Merlet, 1 Parallel robots 2006: Springer-Verlag New York

Inc.

. Dasgupta, B. and T. Mruthyunjaya, The Stewart pla orm

manipulator: a review. Mechanism and Machine Theory,

2000.35(1): p. 1 -40.

4. Gough, V and S. Whitehall, Universal re test machine.

Proceedings of the Institution of Mechanical Engineers, 1962.

. Stewart, D., A pla orm with s degrees of freedom. Proc.

nst. Mech. Eng, 196 . 8 (1): p. 1- 6.

6. Tang, X et a ., On the analysis of active re ector

supporting manipulator for the large spherical radio

telescope. Mechatronics, 2004. (9): p. 10 -10 .

. Yue, Y, et a ., Relationship among input-force, payloa

st ness and displacement of a 3-DOF perpendicular

parallel micro-manipulato Mechanism and Machine

Theory, 2010.

978-0-9555293-7-5/11/$25.00 241

. Hunt, K., Kinematic geometry of mechanisms 1990: Oxford

University Press Oxford.

9. Earl, C. and J. Rooney, Some kinematic structures for robot

manipulator designs. Journal of Mechanisms, Transmissions

andAutomation in Design, 19 . 5(1): p. C22.

10. Hunt, K. Structural kinematics of in-parallel-actuated

robot-arms 19 2.

II Gao, F XLiu, and W. Gruver, Performance evaluation of

wo-degree-o freedom planar parallel robots. Mechanism

and Machine Theory, 199 .33(6): p. 661-66 .

12. Gosselin, C. and E. Lavoie, On the kinematic design of

spherical three-degree-o freedom parallel manipulators.

The International Journal of Robotics Research, 199 . (4):

p. 94.

1 . Gosselin, C. and 1 Angeles, The optimum kinematic design

of a planar three-degree-o freedom parallel manipulato 1

Mech. Transm. Autom. Des., 19 . O( 1): p. -41.

14. Gosselin, C. and 1 Hamel. The agile eye: a

high-performance 3-DOF camera-orienting device 1994.

1 . Gosselin, C. and 1 Angeles, The optimum kinematic design

of a spherical three-degree-o freedom parallel manipulato

Journal of mechanisms, transmissions, and automation in

design, 19 9. (2): p. 202-20 .

16. Clavel, R. DELTA, a fast robot with parallel geomet

19 .

1 . Gao, F et a ., New kinematic structures for 2 3-, 4- and

5-DOF parallel manipulator designs. Mechanism and

Machine Theory, 2002.37( 11): p. 1 9 -1411.

1 . Gao, F YZhang, and W Li, Type synthesis of 3-DOF

reducible translational mechanisms. Robotica, 200 . 3(02):

p. 2 9-24 .

19. Gao, F et a ., Design of a novel 5-DOF parallel kinematic

machine tool based on workspace. Robotica, 200 . 3(01):

p. -4 . 20. Gosselin, c The optimum design of robotic manipulators

using dexteri indices. Robotics and Autonomous Systems,

1992. (4): p. 21 -226.

21. Gao, F XLiu, and W. Gruver, The global condition index

in the solution space of wo-DOF planar parallel wrists.

IEEE SMC'9 , 199 : p. 40 -40 .

22. Kircanski, M. Robotic isotropy and optimal robot design of

planar manipulators 2002: IEEE.

2 . Staicu, S., Power requirement comparison in the 3-R R

planar parallel robot dynamics. Mechanism and Machine



Theory, 2009. 44( ): p. 10 -10 7.

2 . Thomas, M., H. Yuan-Chou, and D. Tesar, Optimal actuator

sizing for robotic manipulators based on local dynamic

criteria. Transactions of the ASME Jou al of Mechanisms,

Transmissions, and Automation in Design, 198 . (2): p.

16 -169.

2 . Liu. X . Z. Jin, and F Gao, Optimum design of 3-DOF

spherical parallel manipulators with respect to the

conditioning and st ness indices. Mechanism and Machine

Theory, 2000. 35(9): p. 12 7-1267.

26. Simaan, N. and M. Shoham, St ness synthesis of a variable

geometry six-degrees-o freedom double planar parallel

robot. The Inte ational Journal of Robotics Research, 200 .

(9): p. 7 7.

27. Tahmasebi, F and L. Tsai, On the st nes of a novel six-degree-freedom parallel minimanipulato Journal of

Robotic Systems, 199 . (12): p. 8 -8 6.

28. Gosselin, c St ness mapping for parallel manipulators.

Robotics and Automation, IEEE Transactions on, 2002. ( ):

p. 77- 82.

29. Koseki, Y et al. Design and accuracy evaluation of

high-speed and high precision parallel mechanism 1998:

Citeseer.

0. Hesselbach, , et a ., Aspects on design of high precision

parallel robots. Assembly Automation, 200 . 4(1): p.

9- 7.

1. Tahmasebi, F and L. Tsai, Workspace and singulari

analysis of a novel six-DOF parallel minimanipulato 199

2. Dasgupta, B. and T. Mruthyunjaya, Force redundancy in

parallel manipulators: theoretical and practical issues.

Mechanism and Machine Theory, 1998. 33(6): p. 727-7 2.

. Kock, S. and W. Schumacher. A parallel xy manipulator

with actuation redundancy for high-speed and

active-st ness applications 2002: IEEE. . Cheng, H., Y Yiu, and Z. Li, Dynamics and control of

redundantly actuated parallel manipulators. IEEE ASME

T ANSACTIONS ON MECHATRONICS, 200 . ( ): p.

8 - 91.

. Gosselin, c Determination of the wor pace of 6-dof

parallel manipulators. Journal of Mechanical Design, 1990.

: p. 1.

6. Agrawal, S. Wor pace boundaries of in-parallel

manipulator systems 2002: IEEE.

7. Merlet, Still a long way to go on the road for parallel

978-0-9555293-7-5/11/$25.00 242

mechanisms 2002.

8. Merlet, J. Closed-form resolution of the direct kinematics of

parallel manipulators using extra sensors data 2002: IEEE.

9. Baron, L. and J. Angles, The kinematic decoupling of

parallel manipulators using joint-sensor data. Robotics and

Automation, IEEE Transactions on, 2002. (6): p. 6 -6 1.

0. Bonev, 1. and J. Ryu, A new method for solving the direct

kinematics of general 6-6 Stewart pla orms using three

linear extra sensors. Mechanism and Machine Theory, 2000.

35( ): p. 2 - 6.

1. Parenti-Castelli, V and R. Di Gregorio, A new algorithm

based on two extra-sensors for real-time computation of the

actual co guration of the generalized Stewart-Gough

manipulato Journal of Mechanical Design, 2000. : p.

29 . 2. Tsai, L., Solving the inverse dynamics of a Stewart-Gough

manipulator by the principle of virtual wor Journal of

Mechanical Design, 2000. : p. .

. Abdellatif, H., M. Grotjahn, and B. Heimann. H gh e cient

dynamics calculation approach for computed orce control

of robots with parallel structures 2006: IEEE.

. Chang-De Zhang, S., An e cient method for inverse

dynamics of manipulators based on the virtual work

principle. Journal of Robotic Systems, 199 . ( ): p.

60 -627.

. Wang, and C. Gosselin, A new approach for the dynamic

analysis of parallel manipulators. Multibody System

Dynamics, 1998. ( ): p. 17- .

6. Song, S. and Y Kin. An alternative method for manipulator

kinetic analysis-the D lembert method 2002: IEEE.

7. Sokolov, A. and P Xirouchakis, Dynamics analysis of a

3-DOF parallel manipulator with RS joint structure.

Mechanism and Machine Theory, 2007. 4 ( ): p. 1- 7.

8. Liu, M., C. Li, and C. Li, Dynamics analysis of theGough' Stewart pla orm manipulato IEEE Transactions

on Robotics and Automation, 2000. (1): p. 9 .

9. Kane, T. and C. Wang, On the derivation of equations of

motion. Journal of the Society for Industrial and Applied

Mathematics, 196 . 3(2): p. 87- 92.

0. Kane, T. and D. Levinson, Dynamics, theory and

applications 198 : McGraw Hill.

1. Kane, T. and D. Levinson, The use of Kane s dynamical

equations in robotics. The International Journal of Robotics

Research, 198 . ( ): p. .



52. Kane, T. and D. Levinson, Multibody dynamics. ASME

Transactions Series E Journal of Applied Mechanics, 983.

: p. 0 - 0 8.

53. ROSENTHAL, D., An order n formulation for robotic

systems. Journal of the Astronautical Sciences, 990. : p.

5 -529.

54. Lesser. M . Analysis of Complex Nonlinear Mechanical

Systems: A Computer Algebra Assisted Approach 995:

World Scienti c Pub Co Inc.

55. Liu, M., Y Tian, and C. Li, Dynamics of Parallel

Manipulator Using Sub-Structure Kane Metho

JOURNAL-SHANGHAI JIAOTONG

UNIVERSITY-CHINESE ED T ON-, 200 . ( ): p.

032- 035.

56. Mitiguy, P and T. Kane, Motion variables leading to

e cient equations of motion. The International Journal of

Robotics Research, 996. 1 (5): p. 522.

5 . Bhattacharya, S., D. Nenchev, and M. Uchiyama, A

recursive formula for the inverse of the inertia matrix of a

parallel manipulato Mechanism and Machine Theory,

998. ( ): p. 95 -964.

58. Geng, Z., et a ., On the dynamic model and k inematic

analysis of a class of Stewart pla orms. Robotics and

Autonomous Systems, 992. (4): p. 23 -254.

59. Liu, K., et a ., The singularities and dynamics of a Stewart

pla orm manipulato Journal of Intelligent and Robotic

Systems, 993. (3): p. 28 -308.

60. Leroy, N., A. Kokosy, and W Perruquetti. Dynamic

modeling of a parallel robot. Application to a surgical

simulator 2003: IEEE.

6 . Nakamura, Y and M. Ghodoussi, Dynamics computation of

closed-lin k robot mechanisms with nonredundant and

redundant actuators. Robotics and Automation, IEEE

Transactions on, 2002. (3): p. 294-302. 62. Dasgupta, B. and P Choudhury, A general strate based on

the Newton-Euler approach for the dynamic formulation of

parallel manipulators. Mechanism and Machine Theory,

999. (6): p. 80 -824.

63. Dasgupta, B. and T. Mruthyunjaya, A Newton-Euler

formulation for the inverse dynamics of the Stewart pla orm

manipulato Mechanism and Machine Theory, 998. (8):

p. 35- 52.

64. Dasgupta, B. and T. Mruthyunjaya, Closed-form dynamic

equations of the general Stewart pla orm through the

978-0-9555293-7-5/11/$25.00 243

Newton-Euler approach. Mechanism and Machine Theory,

998. ( ): p. 993- 0 2.

65. Mukhe�ee, P B. Dasgupta, and A. Mallik, Dynamic

stabili index and vibration analysis of a exible Stewart

pla orm. Journal of sound and vibration, 200 . 7(3-5): p.

495-5 2.

66. Wang, J., et a ., Simpl ed strate of the dynamic model of

a 6-UPS parallel k inematic machine for real-time control.

Mechanism and Machine Theory, 200 . (9): p.

9- 40.

6 . Kim, N., C. Lee, and P Chang, Sliding mode control with

perturbation estimation: application to motion control of

parallel manipulato Control Engineering Practice, 998.

( ): p. 32 - 330.

68. Sirouspour, M. and S. Salcudean, Nonlinear control of

hydraulic robots. Robotics and Automation, IEEE

Transactions on, 2002.17(2): p. 3- 82.

69. Yi, L., H. Baosheng, and F. Zuren. Application of parallel

algorithms to control 2002: IEEE.

0. Yamane, K., et a ., Parallel dynamics computation and H

acceleration control of parallel manipulators for

acceleration displa Journal of Dynamic Systems,

Measurement, and Control, 2005. 1 7 : p. 85.

. Chen, Y and McInroy. Ident cation and decoupling

control of exure jointed hexapods 2000: Citeseer.

2. Lee, S., et al. Controller design for a Stewart pla orm using

small wor pace characteristics 2002: IEEE.

3. Renton, D. and M. Elbestawi, H gh speed servo control of

multi- is machine tools. International Journal of Machine

Tools and Manufacture, 2000. (4): p. 539-559.

4. Su, Y et a ., Integration of saturated PI synchronous

control and PD feedbac k for control of parallel

manipulators. Robotics, IEEE Transactions on, 2006. ( ):

p. 202-20 . 5. Sun, D., Position synchronization of multiple motion es

with adaptive coupling control* I Automatica, 2003. (6):

p. 99 - 005.

6. Yeh, S. and P Hsu, Analysis and design of integrated

control for multi-axis motion systems. Control Systems

Technology, IEEE Transactions on, 2003.11(3): p. 3 5-382.

. Zhang, , et a ., Design and development of a control

system for a novel6-DOF parallel robot and its experiment.

8. Diddens, D., D. Reynaerts, and H. Van Brussel, Design of a

ring-shaped three-axis micro force/torque senso Sensors &



Actuators: A. Physical, 1995.46(1-3): p. 225-232.

79. Doebelin, E., Measurement systems application and design.

New York, London, 1990.

80. Girone, M., et a!., A Stewart pla orm-based system for

ankle telerehabilitation. Autonomous Robots, 2001. (2): p.

203-212.

8 . Zhenlin, J., G Feng, and Z. Xiaohui, Design and analysis of

a novel isotropic six-component force torque senso Sensors

and Actuators A: Physical, 2003. (1-2): p. 17-20.

82. Gao, F., et a!. The design and applications of FIT sensor

based on Stewart pla orm 2007.

83. Merlet, Parallel manipulators: state of the art and

perspectives. Advanced Robotics, 1993. ( ): p. 589-59 .

8 . Singh, N., et a!., Coordinated-motion control of heavy-du

industrial machines with redundanc Robotica, 1995.(0 ): p. 23- 33.

85. Alici, G and B. Shirinzadeh, Enhanced st ness modeling,

ident cation and characterization for robot manipulators.

Robotics, IEEE Transactions on, 2005. ( ): p. 55 -5 .

8 . Van, c. F. Gao, and Y Zhang, Kinematic Modeling of a

Serial" Parallel Forging Manipulator with Application to

Heavy-Du Manipulations#. Mechanics based design of

structures and machines, 2010. (1): p. 105-129.

87. Vi, B., R. Freeman, and D. Tesar, Force And St ness

Transmission n Redundantly Actuated Mechanisms: The

Case for a Spherical Shoulder Mechanism. Proceedings of

ASME Robotics, Spatial Mechanisms, and Mechanical

Systems Conferences, 199 : p. 1 3-172.

88. Chakarov, D., Study of the antagonistic st ness of parallel

manipulators with actuation redundanc Mechanism and

Machine Theory, 200 . ( ): p. 583- 01.

89. Nokleby, S., et a ., Force capabilities of

redundantly-actuated parallel manipulators. Mechanism

and Machine Theory, 2005. 4 (5): p. 578-599.90. Vi, B. and S. Oh. Analysis of a 5-bar nger mechanism

having redundant actuators with applications to st ness

and frequency modulations 1997: INSTITUTE OF

ELECTRICAL ENGINEERS INC (IEEE).

91. Kosuge, K., et a!. Force control of parallel link manipulator

with hydraulic actuators in 1996 EEE nternational

Co erence on Robotics and Automation 199 . Minneapolis,

M , USA

92. Kotzev, A., et a ., Generalized predictive control of a robotic

manipulator with hydraulic actuators. Robotica, 2009.

(05): p. 7- 59.

93. Guo, W and F. Gao, Kinematic Design of a P -Type

Composite Actuator. in EEEIASME nternational

Conference on Advanced ntelligent Mechatronics 2009:

Singapore p. 1 59 - 1 2

9 . Weizhong, G and G Feng, Design of a Servo Mechanical

Press with Redundant Actuation. Chinese Journal of

Mechanical Engineering 2009. 22( ).

95. Sato, M. and T. Inoue, L ME W R OF

R RCH P CS U L Z NG THE 3-D FULL-SCALE

EARTHQUAKE TEST NG FAC L TYJou al of Japan

Association for Earthquake Engineering, 200 . 4(3): p.

8- 5 .

9 . Jianzheng Zhang, et a!., The research on application of a

multi-DOF parallel manipulator as an earthquake simulatorin Proceedings of the 16th nternational Co erence on

Automation & Computing 2010: University of Birmingham,

Birmingham, UK.

97. Zhang, et a ., Application of a Novel 6-DOF Parallel

Robot with Redundant Actuation for Earthquake Simulation

in EEE nternational Co erence on Robotics and

Biomimetics 2010: Tianjin China.

98. Chung, G and K. Choi. Development of Nano Order

Manipulation System based on 3 PR Planar Parallel

Mechanism 2005: IEEE.

99. Yao, Q., Dong, and P Ferreira, A novel

parallel-kinematics mechanisms for integrated, multi- is

nanopositioning:: Part 1. Kinematics and design for

fabrication. Precision Engineering, 2008. (1): p. 7-19.

100. Y Vue, et a!., Relationship among input-force, payloa

st ness and displacement of a 3-DOF perpendicular

parallel micro-manipulato Journal of Mechanisms and

Robotics, 2010. 2.

key issues in studying parallel manipulators 2011

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