Analysis and design of parallel mechanisms for manufacturing

Summary
 2
Innovative Production Systems, Theme 6 (SPI6). The industrial context is described 
and then the final layout of the Dragon Fly PKM is obtained, in terms of position of 
the joints’ ideal center and legs stroke. However, the conceptual design is not enough 
to completely characterize the mechanical behavior of the machine, especially when 
the legs are subjected also to torsion and flexural loads.  
Thus, in Chapter 4 the mechanical design steps of the Dragon Fly prototype are 
described. In the first part of the Chapter, several analyses are performed, in order to 
evaluate the actuator efforts, due not only to external loads but also to gravity and 
inertial effects and to compute the internal loads. Furthermore, the effects of 
manufacturing and assembling errors on the accuracy of the machine and, dually, the 
compliance at the tool tip due to lumped compliances in the structure are estimated, to 
verify if the prototype meets the initial requirements. The main mechanical design 
issues are introduced, and a FEM analysis is performed on the kinematic chain: joint-
leg-joint to individuate the critical elements to stiffen. Next, some considerations on 
the side roughing and gluing work cell are done and its whole control system is briefly 
described. Finally, a calibration strategy is proposed to evaluate and compensate the 
predictable kinematic errors. 
Chapter 5 will draw some conclusions forwarding the future developments of 
the work here presented. 
Appendix 1 gives an up to date review of the most successful PKMs, and of 
the most promising ones, ending up with a comparison table specifying the available 
technical characteristics of 26 prototypes. 
Appendix 2 presents some pictures of the Dragon Fly prototypes, during the 
assembly phase and then installed in the pilot plant, final result of the research project 
SPI6. 
Although parallel kinematic machines (here and after PKM) are well known since 
the early 60s, and in 1966 Tindale specifically discussed the use of PKM for 
machining processes, only in the last decade has a great interest grown for the 
application of these mechanisms in manufacturing. The aim of this Chapter is to give 
an up to date review on the still open research topics in the field of PKMs, with 
particular regards to their manufacturing applications. Advantages and disadvantages 
of PKMs over traditional machining centres are discussed, examining generic aspects 
and dissimilarities.  First, the classification issues and systematic design 
methodologies are debated.  Then, the fundamentals in kinematics, dynamics, errors 
analysis, calibration and control topics are introduced and discussed, highlighting the 
still open research topics.  Finally, a non exhaustive list of PKM prototypes is 
provided.  
1.1 Introduction 
The PKMs nowadays used in industry are mainly applied in traditional robotic 
fields (i.e. pick and place) and for high precision positioning. These applications 
exploit some of the characteristics of parallel kinematic chains, in particular, the 
lightness of structures and consequently their low inertia that allows high speed rate
and acceleration (up to 10g for the Demaureux’s Delta robot, shown in Fig. 1 and 
described in detail in App. 1). On the other side, the high payload to weight ratio, 
combined with the intrinsic structural rigidity given by the parallel links, make 
feasible the use of PKMs for high precision positioning.  Furthermore, their potential 
in manoeuvring quickly and precisely heavy objects or objects under large force has 
led to the development of many applications, from physical motion simulation (flight, 
truck, tank, horse-riding) to medical (position surgical tools), to space application 
(docking system), machining, assembly and disassembly. Many more applications 
have been envisioned by researchers worldwide. 
Chapter 1
PKMs in Manufacturing:
State of the Art
Chapter 1  PKMs and Traditional multi axis machining
 7
The first CNC type hexapod machine tool prototypes (Variax of Giddings & Lewis, 
the Octahedral of Ingersoll and the Geodetic Technologies G500) were presented in 
the International Machine Tool Show (Chicago, 1994). They were enthusiastically 
welcomed as the new generation of machine tools, due to their specific characteristics 
that should guarantee better performances, namely:  
• higher payload to weight ratio (the payload is carried by several links in 
parallel); 
• non cumulative joint error; 
• higher structural rigidity (the load is carried by the parallel links, and in some 
structures there are only compression-tension modes); 
• modularity (each kinematic chain is composed of the same physical modules); 
• location of motors close to the fixed base; and 
• simpler solution of the ‘inverse’ kinematic problem. 
All these advantages induced machine tool builders and researchers to investigate the 
applications of PKM for 5 axis machining, a field where the traditional machine tools 
have not gained the hoped success. 
Since the 1994 debut, several other prototypes of the parallel kinematic machine 
tools have been built and are under evaluation. Conversely, the drawbacks came out. 
PKMs suffer from singular configurations, a well known problem in the robotics field, 
low workspace to footprint ratio, a complicated forward kinematic solution, and, 
consequently, more difficult control techniques. The kinematic and dynamic behavior 
of the physical machine is strongly influenced by manufacturing tolerances and 
assembly errors, and so, especially for machining applications, calibration strategies 
must be defined and consolidated. Several topics are still research items. 
Hence, the question persists: will the full potentials of the parallel kinematic 
machines be realised so that the innovative ideas can become practical production?   
In the next paragraphs, the still open research areas for PKMs are discussed, 
highlighting similarities and dissimilarities with serial devices for manufacturing 
applications.  
1.2 Configuration & Classification 
The most famous PKM is the so-called Stewart-Gough-Gough platform. In 1962, 
Gough and Whitehall devised a six linear jack system for use as universal tyre-testing 
machine. Later on, in 1965, Stewart, a senior mechanical engineer from Elliott 
Automation, Space and Weapons Research Establishment, Frimley, Hampshire, 
proposed a 3 legs- 6 dof platform for use as an aircraft simulator. In his paper, he 
suggested the use of a similar architecture for many other applications
1
, including 
machining.  
                                               
1
 He suggests the following applications: ‘(a) As a vehicle for representing a body in space, subjected 
to all the forces which may be met within its voyage; (b) As representing a platform held stationary in 
space mounted on a vessel such as a ship which is subjected to the random movements of sea; (c) As a 
platform for simulating the actions of helicopter as driven by its pilot, or; (d) As a support for a 
helicopter which is capable of being driven by the pilot, random actions being applied to the supporting 
platform as prescribed; (e) As any vehicle which is subject to control by a human being; (f) As a basis 
of design for a new form of machine tool; (g) As a basis of design for an automatic assembly or transfer 
machine.’  
And… these, up to now, are the most common applications for PKMs, among with high precision 
positioning and surgical and micro-surgical parallel devices. 
Chapter 1  PKMs and Traditional multi axis machining
 8
The general Stewart-Gough platform, is a mechanism (with 6 degrees of freedom) 
with one base (with associated reference frame O
B
X
B
Y
B
Z
B
) connected by six 
extensible legs to the mobile platform (with associated reference frame O
M
X
M
Y
M
Z
M
)
(see Figure 1 (a)). The six legs have spherical joints at both ends (or spherical joints 
on the mobile platform and universal joint on the base). Several works reported in 
literature concern with its mobility [among them, Innocenti, et al, 1992, 1994, 
Faugère, et al, 1995], design and simulation [Fichter, 1986, Bhattacharya, 1995, 
Huang, et al, 1998]; forward position kinematic [Merlet, 2000, Innocenti, 1992, 
Dasgupta, et al, 1994, Husty, 1996]; singularity, stiffness mapping [Gosselin, 1990, 
Ma, et al, 1991, Liu, et al, 1993, El Kawasaneh, et al, 1997, 1999] and workspace 
issues [Ji, 1996, Merlet, 1995, 2000]. 
(a) (b)
Figure 1.1 - (a) Structure of a generalized Stewart-Gough platform. (b) Structure of a 6-3 Stewart-
Gough platform. This mechanism - when the base and the mobile platform are symmetric - is also 
called Triangular Symmetric Simplified Manipulator- TSSM- (Merlet, 2000). 
Many other topologies arise from the coalescence of some of the attachment-points in 
the base or in the mobile platform or both. One interesting example is characterized 
by six distinct joints in the base and three distinct joints in the platform (see Figure 1.1 
(b)). Its practical construction, however, is limited by the difficulties in manufacturing 
a reliable and accurate double spherical joint. 
  Dasgupta et al., 2000, extensively reviewed the literature to identify the trends on 
research and the open problems on Stewart-Gough platform, considering this device 
as representative of the entire class of PKM.  Nevertheless, other types of PKM have 
been explored in several scientific works (Pierrot, et al., 1990; Albus, et al., 1993; 
Tsai, 1996 and 1999; Kim, et al., 1997; Ryu, et al., 1999; Di Gregorio, et al., 1998; 
Company, et al., 1999, Tönshoff, 1999a, , Heisel, et al, 2000), and prototypes with 
different architectures (and different driving principles) have been built. Their kineto-
static and dynamics models, as well as their physical behavior, can’t be reduced to the 
Stewart-Gough Platform’s. Therefore, hereafter, the PKM classification commonly 
used is presented and systematic design criteria discussed. 
Among the multiple possible configurations of parallel devices, a first distinction 
between fully-parallel and hybrid kinematic chains must be done. In the fully PKM, 
the degrees of freedom of the machine are all due to the parallel device (i.e. the 
Ingersoll machine), while in the hybrid PKM a serial device contributes to the total 
dof (i.e. Tricept). In this thesis, even if both a hybrid prototype and a fully parallel 
Chapter 1  PKMs and Traditional multi axis machining
 9
PKM will be studied, only the parallel part of the devices is considered, in terms of 
classification, kineto-static analysis and optimization. The fully serial chain 
classification encompasses the traditional multiaxis machines as well as the majority 
of industrial robots (Fig.1.3).  
Almost all the existing machines’ configurations can be grouped considering which 
joints of the kinematic chain are actively controlled, i.e. which are the active variables 
in the kinematic model. Using this principle, the following classification, shown in 
Fig. 1.2, can be obtained (Negri, et al., 1999): 
• type (a): Machines with variable leg lengths and fixed joints (i.e. Ingersoll like 
machines), commonly known as Stewart Gough platforms. 
• type (b): Machines with fixed leg lengths and base joints movable on linear 
guideways (i.e. Triaglide or Linapod like machines). 
• type (c): Machines with equivalent extensible legs, consisting of two fixed length 
legs and actuated by a revolute joint. (i.e. Delta like machines) 
Fig. 1.2 The PKM classification 
1.2.1 Systematic Enumeration and Design Methodologies  
The need for a configuration software tool that helps the designer in the synthesis 
of a new PKM and in a rapid evaluation of its kinematic performances has been 
addressed in some recent works. In Pritshow, et al., 1997, a systematic procedure for 
the configuration of PKMs for metalwork is presented, while in Molinari-Tosatti, et 
al., 1998; Fassi, et al., 1999, and Bianchi, et al, 2000 an integrated methodology for 
the kineto-static performances evaluation of a generic PKM is described.  
Tsai, 1999, proposed a design methodology based on the mobility analysis and 
Gruebler equation, for the synthesis of both planar and spatial parallel mechanisms, 
with all actuated legs and binary kinematic chains connecting the base with the 
platform. Zanganeh, et al., 1998, developed a formalism to analyse and design serial, 
parallel and hybrid manipulators. They identify and combine different kinematic 
(a)
Stewart Platform 
like. 
Extensible legs. 
(b)
Triaglide like. 
Non extensible legs.
Base joints moveable 
on parallel guideways
(c)
Delta like. 
Equivalent 
extensible legs.
Chapter 1  PKMs and Traditional multi axis machining
 10
modules in the search for all the possible configurations that satisfy a given set of 
functional requirements.  
Innocenti, et al., 1994, proposed a code for the exhaustive enumeration of all 
PKM with 6 binary kinematic chains connecting the base to the mobile platform. 
Faugère, et al. (1995), have obtained similar results, counting 21 different topologies.  
In accordance with to the classification introduced by Faugère and Lazard, and by 
Innocenti and Parenti-Castelli, it’s possible to apply only the combinatorial criterion, 
which consists in sub-classifying the PKMs of type (a) by the number of spherical 
joints on the base and on the platform. Each mechanism is modeled by a graph, the 
edges of it being the legs, the upper vertices being the joints on the mobile platform 
and the lower vertices being the joints on the base.  
Neglecting the classes characterized by zero or infinite number of possible assembly 
configurations, and identifying with N
B
 the number of joints on the base and with N
M
the number of joints on the mobile platform, all the combinatorial classes can be 
represented with the following matrix: 
N
M
=6    1 
N
M
=5   2 1 
N
M
=4  11 5 2 
N
M
=3 4 7 4 2 
 N
B
=3 N
B
=4 N
B
=5 N
B
=6
Although the theoretical contributions to the systematic design and enumeration of 
parallel mechanisms show a wide variety of PKM topologies, the real prototypes 
consist of only a very few number of configurations, mainly due to the fact that:  
• joints connecting more than three rigid bodies (including the platforms) are hard 
to manufacture; 
• it is preferable to have independent actuated legs.   
So, the possible 6 legs- 6 d.o.f. configurations are limited to the 6-6, and 6-3.  
Fig.1.3 Serial kinematic chains 
X
Y
Z
*
I
II
t.m.
s.
m.
t.p.
(b)
The Stanford 
Manipulator 
(a) 
A schematic view of 
the basic modules of a 
milling machine 
Chapter 1  PKMs and Traditional multi axis machining
 11
Also for traditional machine tools, the need of flexible production, among with 
faster ramp-up times for new manufacturing systems, has addressed many research 
works also in the field of systematic design methodologies. Recently, the design of 
traditional multiaxis machines has taken on a new methodology under the auspice of 
‘Reconfigurable Manufacturing Systems’ (Koren, et al., 1996). Instead of designs 
based on the axis payload, range of motion, resolution and linear accuracy, this 
methodology allows for varying the order and orientation of joint axes and rigid 
machine structure components, e. g. rigid machine structure between the XY staged 
table and spindle orientation axis.  Similarly, a modular approach to the functional 
design of machine tools was carried out within the European Project Mosyn (BE95-
1532).  One of the goals included the development of a CAC (Computer Aided 
Configuration) Tool for the design of modular advanced machine tools. 
Hereafter, the CAC tool for PKMs, developed at ITIA within the research project 
Robotool, is introduced. 
1.2.1.1 A Functional Design Methodology 
In general, a systematic conceptual design methodology consists of two engines: a 
generator and an evaluator. This methodology has been synthetically represented by 
Tsai, 1999, with the flowchart in Fig. 1.4, and can be easily applied to the systematic 
design of PKMs. 
Fig.1.4 Flow chart of the design step in a systematic design methodology 
Specifically, some of the functional requirements identified from the customer’s needs 
are transformed into structural characteristics. These structural characteristics are 
incorporated as rules in the generator. The generator defines all possible solutions via 
a combinatorial analysis. The remaining functional requirements are incorporated as 
evaluation criteria in the evaluator to screen out infeasible solutions. This results in a 
set of candidate mechanisms. Finally, a most promising candidate is chosen for 
product design. How many of the desired functional requirements should be 
incorporated in the generator is a matter of engineering compromise. The more 
functional requirements are translated into structural characteristics and incorporated 
Chapter 1  PKMs and Traditional multi axis machining
 12
in the generator, the less work is required of the evaluator. However, this may make 
the generator too complex to develop.  
In the implementation developed at ITIA, and described in Fassi, et al, 1999, the 
generator is structured as a Decision Support System (DSS) to guide the designer in 
choosing the more appropriate PKM topological configuration and in defining its 
geometry.  
The following rules have been implemented: 
• the mechanisms of interest are closed-loop mechanisms. Specifically, they consist 
of a moving platform that is connected to a fixed base by several limbs.  
• The moving platform is to be used as the end-effector. 
• The mechanisms of interest possess multiple degrees of freedom. The number of 
DOF (3 - with or without passive limbs - or 6 in the first version of the Computer 
Aided Configuration Tool) depends on the intended application. 
• the number of active limbs is equal to the number of DOF: only one actuated joint 
is required for each limb and all actuators can share the load on the moving 
platform. 
• all actuators are to be mounted on or near the fixed base. This condition implies 
that there is a base-connected revolute or prismatic joint in each limb, or a 
prismatic joint that is adjacent to a base-connected joint. 
1.3 Kinematics 
During the past 15 years, extensive work has been done in solving the forward 
kinematics analysis of PKM, especially of Stewart like mechanisms, because of their 
high degree of complexity. The problem is determining position and orientation of the 
mobile platform given the legs lengths, or, more in general, assigned the active joints 
variables. For the traditional multiaxis machines, the joint motions are staged, 
orthogonal linear axis with at most two rotational axes at the spindle side. These joint 
arrangements simplify the kinematics to a direct mapping between the machining task 
space and the actuator space.  While for serial manipulators the direct kinematics is 
simple, and the reverse analysis requires the resolution of nonlinear equations, the 
problem is dual for PKM. Nowadays the forward kinematics is solved for most PKM, 
Stewart Platform included, both via numerical approximations and in closed form 
(Nanua, et al., 1990; Innocenti, et al., 1992; Dasgupta, et al., 1994; Husty, 1996; 
Innocenti, 1998). Furthermore, a review of the kinematic modeling of fully parallel 
manipulators is given in Innocenti, et al. (1994), and Parenti-Castelli (1999). 
A related problem with the kinematic analysis is the workspace evaluation, i.e. 
determining all the reachable poses of the mobile platform, for a given orientation, 
and identifying the singular configurations within the workspace. The workspace can 
be defined as a connected set of points, corresponding to the reachable poses, defined 
by the sextet (x, y, z, ψ, θ, ϕ), that identifies position and orientation of the mobile 
platform, without exceeding the limited range for the link lengths or the mechanical 
limits on the passive joints (Negri, et al., 1999). Unlike the orthogonal machine tool, 
the effective useful workspace is strongly affected by the tool orientation. In 
particular, the workspace becomes smaller and smaller increasing the orientation of 
the platform. For PKMs of type (a) the maximum tilting angle is +/- 30˚ within an 
acceptable working volume and also the kinematic stiffness decreases. In some cases, 
in order to overcome these drawbacks providing a good dexterity to the end effector, a 
serial wrist is installed on the mobile platform (i.e. Ingersoll, Tricept).