ACTA TEHNICA CORVINIENSIS Bulletin of Engineering [613300]

ACTA TEHNICA CORVINIENSIS – Bulletin of Engineering
Tome VII [2014] Fascicule 1 [January – March]
ISSN: 2067 – 3809
© copyright Faculty of Engineering – Hunedoara, University POLITEHNICA Timisoara   

1. Zoran PANDILOV, 2. Vladimir DUKOVSKI

COMPARISON OF THE CHARACTERISTICS
BETWEEN SERIAL AND PARALLEL ROBOTS

University “Sv. Kiriil I Metodij”, Facu lty of Mechanical Engineering-Skopje,
Karpos Ii B.B., P.O.Box 464, Mk-100 0, Skopje, Republic of MACEDONIA

Abstract: This paper gives survey of the position analysis, jacobian and singularity analysis, stiffness analysis,
dynamics and applications of serial and parallel robots. Al so a detailed comparison of the characteristics of serial
and parallel robots and their advantages and disadvantages are presented.
Keywords: serial robots, parallel robots, comparison  

INTRODUCTION – Introduction to robotics
Robotics is a field of modern technology that
crosses traditional engineering boundaries.
Understanding the complexity of robots and their applications requires know ledge of mechanical
engineering, electrical engineering, systems and
industrial engineering, computer science, economics, and mathematics. The term robot was first introduced into vocabulary by the Czech playwright Karel Capek in his 1920 play Rossum’s Universal Robots, the
word “robota” being the Czech word for work.
Since then the term has been applied to a great variety of mechanical devices, such as teleoperators, under-water vehicles, autonomous land rovers, etc. Virtually anything that operates with some degree of autonomy, usually under computer control, has at some point been called a robot. There are many definitions for what a robot is and
this often leads to discrepancies between statistics
quoted about robots. An official definition for a
robot comes from the Robo t Institute of America
(RIA): A robot is a reprogrammable multifunctional manipulator designed to move material, parts, tools, or specialized devices through variable programmed motions for the performance of a variety of tasks. The commonly accepted definition in the UK is
that provided by the British Robot Association
which is as follows: An industrial robot is a re-programmable device design ed to both manipulate
and transport parts, tools, or specialised manufacturing implements through variable
programmed motions for the performance of
specific manufacturing tasks.
The definition of a robot used by the Japanese Industrial Robot Asso ciation widens these
definitions in order to include arms controlled directly by humans and also fixed sequence manipulators which are not re-programmable.
The key element in the above definitions is the re-programmability of robots. It is the computer brain that gives the robot its utility and
adaptability. The so-called ro botics revolution is, in
fact, part of the larger computer revolution. Even
this restricted version of a robot has several features that make it attractive in an industrial environment. Among the advantages often cited in favour of the introduction of robots are decreased labour costs, increased precision and productivity, increased flexibility compared with specialized machines, and more humane working conditions as
dull, repetitive, or hazard ous jobs are performed by
robots. The robot, as it is defined, was born out with integration of two earlier technologies: teleoperators and numerically controlled milling machines. Teleoperators, or master-slave devices,
were developed during th e Second World War to
handle radioactive materials. Computer numerical control (CNC) was develope d because of the high
precision required in the machining of certain
items, such as componen ts of high performance
aircrafts.

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| 144 | The first robots essentially combined the
mechanical linkages of the teleoperator with the
autonomy and programmability of CNC machines.
The first successful applications of robot manipulators generally involved some sort of material transfer, such as injection moulding or stamping, where the robot merely attends a press to unload and either transfer or stack the finished parts. These first robots could be programmed to
execute a sequence of movements, such as moving to a location A, closing a gripper, moving to a
location B, etc., but ha d no external sensor
capability. More complex applications, such as
welding, grinding, deburring, and assembly require not only more complex motion but also some form of external sensing such as vision, tactile, or force-sensing, due to the increased interaction of the robot with its environment. It should be pointed out that the important applications of robots are by no means limited to
those industrial jobs where the robot is directly
replacing a human worker. There are many other applications of robotics in areas where the use of humans is impractical or undesirable. Among these are undersea and planetary exploration, satellite retrieval and repair, the defusing of explosive devices, and work in radioactive environments. Finally, prostheses, such as artificial limbs, are
themselves robotic devic es requiring methods of
analysis and design similar to those of industrial
manipulators. One modern robotics system usually consists of a
mechanical manipulator, an end-efector, a
microprocessor-based controller, a computer and internal and external sensors/sensing devices
(contact or noncontact).
Classification of robots (robotic manipulators)
Robots can be classified according various criteria,
such as degrees of freedom, kinematic structure, drive technology, workspace geometry, motion characteristics, control.
Degrees of freedom
One obvious classification scheme is to categorize
robots according to their degrees of freedom. In ideal case, a manipulator should posses 6 degrees of
freedom in order to manipulate an object freely in
three-dimensional space. From this point of view, we call a robot a general-purpose robot if it
possesses 6 degrees of freedom, a redundant robot if
it possesses more than 6 degrees of freedom, and a
deficient robot if it poss esses less than 6 degrees of
freedom
Kinematic structure
Another classification of robots is according to
their structural topologies. A robot is said to be a serial robot (fig.1.1 a) or serial (open-loop) manipulator if its kinematic structure takes the form of an open loop-chain, a parallel manipulator
(fig.1.1 b) if it is made of a closed-loop chain, and
hybrid manipulator if it is consists of both open- and closed-loop chains.
a)
b)
Figure 1.1 a) Serial robot (manipulator) b) parallel
manipulator
Drive technology
Typically, robots (manipulators) are electrically,
hydraulically, or pneuma tically driven. Most
robots use DC- or AC-servo motors or stepper motors, because they are cleaner, cheaper, quieter and relatively easy to control. Hydraulic drives have no rival in their speed of
response and torque producing capability.
Therefore hydraulic robots are used primarily for lifting heavy loads. The drawbacks of hydraulic robots are that they tend to leak hydraulic fluid,
require much more peripheral equipment (such as pumps, which require more maintenance), and
they are noisy. Pneumatic robots are inexpensive
and simple but cannot be controlled precisely, because air is a compressible fluid. As a result,
pneumatic robots are limited in their range of
applications and popularity.
Workspace geometry
The workspace of a manipulator is defined as the
volume of space the en d effector can reach. A
reachable workspace is the volume of space within which every point can be reached by the end
effector in at least one orientation. A dextrous workspace is the volume of space within which

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| 145 | every point can be reached by the end effector in all
possible orientations. De xtrous workspace is a
subset of the reachable workspace.

Figure 1.2 Five most common types
of robots geometry [5]
Most industrial robots (manipulators) at the present
time have six or fewer degrees-of-freedom. These robots are usually classified kinematically on the basis of the first three joints of the arm (R-revolute or P-prismatic) used for manipulating the position, while the rest of joints associated with the wrist are for controlling the orientation. The majority of these robots (manipulatators) fall into one of five geometric types: Cartesian (PPP), cylindrical (RPP), spherical (RRP), SCARA (selective compliance assembly robot arm) (RRP), articulated (RRR) (fig.1.2). Each of these five manipulator arms are serial link robots. A sixth
distinct class of manipulators consists of the so-called
parallel robot. In a parallel manipulator, as we mentioned before, the links are arranged in a closed rather than open kinematic chain.

Figure 1.3 Principle, kinematic chain
and workspace of parallel robot
Motion characteristics
Robot manipulators can also be classified according
to their nature of motion in planar, spherical and spatial. A manipulator is called a planar manipulator if its
mechanism is a planar mechanism (fig.1.4 a). A
manipulator is called a spherical manipulator if it is made of a spherical mechanism (fig.1.4 b). A manipulator is called a spatial manipulator if at least one of the moving links in the mechanism
possesses a general spatia l motion (fig.1.1 b).
a)
b)
Figure 1.4 a) Planar parallel manipulator) b) spherical
parallel manipulator
Control
Robots are classified by control method into servo
and non-servo robots. The earliest robots were non-servo robots. These robots are essentially open-loop devices whose movement is limited to predetermined mechanical stops, and they are useful primarily for materials transfer. In fact, according to the definition given previously, fixed stop robo ts can hardly qualify as
robots.
Servo robots use closed-loop computer control to determine their motion and are thus capable of being truly multifunctional, reprogrammable devices. Servo controlle d robots are further
classified according to the method that the
controller uses to guide the end-effector. The simplest type of robot in this class is the point-to-point robot. A point-to-point robot can be taught
with a discrete set of points, but there is no control
on the path of the end-effector in between taught points. Such robots are us ually taught a series of
points with a teach pendant. The points are then stored and played back. Point-to-point robots are severely limited in their range of applications. In continuous path robots, on the other hand, the
entire path of the end-effector can be controlled. For example, the robot end-effe ctor can be taught to
follow a straight line betw een two points or even to
follow a contour such as a welding seam. In addition, the velocity and/or acceleration of the end-effector can often be controlled. These are the
most advanced robots and require the most
sophisticated computer co ntrollers and software
development.
Accuracy and repeatability
The accuracy of a manipula tor is a measure of how
close the manipulator can come to a given point within its workspace. Repe atability is a measure of

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| 146 | how close a manipulator ca n return to a previously
taught point.

a) b) c) d)
Figure 1.5. a) low accuracy, low repeatability b) high
accuracy, low repeatability c) low accuracy, high
repeatability d) high accuracy, high repeatability
In this target analogy each dot represents an
attempt to get to the central cross. The size of the cluster shows the spread in the result, and the
closeness of the centre of th e cluster to the cross is
measure of accuracy [44]. The primary method of sensing positioning errors in most cases is with position encoders located at the joints, either on the shaft of the motor that
actuates the joint or on th e joint itself. There is
typically no direct measurem ent of the end-effector
position and orientation. One must rely on the assumed geometry of the manipulator and its
rigidity to calculate the en d-effector position from
the measured joint positions. Accuracy is affected therefore by computational errors, machining accuracy in the construction of the manipulator, flexibility effects such as the bending of the links
under gravitational and other loads, gear and joint backlash, and an existing of other static and dynamic effects. It is primarily for this reason that robots are designed with extremely high rigidity.
Without high rigidity, a ccuracy can only be
improved by some sort of direct sensing of the end-effector position, such as with vision. Once a point is taught to the manipulator, however, say with a teach pendant, the above effects are taken into account and the proper
encoder values necessary to return to the given point are stored by the controlling computer.
Repeatability therefore is a ffected primarily by the
controller resolution. Co ntroller resolution means
the smallest increment of motion that the controller
can sense. The resolution is computed as the total distance traveled by the tip divided by 2
n, where n
is the number of bits of encoder accuracy. In this
context, linear axes, that is, prismatic joints typically have higher resolution than revolute joints, since the straight line distance traversed by
the tip of a linear axis be tween two points is less than the corresponding arc length traced by the tip
of a rotational link. In addition rotational axes
usually result in a large amount of kinematic and
dynamic coupling among the links with a resultant accumulation of errors and a more difficult control problem. One may wonder then what the advantages of revolute joints are in manipulator design. The answer lies prima rily in the increased
dexterity and compactness of revolute joint designs. For example, Fi gure 1.6 shows that for the
same range of motion d, a rotational link can be
made much smaller than a link with linear motion.
Thus manipulators made from revolute joints occupy a smaller working volume than manipulators with linear axes. This increases the ability of the manipulator to work in the same space with other robots, machines, and people. At the same time revolute joint manipulators are better able to manuver around obstacles and have a wider range of poss ible applications.

Figure 1.6 Linear vs. rotational link motion.
Accuracy and repeatability are usually of the same
order, typically millimetre for very large robots, tenths of millimetre for ge neral purpose robots and
hundredths of millimetre for the most accurate
assembly robots.
SERIAL ROBOTS – Position analysis
A serial robot consists of several links connected in
series by various types of joints, typically revolute and prismatic. One end of the robot is attached to
the ground and the other end is free to move in
space. The fixed link is called base, and the free end where a gripper or a mechanical hand is attached,
the end effector.
For a robot to perform a specific task, the location of the end effector relati ve to the base should be
established first. This is called position analysis problem. There are two typ es of position analysis
problems: direct position or direct kinematics and
inverse position or inv erse kinematics problems.
For direct kinematics, the joint variables are given
and the problem is to find the location of the end
effector. For inverse kinema tics, the location of the
end effector is given and the problem is to find the

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| 147 | joint variables necessary to bring end effector to the
desired position. For a serial robot direct
kinematics is fairly straightforward, whereas
inverse kinematics becomes very difficult. For a deficient robot the end efec tor can not be positioned
freely in space, and fo r the redundant robot there
may be several infinitudes of inverse kinematics solutions corresponding to a given end-effector location, depending on the degrees of redundancy. In solving the inverse kinematics problem, we are often interested in obtaining a closed-form
solution, that is, in reducing the problem to an
algebraic eqution relating the end-effector location to a single joint variable. In this way, all possible solutions and manipulator postures can be accounted for. To achieve this goal, various methods of formulation have been pr oposed: vector algebra
method, geometric method, 4×4 matrix method (Denavit-Hartenberg), 3×3 dual matrix method,
iterative method, scre w algebra method and
quarternian algebra method [45].
The number of possible inverse kinematics solutions depends on the type and location of a robot manipulator. In general, closed-form solutions can be found for robot manipulators with simple geometry, such as manipulators with three consecutive joint axes in tersecting at a common
point or three consecutive joint axes parallel to one
another. For manipulator of general geometry, the
inverse kinematics proble m becomes an extremely
difficult task. Two commonly used methods for kinematics analysis of serial robot manipulators are Denavit
and Hartenberg’s method and the method of successive screw displacements.
Jacobian and singularity analysis
For some applications, such as spray painting (fig. 2.1), it is necessary to move the end effector of the
robotic manipulator along some desired paths with prescribed speed. To achieve this goal, the motion of the individual joints must be carefully coordinated.
There two types of velocity coordination problems,
called direct velocity and in verse velocity problems.
For the direct velocity problem, the input joint rates are given and the objective is to find the
velocity state of the end effector. For the inverse
velocity problem, the velocity state of the end effector is given, and the input joint rates required
to produce desired velocity are to be found.

Figure 2.1 Spray painting robots [57]
Vector space spanned by the joint variables is
called joint space, and the vector space spanned by
the end-effector location, th e end-effector space. For
robot manipulators, the Jacobian matrix, or simply Jacobian, is defined as the matrix that transforms the joint rates in the actuat or space to velocity state
in the end effector state. The Jacobaian matrix is a
critical component for generating trajectories of prescribed geometry in the end effector-space. Most coordination algorithms u sed by industrial robots
avoid numerical inversion of the Jacobain matrix by deriving analytical inverse solutions on an ad hoc basis. Therefore, it is important that efficient
algorithm be developed. Since the velocity state of the end-effecor can be
defined in various ways, a variety of Jacobian
matrices and consequently, different methods of formulation have appeared in the literature. The most frequently used in practice are a conventional Jacobian and screw-based Jacobian [45] .
For a serial robot solving di rect velocity problem is
relatively easy, whereas inverse velocity problem becomes very difficult, especially for robots of
general geometry.
The Jacobian matrix is also useful in other
applications. For some manipulator configurations, the Jacobian matrix may lose its full rank. Such conditions are called singular conditions or singular configurations. Physically this implies that the instantaneous screws spanning the n-dimensional space of the Jacobian matrix became linearly dependent. Theref ore, at a singular
condition, a serial robot manipulator may lose one
or more degrees of freedom, and it will not be able
to move in some directions in the end-effector space. Singularity configurations can found by setting the determinant of the Jacobian matrix to zero. In

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| 148 | general, this will result in a single algebraic
equation. For serial ro bot manipulators, the
singular condition is a function of the intermediate
joint variables, not of the first and the last joint variables. This is because the presence of the singularity depends solely on the relative locations of the joint axes. Rotations of the entire manipulator about the first axis not change the relative locations of the joint axes. Similarly, rotation of the end effector about the last joint axis
does not affect the location of any joint axis.
Therefore, the first and the last joint variables do
not appear in the determinant of Jacobian matrix. There two types of singularities for a serial robot manipulator: boundary si ngularity and interior
singularity. A boundary singularity occurs when
the end effector is on th e surface of the workspace
boundary, and it usually happens when the manipulator is either in a fully stretched-out or a folded-back configuration. Boundary singularity
can also occur when one of its actuators reaches its
mechanical limit. An interior singularity occurs inside the workspace boundary. Several conditions may lead to an interior singularity. For example,
when two or more joint axes line up on a straight line, the effects of a rota tion about one joint axis
can be cancelled by counterrotation about another joint axis. Thus the end effector remains stationary
even though the intermediate links of the robot
manipulator may move in space. Another example of interior singularity occurs when four revolute
joint axes are parallel to one another or intersect in
common point.. For a manipulator of general geometry, the problem of identifying interior singularities becomes a much more complex problem. Basically, an int erior singularity occurs
whenever the screws of two or more joint axes
become linearly dependent. Boundary singularities
are not particularly serious, since they can always be avoided by arranging the task of manipulation far away from the workspace boundary. Interior singularity is more troubl esome because it is more
difficult to predict during the path planning process.
Stiffness analysis of serial robots
When a robot manipulator performs a given task,
the end effector exerts so me force and/or moment
on its environment. This contact force and/or moment will cause the end effector to be deflected
away from its desired location. Intuitively, the
amount of deflection is a function of the applied
force and the stiffness of the manipulator. Thus the stiffness of a robot manipulator has a direct impact on the position accuracy. Furthermore some advanced control strategies use the stiffness characteristics for feedba ck control of a robot
manipulator. The overall stiffness of a robot manipulator depends on several factors, including the size of
and material used for th e links, the mechanical
transmission mechanisms , the actuators and the
controller. As the links become longer and more slender. Link compliance becomes the major source
of deflection. This is particularly true for space robots, for which light we ight and compactness are
the major concern. (fig. 2.2)

Figure 2.2. Serial space robotic manipulator [1]
Most of the modern serial industrial robots are
constructed with fairly rigid links, and the major
sources of compliances come from the mechanical transmission mechanisms and control system. For a serial robot manipulator, each joint is typically driven by an actuator through a multiple-stage speed reducer along several drive shafts. The speed reducer and the drive shafts may deflect when torque or force is transmitted. Further, the drive torque or force ge nerated by a servo system
usually depends on the position and error signals
and its feedback gains. The stiffness of the speed reducer, the drive shafts, and the servo system may be combined into an equivalent stiffness.
Dynamics of serial robots
For some applications, such as arc welding,
(fig.2.3), it is necessary to move the end effector of
manipulator from point to point rapidly. The dynamics of the robot manipulator plays an
important role in achieving such high-speed
performance. The developm ent of dynamical model
is important in several ways. First, a dynamical model can be used for computer simulation of a

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| 149 | robotic system. By examin ing the behaviour of the
model under various operating conditions, it is
possible to predict how a robotic system will behave
when it is built. Various automation tasks can be examined without the need of real system. Second, it can be used for the development of suitable control strategies. A so phisticated controller
requires the use of a realistic dynamical model to achieve optimal perfor mance under high-speed
operations. Some control sc hemes rely directly on a
dynamic model to compute actuator torques
required to follow a desired trajectory. Third, the
dynamic analysis of the manipulator reveals all the joint reaction forces (and moments) needed for the design and sizing of links, bearings and actuators. There are two types of dynamical problems: direct dynamics and inverse dynamics. The direct dynamic problem is to find the response of a robot
arm corresponding to some applied torques and/or forces. That is, given a vector of joint torques or
forces, we wish to compute the resulting motion of
the robot manipulator as a function of time. The inverse dynamic problem is to find the actuator torques and/or forces required to generate a desired trajectory of the manipulator. The problem can be formulated in joint space, or the end effector space.
The two formulations are related by the Jacobian
matrix and its time derivative. In general, the
efficiency of computation for direct dynamics is not
as critical since it is used primarily for computer simulations of a manipulator. On the other hand an efficient inverse dynamical model becomes extremely important for real-time feedforward control of a robot manipulator.

Figure 2.3. Arc welding robot [57]
The dynamical equations of motions can be
formulated by several methods. The most
frequently used are the a pplication of the Newton
and Euler laws and the Langranges’s equations of motion.
Applications of serial robots
Robots, basically serial robots, are used in
applications that require repetitive tasks over long periods of time, opera tions in hazardous
environments (like nuclear radiation, under water,
space exploration, etc.), and precision work with
high degree of reliability. They can also be used by handicapped persons to overcome some of their physical disabilities. Some examples of use of industrial robots are
following: machine loading and unloading (fig 2.4), palletizing, die cast ing, forging, press work,
arc welding and spot welding (fig.2.5), heat treatment, spraying (paint, enamel, epoxy resin
and other coatings), deburring, grinding,
polishing, injection moulding, cutting (laser, plasma), inspection, asse mbly (fig.2.6) , packaging
(fig.2.7), material ha ndling (fig.2.8), etc.

Figure 2.4 Robot application in machine loading and
unloading [56]

Figure 2.5. Application of robot in welding process [56]

Figure 2.6 Robot application in assembly [56]

Figure 2.7 Application of robot in packaging [56]

Figure 2.8 Application of two robots in handling heavy
objects (materials) [56]

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| 150 | According to the Internat ional Federation of
Robotics (IFR) of all inst alled industrial robots,
approximately 33% are in assembly, 25% are used
in different welding applications, 2,8% in packaging/palletizing, but with intention to grow-
up, etc. Main characteristics of th e serial robots are given
in the table below:
Table 2.1. Characteristics of serial robots
Feature Serial robot
Workspace Large
Solving forward
kinematics Easy
Solving inverse kinematics Difficult
Position error Accumulates
Force error Averages
Maximum force Limited by minimum
actuator force
Stiffness Low
Dynamics characteristics Poor, especially with
increasing the size
Modelling and solving
dynamics Relatively simple
Inertia Large
Areas of application A great number in different
areas, especially in industry
Payload/weight ratio Low
Speed and acceleration Low
Accuracy Low
Uniformity of components Low
Calibration Relatively simple
Workspace/robot size ratio High

PARALLEL ROBOTS – Position analysis
A parallel robot manipulator is composed of two or
more closed-loop kinematic chains in which the end-effector (mobile platfo rm) is connected to the
fixed base platform by at least two independent kinematic chains. Between the base and end-effector platforms are serial chains (called limbs or
legs). (fig.3.1)

Figure 3.1 Example of parallel robot manipulator,
Patent US 5388935: VARIAX machining center,
(Courtesy: Giddings & Lewis, Inc ., Fond du Lac, WI)
Typically, the number of limbs is equal to the
number of degrees of freedom such that every limb is controlled by one actu ator and all actuators can be mounted at or near the fixed base. For this
reason , parallel manipulators are sometimes called
platform manipulators. Be cause the external load
can be shared by the actuators, parallel manipulators tend to have a large load-carrying capacity. Parallel manipulators have been used in
applications like airplane simulators [43], adjustable articulated trusses [40], mining
machines [4], pointing devices [22],, walking machines [46], machining centres [20], etc.
The development of parallel manipulators can be
dated back to the earl y 1960's when Gough and
Whitehall [23], first devi sed a six-linear jack
system for use as a universal tire testing machine. Later, Stewart [43] developed a platform manipulator for use as an aircraft simulator. Hunt
[26] first made a systematic study of the structural
kinematics of parallel manipulators. Since then, parallel ma nipulators have been
studied by numerous researches [45]. More than
100 different mechanical architectures of parallel robots have already been proposed. Most of the 6-DOF parallel manipulators studied to date consist of six extensible limbs. These parallel manipulators possess the advantages of
high stiffness, low inertia and large payload capacity. However, they suffer the problems of
relatively small useful workspace, design
difficulties and difficult control. For parallel robot manipulators two position analysis problems have to be solved: direct kinematics and indirect kinematics. A parallel
robot indirect kinematics is fairly straightforward, whereas direct kinematics is very difficult problem.
Perhaps, the only six limbed 6 DOF parallel manipulators for which closed-form direct
kinematics solutions have been reported in the
literature are special forms of the Stewart-Gough platform. As to the general Stewart-Gough
platform, research has to resort to numerical
techniques for the solutions. Parallel robot manipulators can be classified as planar (fig.3.2 a), spherica l (fig. 1.4 b), or spatial
(fig.3.2 b) manipulators in accordance with their
motion characteristics.
Position analysis of planar and spherical parallel
robot manipulators is easier than position analysis

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| 151 | of parallel robot manipulators, or if the spatial
manipulator has less than 6 DOF, or if the parallel
manipulator is symmetrical.

Figure 3.2 a) planar parallel robot manipulator b)
spatial parallel robot manipulator
The parallel manipulator is symmetrical if it
satisfied the following conditions: 1. The number of limbs is equal to the numbers of
degrees of freedom of the moving platform. 2. The type and number of joints in all the limbs are arranged in an identical pattern. 3. The number and location of actuated joints in all
the limbs are the same. When the conditions above are not satisfied, the
manipulator is called asymmetrical.
For position analysis (direct and indirect kinematics) for parallel ma nipulators, both vector
and algebraic techniques are used. Details about position analysis for different types of planar parallel robot manipulators are given by [49, 48, 12, 24] and for different types of spatial parallel robot manipu lators [37, 15, 35, 65, 66, 13,
8, 31, 67, 27, 11, 19, 41] etc.
Jacobian and singularity analysis
The Jacobian analysis of parallel manipulators is a
much more difficult problem than that of serial manipulators because they are many links that form a number of closed loops. An important limitation of parallel manipulator is that singular configurations may exist within its workspace where the manipulator gains one or
more degrees of freedom and therefore loses its
stiffness completely. This property has attracted the attention of several researches. For example, Gosselin & Angeles [21] st udied the singularities
of closed-loop mechanisms and suggested a separation of the Jacobian matrix into two matrices: one associated wi th the direct kinematics
and the other with the inverse kinematics. Depending on which matrix is singular, a closed-
loop mechanism may be at a direct kinematic singular congiguration, an inverse kinematic
singular configuration, or both.
The most widely used methods for Jacobian
analysis for parallel robot manipulators are the method of velocity vector-loop equations and the method of reciprocal screws. A parallel manipulator such as VARIAX machining center shown in fig 3.1 typically consists of a moving platform and a fixed base connected by several limbs. This moving platform serves as the end effector. Because of the closed-loop
construction, not all jo ints can be controlled
independently. Thus some of the joints are driven
by actuators, whereas others are passive. In general, the number of actuated joints should be equal to the number of de grees of freedom of the
manipulator. Let the actuated joint va riables be denoted by a
vector q and the location of the moving platform be described by vector x. Then the kinematic
constrains imposed by limbs can be written in the
general form
f(x,q)=0 (3.1)
where f is an n-dimensional implicit function of q
and x and 0 is n-dimensional zero vector. Differentiating equation (3.1) with respect to time,
we obtain a relationship between the input joint rates and the end-effector output velocity as
follows:
Jx
x&= Jq q& (3.2)
where
xfJx∂∂= and
qfJq∂∂-=
The derivation above leads to two separate Jacobian
matrices. Hence the overall Jacobian matrix, J, can
be written as,
q&= J x& (3.3)
where Jx Jq J1-= . Jacobian matrix defined in
equation 3.3 for a parallel manipulator corresponds
to the inverse Jacobian of a serial manipulator.
Due to the existence of two Jacobian matrices, a parallel robot manipulator is said to be at singular configuration when either Jx or Jq or both are singular. An inverse kinematic singularity occurs when the determinant of Jq goes to zero, namely,
det(Jq)= 0 (3.4)
When Jq is singular ant th e null space of Jq is not
empty, there exist some nonzero
q& vectors that

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| 152 | result in zero x& vectors. Infinitesimal motion of the
moving platform along certain directions cannot be
accomplished. On the other hand, at the inverse
kinematic singular configuration, a parallel manipulator can resist forces or moments in some directions with zero actuator forces or torques. Inverse kinematic singularities usually occur at the workspace boundary, where different branches of the inverse kinematic solu tions converge. It is
similar to that of serial manipulator. A direct kinematic singul arity occurs when the
determinant Jx is equal to zero, namely
det(Jx)= 0 (3.5)
Assuming that in presence of such a singular condition the null space of Jx is not empty, there exist some nonzero
x& vectors that result in zero q&
vectors. That is, the moving platform cans posses
infinitesimal motion in so me directions while all
actuators are completely locked. Hence the moving platform gains one or more degrees of freedom. This is in contradiction with the serial manipulator, which loses one or more degrees of freedom [47]. In other words, at a direct kinematic singular configuration, the manipulator cannot resist forces or moments in some directions. In
those directions the st iffness is zero. Direct
kinematic singulariti es usually occur where
different branches of direct kinematic solutions meet. A combined singularity occurs when the determinants of Jx and Jq are both zero. Generally, this type of singularity can occur only for manipulators with special kinematic architecture. At a combined singular configuration, equation
(3.1) will degenerate. Th e moving platform can
undergo some infinitesimal motions while all the actuators are locked. On th e other hand, it can also
remain stationary while actuators undergo some infinitesimal motions. Singualarity analyses for different types of parallel robot manipulators are presented by [30, 13, 65, 66, 63, 64, 62, 2, 3, 31, 68, 69, 33, 28] etc.
Dynamics of parallel robots
While the kinematic of para llel robot manipulators
have been extensively studied during the last two decades, fewer papers can be found on the dynamic
of parallel manipulators [45]. The dynamic analysis of parallel manipulators is complicated by the existence of multiple cl osed loop chains. Several
approaches have been pr oposed, including the
Newton-Euler formulation the Langrangian
formulation and the principle of virtual work. Details about dynamic modelling of parallel robots are given by [14, 34, 29, 36, 63, 64, 32, 25, 18] etc. The traditional Newton-Euler formulation requires the equations of motion to be written once for each
body of the manipulator, which inevitably leads to a large numbers of equations and results in poor computational efficiency. The Lagrangian
formulation eliminates all of the unwanted reaction
forces and moments at th e outset. It is more
efficient than the Newton-Euler formulation. However, because of the numerous constrains imposed by closed loops of a parallel manipulator, deriving explicit equations of motion in terms of a
set of independent generalized coordinates becomes a prohibitive task. To simplify the problem additional coordinates along with set of
Lagrangian multipliers are often introduced. In
some cases, limbs are approximated by point masses by arguing that such approximation does not introduce significant modelling errors. In this
regard, the principle of virt ual work appears to be
the most efficient method of analysis.
Applications of parallel robots
After spending almost 20 years in the laboratories
for preliminary studies parallel robots are now
used in real-life applic ations. This interest for
parallel robots come from the potentially
interesting features of parallel mechanisms: high accuracy, rigidity, speed and large load carrying
capability, which in a v ery large number of cases
may overcome the drawbacks of the more complex kinematics, dynamics and smaller workspace.
But a fact is that these advantages are only
potential and any real parallel robot will present in
practice impressing perfor mances only if all its
components (either hardware or software) present a high level of performance. The current applications of parallel robots are in
domains such as fine positioning devices (fig.3.3 and fig.3.4 ), simulators (fig. 3.5), motion generators (platforms) (fi g. 3.6), ultra-fast pick and
place robots (fig.3.7), machine-tools (fig. 3.8,
fig.3.9 and fig.3.10), medical a pplications (fig.3.11,
fig.3.12 ), haptic devices (fig.3.13), entertainment,

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| 153 | force sensors, micro-robots (fig. 3.14), articulated
trusses, etc.

Figure 3.3 Application of parallel robots for fine
positioning UKIRT (United Kingdom Infrared
Telescope), collaboration between Royal Observatory
Edinburgh and Max-Planck-Institut für Astronomie
Heidelberg [61]

Figure 3.4 Parallel robots for fine positioning [60]

Figure 3.5 Application of parallel robots as simulators
NASA LARC-simulator [61]

Figure 3.6 Parallel robots
as motion platforms [55],[53]

Figure 3.7 Ultra-fast pick and place robot ABB-Flex
Picker IRB 340 [50]

Figure 3.8 Side and top view, solid model and photo of
Ingersoll Octahedral Hexapod machine tool installed at
NIST [16]

Figure 3.9 Hexapod parallel robot based machine tool
[6]

Figure 3.10, Hybrid parallel-serial robot Tricept 805
tripod and a complete machining center [42]

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| 154 | 

Figure 3.11 Hexapod for brain surgery. Photo courtesy
of IPA [59]

Figure 3.12 Parallel robot SurgiScope in action at the
Surgical Robotics Lab, Humboldt-University at Berlin
(courtesy of Prof. Dr. Tim C. Lueth) [58]

Figure 3.13 Cobotic parallel platform [17]

Figure 3.14 Parallel micro robot [52]
But in spite of above given examples and high
performance potential of parallel robots, this
technology has not yet made a dramatic impact on industrial automation. However, there is an
interesting trend towards the use of general
purpose industrial serial robots for applications
with higher demands on accuracy, stiffness, natural frequency, cycle time etc. Thus, significant efforts are now being made to use industrial robots for such applications as measurements, laser cuttin g, laser welding, high
precision assembly, grinding, deburring, milling etc. Because of the ineffic ient robot performance for
these applications, several compensation methods are used, which add cost and make installation,
programming, maintenance etc., difficult [9].
Moreover, in most cases the industrial serial robots
of today probably will ne ver reach the application
requirements for high p erformance applications.
One way to solve these prob lems could be using of
robots based on parallel kinematics. But it is not easy to challenge and change the mature industrial robot technology, even if some successful structures find increasing market shares today, too.
Parallel kinematic structures provide such high
performance potential, but it is very important for
the research community to come up with concepts and technologies which will make parallel kinematic robots a natural choice when flexible automation systems are designed. One example of a successful parallel kinematic robot structure is the De lta structure (fig. 3.7),
designed in 80's from Prof. Reymond Clavel (professor at EPFL – École Polytechnique Fédérale
de Lausanne). The reason for this success is that
the features of this structure fit into applications requiring very fast handling of light weight products, for example in the consumer goods, food and electronics industries. Thus, to be successful with the transfer of results from parallel kinematics
robots research to industri al product development,
it is very important to understand the application
requirements. Morever, it is important to
understand what advantages parallel kinematics robots features, provide in potential applications.

Parallel robot features Applications End Users
Figure 3.15 Diagram exemplifying the relations
between potential performance features of a parallel
kinematic robot and the applications and industries
needing this performance for improved flexible
automation [9]
For example, parallel kinematic robot structures
may give higher speed and acceleration, higher

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| 155 | static and dynamic accuracy and higher stiffness
than what is possible wi th the serial industrial
robots used today. Starting with these competitive
features, potential applications and end users can be evaluated, like the exam ple diagram given in fig.
3.15. For each application and for each type of installation in the manufac turing plants of the end
users, a detailed study is n eeded to find out if the
parallel kinematic robot will satisfy all requirements.
Several examples of sucessful parallel robots – Delta parallel robot
It is in the early 80's when Reymond Clavel
(professor at EPFL – École Polytechnique Fédérale de Lausanne) comes up with the brilliant idea of using parallelograms to build a parallel robot with three translational and one rotational degree of
freedom. Latter called his creation the Delta robot (fig.3.16), without suspecting that at the turn of
the century, it will estab lish itself as one of the
most successful parallel robot designs, with several
hundreds active robots worldwide. The basic idea behind the Delta robot design is the use of parallelograms. A parallelogram allows an output link to remain at a fixed orientation with respect to an input link. The use of three such
parallelograms restrain co mpletely the orientation
of the mobile platform which remains only with
three purely translational degrees of freedom. The
input links of the three parallelograms are mounted on rotating levers via revolute joints. The revolute joints of the rotating le vers are actuated in two
different ways: with rotational (DC or AC servo) motors or with linear actuators. Finally, a fourth leg is used to transmit ro tary motion from the base
to an end-effector mounted on the mobile platform. The use of base-mounted actuators and low-mass
links allows the mobile platform to achieve
accelerations of up to 50 G in experimental environments and 12 G in industrial applications. This makes the Delta robo t a perfect candidate for
pick and place operations of light objects (from 10
gr to 1 kg). Ideally, its workspace is the intersection of three right circular tori. The Delta
robots available on the market operate typically in a cylindrical workspace which is 1 m in diameter and
0.2 m high.

Figure 3.16 Schematic of the Delta robot (from US
patent No. 4,976,582) [51]
As simple as it is, the d esign of the De lta robot is
covered by a family of 36 patents of which the most important are the WIPO patent issued on June 18, 1987 (WO 87/03528), the US patent issued on
December 11, 1990 (US 4,976,582), and the
European patent issued on July 17, 1991 (EP 0
250 470). Overall, these patents protect the invention in USA, Canada , Japan, and most West
European countries. The patents do not specify the way in which the Delta structure is actuated in order to incorporate the basic design as well as its variants [7]. The Delta robot is mostly used as a pick-and-place
robot ( C33 and CE33 Ro bots, fig.3.17, from SIG
pack Systems-from 2 004 part of Packaging
Technology division of Bo sch and IRB 340 Flex
Picker Robot from ABB Automation fig. 3.7), although there exist some other applications in
medicine (SurgiScope fig.3.12)- and machine tools (Krause & Mauser Group Quic kstep 3-axis milling
machine is in fact Delta robot with linear motors, fig. 3.18).
The Delta robot was licensed to various companies.
In addition, some machine tool manufacturers managed to get their own patents and have built parallel kinematics machines based on the Delta robot architecture.

Figure 3.17 Two of the three Delta robot models offered
by SIG Pack Systems, C33 and CE33 (courtesy of SIG
Pack Systems-now Bosch Packaging Technology
division)

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| 156 | 

Figure 3.18 The Quickstep 3-axis machining center and
Quickstep's kinematic structure [58]
– FANUC parallel robot
Another sucssesful type of parallel robot is F-200iB
(fig 3.19) a product of FANUC Robotics North America of Rochester Hills , MI. The F-200iB is a
six degrees of freedom serv o-driven parallel link
robot designed for use in a variety of
manufacturing and automoti ve assembly processes.

Figure 3.19 A FANUC parallel robot F-200iB [57]
(US patent No. 5987726) [51]
The F-200iB is engineered for applications
requiring extreme rigidity and exceptional repeatability in a compact, powerful package. F-200iB, the solution for: sub-compact robot welding,
pedestal welding, part loading/positioning, nut
running, vehicle lift and lo cate, flexible/convertible
fixturing, material remova l, dispense. The F-200i
is very rigid when compared to serial linked robots. There is less flexing of the arms and high repeatability. With serial li nked robots, the end-of-
arm flexing errors are cumula tive. In a parallel link
structure they are average d. Compared to a serial
link machine, this type of robot has a small range of
motion due to the configuration of the axes,
although it has a broad mix of applications. It has motion speed in vertical z axis 300 (mm/sec), in horizontal x and y ax es 1500 (mm/sec) and
repeatability ± 0.1(mm). Other atypical applicatio ns for the F-200iB include
education, medical and sc ientific research uses.
– TRICEPT robot
In 1987 a new type of robot, the 3 DOF parallel
kinematic robot, was designed and built by Karl-Erik Neumann (fig.3.20). Th is type of robot has
three or more linear axes wh ich function parallel to
one another. It has three prismatic actuators which
control two rotational and one translational degree
of freedom of the mobile platform. A conventional
wrist is additionally mounted on the mobile platform (fig.3.21)

Figure 3.20 3-DOF Parallel kinematic robot Tricept
(US Patent No.: US 4,732,525) [51]

Figure 3.21 Parallel kinematic robot Tricept IRB 940 [50]
The initial challenge for this system was that it
required computer power that was unavailable at the time. Karl-Erik Neumann, the inventor of the Tricept robot, explains: ''There was no control
system to run the mach ine until 1992 when the
company Comau Pico launched the first multiprocessor controller. That, and open architecture, made it so we could adapt its complex kinematics [10]. Neumann founded Neos Robotics in Sweden. Neos Robotics has purchased another Swedish machining company, and strated to go under the name of SMT Tricept. Now SMT Tricept is in a
strategic alliance with ABB robotics.
The Tricept robot is the system that greatly influenced the parallel kinematic robot phenomenon. Although initially designed as an assembly robot, the demands from the market transformed it into a machine tool. This market demand led introduction in 1999 of Tricept model 805, a larger version of Tric ept. This was developed
as a machine tool robot, which combined the
flexibility of a robot with the stiffness of a machine
tool. The last few years, the biggest application of Tricept is metal cutting. The Tricept can also be used to hold laser and saw cutting tools, as well as friction welders. Customers who use Tricept robots

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| 157 | include automobile makers in Europe and North
America: Peugeot, Ford, Renault, Volvo, General
Motors, BMW, and Volkswagen. The aerospace
industry uses Tricept robots for fabricating propellers, turbine blades, impellers and any other item that requires a co nsiderable amount of
contouring. Other applications for the Tricept include assembly with thrust, deburring, polishing, woodworking, water-jet cutting and spot-welding. In October 2002 ABB and SMT Tricept launched
the last type of an except ionally powerful and stiff
Tricept robot IRB 940 – fo r heavy-duty cleaning
and pre-machining of aluminium parts (vertical machining power of 1300 k g, horizontal machining
power of 350 kg, accuracy ± 0.2 mm, and repeatability of ± 0.02 mm). IRB 940 Tricept is designed to form an integrated
part of optimized production lines, teaming up with traditional arm robots and CNC machine
tools. Arm robots handle material, machine
tending and light cleaning. Tricept robots then take over to do heavy-duty cleaning and pre-machining, while CNC machines put the finishing touches to cleaning and part processing. Main characteristics of the parallel robots are given
in the table below:
Table 3.1. Characteristics of parallel
Feature Parallel robot
Workspace Small and complex
Solving forward kinematics Very difficult
Solving inverse kinematic Easy
Position error Averages
Force error Accumulates
Maximum force Summation of all actuator
forces
Stiffness High
Dynamics characteristics Very high
Modelling and solving
dynamics Very complex
Inertia Small
Areas of application Currently limited,
especially in industry
Payload/weight ratio High
Speed and acceleration High
Accuracy High
Uniformity of components High
Calibration Complicated
Workspace/robot size ratio Low

Comparison of the characteristics of serial
and parallel robots Table below gives comparison between main characteristics of serial and parallel robots: Table 4.1. Caracteristics of serial and parallel robots
Feature Serial robot Parallel robot
Workspace Large Small and
complex
Solving forward
kinematics Easy Very difficult
Solving inverse
kinematics Difficult Easy
Position error Accumulates Averages
Force error Averages Accumulates
Maximum force Limited by
minimum
actuator force Summation of
all actuator
forces
Stiffness Low High
Dynamics
characteristics Poor, especially
with increasing
the size Very high
Modelling and
solving dynamics Relatively simple Very complex
Inertia Large Small
Areas of
application A great number
in different areas,
especially in
industry Currently
limited,
especially in
industry
Payload/weight
ratio Low High
Speed and
acceleration Low High
Accuracy Low High
Uniformity of
components Low High
Calibration Relatively simple Complicated
Workspace/robot
size ratio High Low

CONCLUSION
If we analyse the table 4.1 we will see that the both
types of robots have a dvantages and disadvantages.
For example parallel robots offer potential
advantages compared with serial, with higher overall stiffness, higher precision, low inertia, and higher operating speeds and accelerations. However these advantages could be easy relativised by reduced workspace, diff icult mechanical design,
and more complex kinematics and control algorithms. It is really very difficult to say what kind of robot
is better, serial or pa rallel. A robot selection
procedure is very difficul t and complex activity. It
depends on many different factors like type of
application (dangerous, repetitive and boring, precise, etc.), task requirements (DOF, speed, accuracy, repeatability) , load requirements,
workspace, economic just ification, programming
time, maintaining, etc. Parallel robots are most successful in applications
like motion simulators, ultra precision positioning
devices, medical applicatio ns, ultra-fast pick and

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| 158 | place robots and micro-rob ots. But serial robots
dominate almost in all ma nufacturing applications.
Probably this will change with continuously
solving of the open problems in parallel robotics given in [38, 39] or us ing hybrid structures.
Hybrid structures are in fact compromise between advantages and disadva ntages of both robot
structures, serial and parallel. The two most successful manufacturing applications of parallel robots are in fact hybri d structures. First one,
Tricept robot is (parallel- serial) structure, 3-axis
parallel machine tool-robot plus 2-axis,
conventional serial wrist. The second, Sprint Z3 3-axis parallel kinematic tool head by DS Technologie (fig.5.1) that may advance in Z and tilt in all directions, and may be mounted on a conventional XY stage. The machining centre lines
ECOSPEED and ECOLINER equipped with the Sprint Z3 tool head are in fact hybrid structures
(serial-parallel).
This two robot structures probably will live
parallel a long years. If we compare about 20 years research in parallel mechanisms and more than 200 years in research to re ach the current level of
knowledge for serial mechan isms, it is easy to
conclude that this process of solving problems in parallel robotics will be long term.

Figure 5.1. Sprint Z3 parallel kinematic tool head [54]
ACKNOWLEDGMENTS This research was done during my research stay at the Department of Machine Tools and Automation, TU Hamburg-Harburg, Germany, financed by DFG (Deutsche Forschungsgemeinschaft).
REFERENCES/BIBLIOGRAPHY
[1.] ALAZARD D., CHRETIEN J.P., 1994, Dexterous
External Space Manipulation: Serial Or Parallel Concepts Comparison, Proceedings of the IFAC Automatic Control in A erospace 94, Palo Alto
(CA), USA, Sept. 12th-16th, 1994
[2.] ANGELES J., YANG G., CHEN I. M., 2001,
Singularity Analysis of Three-Legged, Six-DOF Platform Manipulators with RRRS Legs, 2001 IEEE/ASME International Conference on Advanced Intelligent Mech atronics Proceedings, 8-
12 July 2001, Como, Italy, pp.32-36
[3.] ANGELES J., YANG G., CHEN I. M., 2003,
Singularity Analysis of Three-Legged, Six-DOF Platform Manipulato rs With URS Legs,
IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 8, NO. 4, DECEMBER 2003, pp.469-475
[4.] ARAI, T., CLEARY, K., HOMMA, K., ADACHI,
H., AND NAKAMURA, T., 1991, Development of Parallel Link Manipulator for Underground Excavation Task, Proc. 1991 International Symposium on Advanced Robot Technology, pp.
541-548, 1991.
[5.] BI Z., 2002, Adaptive Robot Systems for
Manufacturing Applications, Ph.D. Thesis, Department of Mechanical Engineering, University of Saskatchewan Saskatoon
[6.] BLÜMLEIN W. J., 1999, The Hexapod, Maschine
+ Werkzeug, 10/99
[7.] BONEV I., 2001, Delta Parallel Robot — the
Story of Success, /www.parallemic.org/
[8.] BONEV A. I., RYU J., KIM S. G. AND LEE S.
K., 2001, A Closed-Form Solution to the Direct Kinematics of Nearly General Parallel Manipulators with Optima lly LocatedThree Linear
Extra Sensors, TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 17, NO. 2, APRIL 2001, pp.148-156
[9.] BROGARDH T., 2002, PKM Research –
Important Issues, as seen from a Product Development Perspective at ABB Robotics, Proceedings of the WORKSHOP on Fundamental
Issues and Future Research Directions for Parallel
Mechanisms and Manipulators October 3–4, 2002, Quebec City, Quebec, Canada, pp.68-82
[10.] BRUMSON B., 2002, Parallel Kinematic Robots,
/www.roboticsonline.com/public/ articles/
[11.] CALLEGARI M. AND MARZETTI, P. 2004,
Kinematic Characterisation of a 3-PUU Parallel Robot, Proc. Intelligent Manipulation and Grasping: IMG04 (R. Molfino Ed.), Genova, June 30-July 1, 2004, pp. 377-382
[12.] CHABLAT D., CARO S., WENGER P. ET
ANGELES J., 2002, The Isoconditioning Loci of Planar Three-DOF Parallel Manipulators, 4ème Conférence Internationale su r la Conception et la
fabrication Intégrées en Mécanique, IDMME,Clermont-Ferrand, France, Mai,2002.
[13.] CHEN S.-L. AND YOU I.-T., 2000, Kinematic
and Singularity Analyses of a Six DOF 6-3-3 Parallel Link Machine Tool, Int J Adv Manuf Technol (2000) 16:835–842
[14.] CODOUREY A., HONEGGER M., BURDET E.,
1997, A Body-oriented Method for Dynamic

ACTA TEHNICA CORVINIENSIS Fascicule 1 [January – March]
– Bulletin of Engineering Tome VII [2014]
| 159 | Modeling and Adaptive Control of Fully Parallel
Robots, SYROCO'97, Nantes, France, September 1997
[15.] DANIALI H. R. M., MURRAY P. J. Z.,
ANGELES J., 1996, Di rect Kinematics of
Double_Triangular Parallel Manipulators, Mathematica Pannonica 7/1 (1996), pp.79-96
[16.] FALCO, J.A., 1997, Simulation Tools for
Collaborative Exploration of Hexapod Machine Capabilities and Applications, Proceedings of the 1997 International Simulation Conference and Technology Showcase, Auburn Hills, MI, September 29 – October 3, 1997
[17.] FAULRING E. L., COLGATE J. E. AND
PESHKIN M. A., 2004, A High Performance 6-DOF Haptic Cobot, Proceedings of IEEE International Conference on Robotics and Automation, 2004
[18.] GALLARDO J., RICO J.M., FRISOLI A. ,
CHECCACCI D., BERGAMASCO M., 2003, Dynamics of parallel manipulators by means of screw theory, Mechanism and Machine Theory 38
(2003) pp. 1113–1131
[19.] GAO X.-S., LEI D., LIAO Q., ZHANG G.-F.,
2005, Generalized Stewart–Gough Platforms and Their Direct Kinematics, IEEE TRANSACTIONS ON ROBOTICS, VOL. 21, NO. 2, APRIL 2005, pp.141-150
[20.] GIDDINGS AND LEWIS, 1995, Giddings and
Lewis Machine Tools, Fond du Lac, WI, 1995.
[21.] GOSSELIN C., ANGELES J., 1990, Singularity
analysis of closed-loop kinematic chains, IEEE Trans. on Robotics and Automation, 6(3), June
1990, pp.281-290.
[22.] GOSSELIN, C. AND HAMEL, J., 1994, The Agile
Eye: A High – Performance Three – Degree – of – Freedom Camera-Orienting Device, Proc. IEEE International Conference on Robotics and Automation, pp. 781-786, 1994.
[23.] GOUGH V. E., WITEHALL S. G., 1962,
Universal Tire Test Machine, Proceedings of the 9th International Automobile Technical Congress FISITA, London (UK), ImechE (pp. 117 – 137) 1962.
[24.] HAYES M. J. D., MURRAY P. J. Z., CHEN C.,
2004, Unified Kinematic Analysis of General Planar Parallel Manipulators, Journal of Mechanical Design 2004 by ASME, September 2004, Vol. 126 , pp.1-10
[25.] HUANG Q., HADEBY H. AND SOHLENIUS
G., 2002, Connection Method for Dynamic Modelling and Simulation of Parallel Kinematic Mechanism (PKM) Machines, Int J Adv Manuf Technol (2002) 19: pp.163–173 [26.] HUNT, K.H., 1983, Structural Kinematics of In-
Parallel-Actuated Robot Arms, ASME Journal of
Mechanisms, Transmissions, and Automation in Design, Vol. 105, pp. 705-712.
[27.] JAKOBOVIC D., BUDIN L., 2002, Forward
Kinematics of a Stewart Platform Mechanism, INES 2002, 6th Internat ional Conference on
Intelligent Engineering Systems 2002, Opatija, Croatia
[28.] JIN Y., CHEN I-M., YANG G., 2004, Structure
synthesis and singularity analysis of a parallel
manipulator based on selective actuation, Proceedings of IEEE Int. Conf. on Robotics and Automation, pages 4533-4538, New Orleans, 28-30 April 2004
[29.] KHALIL W., GUEGAN S., 2001, A New Method
for the Dynamic Formulation of Parallel Manipulators, Journées Franco-Mexicaines d'automatique appliquée, 12-14 Septembre, 2001
[30.] KIM D. AND CHUNG, W., 1999, Analytic
Singularity Equation and Analysis of Six-DOF Parallel Manipulators Using Local Structurization Method, IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 15, NO. 4, AUGUST 1999, pp.612-622
[31.] KONG X., GOSSELIN C. M., 2002, Kinematics
and Singularity Analysis of a Novel Type of 3-CRR 3-DOF Translational Parallel Manipulator, The International Journal of Ro botics Research, Vol. 21,
No. 9, September 2002, pp. 791-798,
[32.] KOVECSES J., PIEDBOEUF J.-C., LANGE C.,
2002, Methods for Dynamic Models of Parallel Robots and Mechanisms, Proceedings of the
WORKSHOP on Fundamental Issues and Future
Research Directions for Parallel Mechanisms and Manipulators October 3–4, 2002, Quebec City, Quebec, Canada, pp.339-347
[33.] LIU G., LOU Y., AND LI, Z. 2003, Singularities
of Parallel Manipulators: A Geometric Treatment,
IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 19, NO. 4, AUGUST 2003, pp.579-594
[34.] McAREE P. R., SELIG J. M., 1999, Constrained
Robot Dynamics II: Parall el Machines, Journal of
Robotic Systems 16(9), 487-498 (1999)
[35.] MERLET J-P., 1999, Forward kinematics of
parallel robots, Proceedings of IMACS Conf. on Applications of Computer Algebra, El Escorial, 24-27 June 1999
[36.] MILLER K., 2001, Dynamics of the New UWA
Robot, ACRA 2001,Australian Conference on Robotics and Automation, Sydney, 14 – 15 November 2001, pp.1-6
[37.] NANUA P., WALDRON K.J., 1989, Direct
kinematic solution of a Stewart platform,

ACTA TEHNICA CORVINIENSIS Fascicule 1 [January – March]
– Bulletin of Engineering Tome VII [2014]  
| 160 | Proceedings of the IEEE Int. Conf. on Robotics and
Automation, Scottsdale, 14-19 May 1989, pp. 431-437
[38.] PANDILOV Z., V. DUKOVSKI V., 2011, Several
open problems in parallel robotics, ACTA TECHNICA CORVINIENSIS-Bulletin of Engineering, Tome IV (Y ear 2011), Fascicule 3
(July-September), pp. 77-84, ISSN 2067-3809
[39.] PANDILOV Z., RALL K., 2008, Open problems in
parallel robotics. Mechanic al Engineering-Scientific
Journal, Published by Faculty Mechanical Engineering, Ss. Cyril an d Methodius University,
Skopje, Vol.27, No.1, (2 008), pp.31-41. CODEN:
MINSC5-392, ISSN 1857-5293.
[40.] REINHOLTZ, C. AND GOKHALE, D., 1987,
Desgin and Analysis of Variable Geometry Truss Robot, Proc. 9
th Applied Mechanisms Conference,
Oklahoma State University, Stillwater, OK, USA.
[41.] SADJADIAN H., TAGHIRAD H.D., FATEHI A.,
2005, Neural Networks Approaches for Computing the Forward Kinematics of a Redundant Parallel Manipulator, International Journal of Computational Intelligence Volume 2 Number 1 2005, pp.40-47
[42.] SELLGREN U. AND PETTERSSON J., 2001,
Modeling of conformal mechanical interfaces in technical systems, Proc. of NAFEMS World Congress, April 24-28, La ke Como, Italy, pp. 943-
954.
[43.] STEWART, D., 1965, A Platform with Six Degrees
of Freedom, Proc. Inst. Mech. Eng. London, Vol 180, 1965, pp. 371-386.
[44.] TODD, D.J., 1986, Fundamentals of Robot
Technology, Kogan Page, 1986.
[45.] TSAI L. W., 1999, Robot Analysis: The Mechanics
of Serial and Parallel Manipulators, New York: John Wiley & Sons, Inc., 1999.
[46.] WALDRON, K. J., VOHNOUT, V.J., PERY, A.,
AND MCGHEE, R.B., 1984, Configuration Design of the Adaptive Susp ension Vehicle, Int. J.
Robot. Res., Vol. 3, 1984, pp. 37-48
[47.] WALDRON K.J. ET HUNT K.H., 1987, Series-
parallel dualities in actively coordinated mechanisms, Proccedings of 4th ISRR, Cambridge, MA, pp. 175-182
[48.] WANG J., TANG X., DUAN G., LI J., 2001,
Design Methodlology For a Novel Planar Three Degrees of Freedom Parallel Machine Tool, Proceedings of the 20 01 IEEE International
Conference on Robotics & Automation Seoul, Korea . May 21-26, pp.2448-2453
[49.] W I L L I A M S I I R . L . , J O S H I , A . R . 1 9 9 9 , P l a n a r
Parallel 3-RPR Manipulator, Proceedings of the Sixth Conference on Applied Mechanisms and Robotics, Cincinnati OH, December 12-15, 1999 [50.] www.abb.com
[51.] www.delphion.com
[52.] www.alioindustries.com /p arkin_robotics.htm
[53.] www.cmtec.com/contmeas/motion.htm
[54.] www.ds-technologie.de
[55.] www.moog.com
[56.] www.fanuc.co.jp
[57.] www.fanucrobotics.com
[58.] www.parallemic.org
[59.] www.physikinstrumente.de/products
[60.] www.physikinstrumente.com/ micropositioningsyst
ems
[61.] www-sop.inria.fr
[62.] YANG G., CHEN I.-M., LIN W. AND ANGELES
J., 2001, Singularity An alysis of Three-Legged
Parallel Robots Based on Passive-Joint Velocities,
IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 17, NO. 4, AUGUST 2001, pp. 413-422
[63.] YIU Y.K., AND LI Z.X., 2001-1, Modeling
Configuration Space and Si ngularities of Parallel
Mechanisms, International Conference on Mechatronics Technology, 6 – 8 June 2001, Singapore pp. 298-303
[64.] YIU Y.K., AND LI Z.X., 2001-2, Dynamics of a
Planar 2-dof Redundant Parallel Robot, International Conference on Mechatronics Technology, 6 – 8 June 2001, Singapore, pp.339-344
[65.] ZHAO X. AND PENG S., 2000-1, Uncertainty
configurations of parallel manipulators, Robotica (2000) volume 18, pp. 209–211.
[66.] ZHAO X., PENG S., 2000-2, Direct Displacement
Analysis of Parallel Manipulators, Journal of
Robotic Systems 17(6), (2000), pp.341-345
[67.] ZHOU K., MAO D. AND TAO Z., 2002,
Kinematic Analysis and Application Research on a High-Speed Travelling Doub le Four-Rod Spatial
Parallel Mechanism, Int J Adv Manuf Technol (2002) 19: pp.873–878
[68.] ZLATANOV, D., BONEV, I.A., GOSSELIN,
C.M., 2002, Constraint Singularities as C-Space Singularities, 8th Int ernational Symposium on
Advances in Robot Kinematics (ARK 2002), Caldes de Malavella, Spain, 24–28 June, 2002.
[69.] ZOPPI M., BUZZONE L. E., MOLFINO R. M.,
NICHELINI R. C., 2003, Constraint Singularities of Force Transmission in Nonredundant Parallel
Robots With Less Than Six Degrees of Freedom, Journal of Mechanical Design 2003 SEPTEMBER 2003, Vol. 125, pp. 557-563