A model-based and simulation-driven methodology for design of haptic devices

Mechatronics xxx (2014) xxx–xxx

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Mechatronics

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A model-based and simulation-driven methodology for design of hapticdevices

http://dx.doi.org/10.1016/j.mechatronics.2014.01.0060957-4158/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +46 87906305; fax: +46 8202287.E-mail address: [email protected] (A. Ahmad).

Please cite this article in press as: Ahmad A et al. A model-based and simulation-driven methodology for design of haptic devices. Mechatronicshttp://dx.doi.org/10.1016/j.mechatronics.2014.01.006

Aftab Ahmad ⇑, Kjell Andersson, Ulf SellgrenMachine Design, Royal Institute of Technology, KTH Stockholm, Sweden

a r t i c l e i n f o a b s t r a c t

Article history:Received 2 May 2013Received in revised form 23 December 2013Accepted 12 January 2014Available online xxxx

Keywords:EstimationHaptic deviceModel-based design

High precision and reliable haptic devices are highly complex products. The complexity that has to becarefully treated in the design process is largely due to the multi-criteria and conflicting character ofthe functional and performance requirements. These requirements include high stiffness, large work-space, high manipulability, small inertia, low friction, high transparency, as well as cost constraints.The requirements are a basis for creating and assessing design concepts. Concept evaluation relies to alarge extent on a systematic usage of kinematic, dynamic, stiffness, friction, and control models. Thedesign process can benefit from a model-based and simulation-driven approach, where one starts froman abstract top-level model that is extended via stepwise refinements and design space exploration intoa detailed and integrated systems model that can be physically realized. Such an approach is presented,put in context of the V-model, and evaluated through a test case where a haptic device, based on a Stew-art platform, is designed and realized. It can be concluded, based on simulation and experimental resultsthat the performance of this deterministically optimized haptic device satisfies the stated user require-ments. Experiences from this case indicate that the methodology is capable of supporting effective andefficient development of high performing haptic devices. However, more test cases are needed to furthervalidate the presented methodology.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction system, and dimensioning of the components play an important

A haptic device act as a communicating bridge to reflect forcesand torques to a user resulting from interactions with a virtualenvironment or tele-operation tasks, so that human users can indi-rectly feel several physical sensations as in real situations. The hap-tic device works based on haptic feedback and a haptic collisiondetection algorithm while manipulating in a virtual environment;the position of the end-effector is calculated by a computer-basedcontrol algorithm that receives signals from position sensormounted on the device. The haptic collision detection algorithmcalculates in real-time the force/torque to be applied by the actua-tors on the haptic device, so that appropriate reaction forces aresensed by the user, leading to a haptic perception of an interactionwith a virtual object [1]. Research on the development of hapticdevices has been conducted since the late 1940s. Variousforce-reflecting haptic devices are available in both market andin laboratories. However, in the design of these devices there arecompromises between performance and functionality.

The physical design of haptic devices in terms of selecting thetype of mechanism, the number, location, and type of actuation

role for the capabilities and overall performance of the system.Thus, from a design point of view further research is needed toimprove the performance and functionalities, such as workspacesize in relation to device dimensions, actuated degrees of freedom(DOFs), stiffness, transparency, resolution, and bandwidth of thesedevices. Furthermore, applying optimization techniques in thedesign process can improve the performance further. Improvementin the performance of these devices may create new opportunitiesfor surgical procedures that are impossible using the current devices.

Designing a haptic device is an iterative process, and to developan efficient design requires a lot of computational efforts forsearching and mapping design parameters into design criteria,hence turning out to be a multi-objective design optimizationproblem. Thus, finding an optimal design solution is a computa-tionally highly complex task. The main focus of the presentedresearch is to develop a model-based and simulation-drivenmethodology for the design of haptic devices.

The methodology will be based on a parametric, iterative, mod-el-based and simulation-driven design approach that enables effi-cient design space exploration and early verification duringproduct development. Development of mechatronics productsneeds to consider many different system designs in paralleland in an iterative manner. In early mechatronics design

(2014),

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2 A. Ahmad et al. / Mechatronics xxx (2014) xxx–xxx

methodologies, the mechanical system was developed indepen-dently of the electronic and control system, and at a later stagethey were integrated to a complete system [2]. Such a procedurecan give some advantages like possibilities to divide a large andcomplex design problem into several smaller design problems[3]. Here the mechanism, actuation and control design aredesigned independently, which reduces the complexity of the pro-cess. On the other hand, if we neglect dynamics and control aspectswhen designing the mechanical system this may result in a systemwith non-optimal dynamic performance. This may, in the worstcase, require late major redesign of the electromechanical systemin the design process, e.g. as reported in [2,4–6].

Fathy et al. [5] identified four different design approaches forintegrated optimization of mechanical and control system design;sequential, iterative, nested, and simultaneous, as shown in Fig. 1.

The sequential strategy solves the plant and controller optimi-zation problem serially by, 1) optimizing the plant 2) and for theoptimized plant, optimize the controller. While in case of iterativestrategies, given some initial plant/controller design, iterativestrategies attempt to improve on that initial design by first improv-ing the plant design without compromising control performance,then optimizing the controller design without compromising plantperformance. In a nested plant/controller optimization strategy,two nested optimization loops are used. The outer loop optimizesthe scalar substitute objective function by changing only the plantdesign. The role of the inner loop is to generate the optimal con-troller for each plant selected by the outer loop. Nested strategiesare commonly used in the integrated plant/controller optimization.The simultaneous strategy optimizes the system by varying bothplant and controller. The simultaneous strategy can be mathemat-ically and computationally challenging for several reasons. Forexample if both plant and controller optimization sub-problemsare convex, the combined problem may not be convex.

The sequential and iterative strategies have the potential offinding designs that are optimal within each domain, but sub-opti-mal on the system level. The nested and simultaneous representstrategies that are optimal from a system perspective [3].

Optimize the Plant

Optimize the controller

Optimize the Plant


Optimize the system by

only varying the plant

Optimize the system

varyingboth plant and controller

Sequential Iterative

Nested Simultaneous


Fig. 1. Design strategies for mechatronic systems [5].

Please cite this article in press as: Ahmad A et al. A model-based and simulatihttp://dx.doi.org/10.1016/j.mechatronics.2014.01.006

As stated before, design of a haptic device is an iterative process,where interactions between the different subsystems are investi-gated continuously throughout the design process. This corre-sponds roughly to the ‘‘nested’’ approach; where one loop isconcerned with subsystem optimization and one with controlleroptimization as in Fig. 1.

Khan et al. [7] presented a design methodology for hapticdevices based on a combination of the ‘‘nested’’ approach inFig. 1, and the general design process by [8]. This paper is using thisapproach as a basis for further development of a methodology thatfocus on the need for a set of different models during development,thus a model-based approach.

In addition to the previous work by Khan et al. [7], we includedmodels of device stiffness and joint friction and further developedthe optimization procedure. This means that we can investigateand assess additional properties and behavior of the device duringthe development process.

The performance of haptic devices is often deteriorated by fric-tion. Friction, which is related to the wear down process ofmechanical systems [9] such as robot joints [10], can induceunwanted effects such as steady-state errors and limit cycling.One reason for the interest in friction in manipulator joints is theneed to model friction for control purposes. A precise frictionmodel can considerably improve the overall performance of amanipulator with respect to its accuracy and control stability. Stiff-ness and friction models can be used efficiently in hardware in theloop applications for stiffness and adaptive friction compensation.

The motivation for developing a model-based simulation-driven design methodology for haptic devices, specifically usingparallel kinematic structures, is that this type of device has com-plex structures, which give many structural advantages like highstiffness and low inertia, but also represent a complex optimizationproblem and a complicated control system.

The remaining part of the paper is organized in sections. Section2 presents a model-based and simulation-driven design, Section 3evaluates the proposed approach on a design case study by design-ing a 6-DOF haptic device, Section 4 discuss the performance eval-uation, and Section 5 conclude the paper.

2. Model-based and Simulation-driven design

Development of high performing and complex productsinvolves dealing with a great deal of uncertainties and project risk,i.e. we know what we should have done, and when we should havedone it, at the time when we have completed the project, but wehave to make the decisions in real time based on incomplete anduncertain knowledge. To deal with this dilemma, a large numberof process models have been developed, adapted and implementedas industrial process models. A commonly used process model isthe V-model, that is focused on minimizing technical risks bydividing the product development process from abstract ideas torealization of the physical product into a sequence of decomposi-tion stages, often referred to as the left leg of the V, that arefollowed by integration stages, i.e. the right leg. How to properlydecompose the design tasks for a product with hybrid technologi-cal constituents, like a mechatronics product, is not obvious, butone attempt to adapt and formalize the generic V-model for mech-atronics development is the German standard VDI 2006 [11]. Acoarse representation of VDI 2006 is shown in Fig. 2. On top ofV-model a stage-gate sequential process model (e.g. [12,13]) isshown in Fig. 2, which has as its main purpose to reduce theeconomical project risks, by providing company management amechanisms to make a go/no-go/wait decision at each maindecision gate. In many industrial organizations, the V- andextended stage-gate models are synchronized.

on-driven methodology for design of haptic devices. Mechatronics (2014),


Mechanical engineering

Electronics engineering

Control engineering

Product requirements Product/unit

Domain specific design

G0G-1 G1 G4 G5 G6 G7G2 G3

Fig. 2. The mechatronics development V-model combined with the stage-gatemodel.

Requirement specification

ProblemQuestion

Model specification

Simulation model

Answer

Decision basis

P1

Q1M1

S1

A1

Fig. 4. A concept evaluation sequence from requirement to decision [17].

product requirements product/unit

G0G-1 G1 G4 G5 G6 G7G2 G3

A. Ahmad et al. / Mechatronics xxx (2014) xxx–xxx 3

The presented methodology addresses the need to be able toperform mechanical, electronics, and control conceptual engineer-ing design and detailing in parallel domain specific settings, i.e. thelower part of the V-model in Fig. 2, but within a holistic systemscontext. To allow for a highly iterative domain design process,the approach is model-based and simulation-driven (e.g. [14,15]),where one starts from an abstract top-level model that is extendedvia stepwise refinement and design space exploration into adetailed and complete systems model that is then physically real-ized. Stepwise refinement is to gradually add more details to themodels, which are quite coarse in the first instance towards sucha detail that the model can predict the complete behavior of thesystem. Design space exploration is to try out several alternativesolutions, whereby all possible solutions together span the designspace. During the route from idea to final realization, many designdecisions need to be made which all have their own influence onthe final result. Every decision restricts the design space and startsa new smaller design pyramid, as shown in Fig. 3. The reachablesolutions (feasible design space), whether optimal or not, dependon all these decisions, and all decisions are evaluated throughdesign evaluation, e.g. concept evaluation.

Abs

trac

tion

Lev

el

Lev

el o

f de

tail

Alternativesexploration

Different design, different solutions

•

•

Fig. 3. Design pyramid with different abstraction levels [15].


A generic description of concept evaluation is proposed by [16]and further elaborated on by [17] and is shown in Fig. 4, where themain activity in this process is to ‘‘investigate the problem’’, wherethe problem is whatever is unknown about how well a require-ment is satisfied by a concept, which thus raises new questionsthat needs to be investigated further in new sequences ofquestion–answer modeling, simulation, and analysis steps.

These stepwise refinements and evaluations during the designprocess going from product idea, market analysis, requirementsspecification, conceptual design, detail design, and finally into arealization of the product, can be fitted into a general stage gatedesign process as shown in Fig. 5. The investigation loop in thelower part of the right portion of Fig. 5 can be seen as a result ofthis combination. A brief overview of involved design activities isgiven in the coming sections.

The types of models that are needed to handle and documentthe data created during the evaluation process are illustrated inFig. 4. The database symbols in Fig. 5 indicate that for each step

RequirementsSpecification

ConceptualDesign

DetailDesign


ConceptualDesign

DetailDesign

Industriali-zation

Production

G1 G2 G3 G4


ConceptualDesign

DetailDesign

Requirements specification

Create behaviormodel

Formulate question

Simulate behavior

Design Concept

Decision basis

Investigate problem

Formulate answer

Electronics

Mechanics

Control system

ig. 5. The general design process for haptic devices [18] in context of the V-model.
F



in this process, there are a number of predefined models that maybe candidates for being experimented on, i.e. used for simulations,to efficiently explore and solve an identified problem.

2.1. Product idea

This first step deals with identifying a potential product. Wehave limited ourselves to focus on haptic devices that can be usedin a virtual reality simulator, e.g. a simulator for surgical trainingon hard tissues like bone and dental procedures, which requires5 or 6 DOFs. The simulator should provide a feedback of forcesand torque to the user based on manipulation and interactionbetween tool and tissues in the virtual environment as shown inFig. 6. The device must also have sufficient stiffness, large work-space, high manipulability, small inertia, low friction, and hightransparency.

2.2. Market analysis

In the first phase, an information search and a market analysis isto be made in order to identify haptic devices that are currentlyavailable on the market as well as the potential users and theirdemands and wishes on this type of device. To develop a productthat has a large success potential it is of vital importance to makea comprehensive study of the needs of potential customers. In thisreview, different configurations, based on serial, parallel, andhybrid architectures should be studied [18]. Based on analyses oftheir specifications and current application areas a number ofcandidate architectures should be identified. This analysis will bea basis for defining the initial preliminary requirementsspecification.

2.3. Requirements specification

Although a quantified set of requirements is not yet deter-mined, it is clear from the literature that many researchers seekto build a device with:

� A number of degrees of freedom� Sufficient workspace� Low apparent mass/inertia� Low friction� High structural stiffness� Back-drivability� Zero (or very low) backlash� High force bandwidth� Absence of mechanical singularities� Sufficient force dynamic range� Proper ergonomics that eliminate pain and discomfort when

manipulating the haptic device

Fig. 6. Haptic milling surgery simulator concept.


� High isotropy and transparency

Elaborating on the product idea, performing a market analysis,and defining product requirements, are here viewed as pre-studyactivities that precedes product development.

2.4. Systems design

In the system design phase, sometimes referred to as thearchitecting stage, a conceptual structure of functions and princi-pal solutions are synthesized, based on the input requirements.Since the performance of a haptic device is highly dependenton a synergetic interaction between the mechanics, electronics,and control systems, the architecting stage must be an integratedteam effort, where all of the domain experts are active. Thefunctional structure and the system of conceptual constituentsis usually referred to as the systems architecture.

Some important activities (and suggested tools to use) in thisphase are listed below:

� Identification of the main function of the haptic device, basedon the formulated product requirements This is an abstractionprocess that should be made to sort out the main functionand of the product [19–21]. Then follows a search for principleconceptual solution candidates, i.e. design synthesis, which arethen assessed and compared by the team.� The chosen concept(s) is/are then a basis for further functional

decomposition. The method of functional decomposition overintermediate steps of conceptual means is represented by afunction-mean tree; a method and model that was initiallyproposed by Andreasen [22]. The main motivation for usingfunction-means decomposition is to expand the solution space.� The preferred architecture is then chosen to be further devel-

oped and the requirements specification is further detailed asinput to the next process stage.

2.5. Conceptual design

In the conceptual design stage, the systems architecture isdecomposed into mechanical structure, electronics, and controlsystem, which are then elaborated on in parallel developmentactivities. Systems design and conceptual design are essentialsteps in successful mechatronic product development. Efficientconceptual development should be supported by mathematicaland computer models to be used and detailed in the further pro-cess toward a detail design [23].

Some important activities and suggested tools using conceptualdesign are listed below:

� Identification of the function structure from the conceptual sys-tems architecting stage for each domain (i.e. mechanics, elec-tronics, and control) of the haptic device, followed by furtherfunction-means decomposition until the base functions [24]have been found. This result in additional concept structures.Based on the initial requirements some of the generated conceptstructures should be chosen, e.g. using the selection chart byPahl et al. [19], for further development.� Modeling and analysis to determine the number of DOFs, preli-

minary actuator requirements, and preliminary dimensions forthe wanted workspace for the selected structures. These aresome of the basic requirements for a haptic device to achievecapabilities for feedback in the required DOFs in the workspace.For these types of analysis, lumped parameter multi-body sys-tems (MBS) modeling and simulation software, e.g. Adams View[25], Simulink [26], or Modelica [27] based tools like MapleSim[28] is recommended.




� Investigation and preliminary selection of motors based on thecalculated actuator requirements. In addition, evaluation andpreliminary selection of encoders and transmission should bemade.� Inverse and direct kinematic modeling of the selected struc-

tures. Development of inverse and direct kinematic models isa pre-condition for performing kinematic optimization and isalso needed for development of the control system. For this typeof modeling and analysis, Matlab [26] is recommended.� Optimization of the kinematic structure. This is a crucial task for

haptic devices that are based on parallel kinematic structures. Theoptimization turns out to be a multi-criteria optimization problem.For these types of problems, the use of genetic algorithms has provedto be successful in finding a global optimum solution. The goal func-tion for the device should include indices for workspace, isotropy, tor-que/force, stiffness, and inertia. For devices with DOFs >3, we adviseto use dexterous workspace and for mechanisms with non-homoge-nous units of the elements in the Jacobian matrix, we suggest to nor-malize it before using it for calculating performance indices in theoptimization process [18]. Probabilistic simulations, e.g. Monte Carlosimulations [29] should be performed in order to evaluate the robust-nessof theperformanceindicestovariationinthedesignparameters;this will help to select the most appropriate manufacturing toler-ances in the detailed design phase. Suggested software to use hereis Matlab [30] and the MOGA (Multi Objective Genetic Algorithm)toolbox [31].� Rough layout of the mechanical design based on the MBS anal-

ysis and optimization results. This is a traditional engineeringdesign task to make a preliminary assembly layout of the devicebased on optimization results and MBS analysis. Tasks to con-sider in this phase are selection of motor, transmission, andsearch for standard components to use, e.g. joints, as well asbasic design and a preliminary material selection for the sup-port structure. For these tasks, any CAD 3D modeling tool isfeasible.� Alternative control strategies for the haptic device. The require-

ments on the device are to get a frictionless feeling when mov-ing the device in free space and to achieve force/torquefeedback when entering contact with a virtual object. Thismeans that the control system has to compensate for the inertiaand friction that always occur in real systems. The task here isto investigate optimal control strategies and differentapproaches to compensate for these effects.

After selecting the candidate structures to consider for thedevice in hand, the above steps can be done in parallel if a para-metric modeling approach is used for all these activities.

2.6. Detail design

The detail design phase focus on development of a prototype ofa haptic device. This includes mechanical and controller designbased on the results from the previous design phase. Also, selectionof standard components (e.g. joints, electric motors) for the drivesystem, and the transmission system; bearings and cabling areselected. In addition, evaluation and preliminary selection ofencoders and transmission should be made. Some activities (andsuggested tools to use), that should be performed during the detaildesign phase are listed below:

� Mechanical design to make the detail design of the device basedon the optimization results. This includes careful selection ofstandard components, if possible (e.g. joints, electric motors),detail design, material selection and manufacturing informationfor the components to be manufactured.


� Prototype creation. Once the mechanical design is determined, aphysical prototype should be built. This includes manufacturingof some components, ordering of standard components likecommunication board, and assembling the parts.� Control design. As soon as we have a physical prototype, we can

start testing different control strategies that have been investi-gated in the previous design phase. For the initial tasks, dSpace[32] can be used, but for the final implementation, a suitablemicro controller should be selected as well as a software-devel-opment tool for implementing the control system in the microcontroller. The inertial and friction forces in active and passivejoints of the haptic device limit the transparency of the transfer-ring forces and torques from the virtual environment to theoperator. This makes the free motion not feel free, and an over-estimated force torque may be observed on the operator side. Inorder to compensate for this friction, the model-based and sim-ulation-driven design approach should be used to develop afriction model with an appropriate detailing level.� Verification of the prototype. After the prototype has been built,

we should start testing the device. Initially, mechanical stiffnessand clearance can be tested using a CMM (Coordinate Measur-ing Machine). After that, testing of the complete device shouldbe made in a controlled and restricted environment. First, sim-ple tests of contact conditions and free space motion should bemade and thereafter more complicated contact conditions,requiring many DOF’s feedback as a result of a contact, shouldbe investigated.� Validation of the total simulation system for surgical training.

Once the total system with mechanical haptic device, controlsystem, collision detection in the virtual environment andgraphical interface is complete it should be used for face valid-ity tests on real end users [18,33].

3. Design case study: design of a 6-DOF haptic device

The proposed model-based design approach in Section 2 hasbeen applied to the development of a 6-DOF haptic device.

3.1. Product idea

The first step of the design approach is to identify the need for anew product to be developed. In our case, we have identified aneed for a milling simulator that can be used in the curriculumfor surgical training on hard tissues like bone and dental proce-dures [33]. Such operations involve removing bone by drilling ormilling, including processing of channels and cavities, hencerequiring 5–6 degrees of freedoms and stiff contact feedback tothe user. In this scenario, a haptic device is used to provide manip-ulation capabilities and force/torque feedback in simulations togive a realistic impression of a real milling process in bone tissueas in dental procedures. Further the design should provide a devicewith (1) minimum footprint/size to workspace ratio; (2) uniformmotions, forces and stiffness capabilities over the workspace; and(3) minimum inertia of mechanical structure, actuation systemand transmission.

3.2. Requirements specification

In the second step, an information search and market analysishas been performed in order to identify the potential users andtheir requirements. From the statements of needs, a requirementspecification is formulated. The preliminary specifications givenhere have been obtained in dialog with a tentative user, in this casea surgeon. The application domain is completely new and unique,



(a) Conceptual model (Adams View)


thus it is difficult to obtain specific requirements. The functionalrequirements are derived from the user and device requirements.The initial user requirements for the haptic device are as follows[34].

� The device should have 5–6 actuated degrees of freedom.� The whole device should fit within the space of

250 � 250 � 300 [mm].� The translational workspace should be a minimum of

50 � 50 � 50 [mm].� The stiffness of the device including actuation and control

should be a minimum of 50 [N/mm].� The tool center point (TCP) peak force/torque performance

should be at least 50 [N] and 1 [Nm] in all directions.� It should be possible to place it on a table in front of the oper-

ator, easy to access for the user.

The device requirements specification included kinematic andkinetostatic requirements, and requirements of transparency andstability. The kinematic requirements include required DOFs,workspace, manipulability and quasi-static force/torque, whilekinetostatic requirements included inertial and stiffness proper-ties, and lastly, transparency requirements are based on frictionand joint clearance (backlash).

L

Platform

xA

yAzA

xB

yBzB

xC

yCzC

xP

yP

zP

Spherical joint

Base

1

Universal joint

2L

Linear guideway

Proximal link

b

p

(b) Kinematic model

Fig. 7. Conceptual and kinematic models.

3.3. System and conceptual design

The requirements specification is the basis for identifying themain function of the device as well as basic constraints on the solu-tion space. The main function is then decomposed into sub-func-tions which all are used for concept generation. In our case themain function can be expressed as ‘‘allow feedback in 6-DOFs’’.The concepts that are found are all allowing 6 DOFs and thoseselected for further evaluation also satisfy other constraints, e.g.on TCP peak torque/force performance.

Two concepts based on parallel kinematics; one modified Stew-art Gough mechanism and one TAU mechanism [35], were chosenas candidate solutions for further investigations. In the next step,additional structural analyses were made on these concepts con-cerning workspace and force/torque performance. For structuralanalysis, these concepts were modeled using Adams View MBSsoftware [25] as the main tool. These steps and evaluations havebeen reported in an earlier paper; see Khan et al. [34].

As a result of these investigations, a modified Stewart Goughmechanism [36] was chosen as our solution concept to continuewith. This mechanism consists of a fixed base, a moving platform,and six identical legs connecting the platform to the base, as shownin Fig. 7. Each leg consists of an active linear actuator fixed to thebase, a spherical joint, a constant length proximal link, and a uni-versal joint. This 6-PSU (active Prismatic, Spherical, and Universal)joint configuration was used to get the 6-DOF motion at TCP of theplatform.

The properties of this solution concept are then evaluated usingvarious models that have been developed for this purpose, seeFig. 8. These models are then used in the simulation-drivenapproach to evaluate the different properties and finally end upin a deterministic optimal conceptual structure of the hapticdevice. Among the models shown, the kinematic model plays acentral role in these analyses.

3.3.1. Models and criteria for design concept evaluationTo evaluate the properties listed in Fig. 8, we have developed a

set of focused models for kinematic, dynamic, and kinetostaticproperties, as well as the evaluation criteria. These models andcriteria are briefly described below.


3.3.1.1. Development of focused models. The first concern in a kine-matics study of a mechanism is the number of DOFs. The DOFs of amechanism are the number of independent parameters or inputsneeded to specify the configuration of the mechanism completely.The Grubler criterion was used to find the number of independentcoordinates of the system by using (1).

F ¼ kðn� j� 1ÞX

i

fi ð1Þ

where F; k;nl and fi represents, degrees of freedom of the mecha-nism, degrees of freedom of the intended space, number of linksin the mechanism including the fixed link, number of joints in themechanism and degrees of relative motion permitted by joints. Thisanalysis was made in the initial evaluation of the two alternativesolution using the Adams View MBS software [37].



Payload

Stiffness

Inertia

Friction

Backlash

Design concept

DOF

Functionalrequirements

Workspace

Kinematic Model

Inverse kinematic

modelForward

kinematic model

Friction ModelStiffness

Model

Dynamic Model

Jointclearance

Model

Kinematic isotropy

Quasi-static force

Stiffness isotropy

Dynamic isotropy

Jacobian matrix

Control design

Transparency

Backlash

Workspace

Manipulability

Userrequirements

Devicerequirements

Fig. 8. Relations between functional requirements, design concept, properties and models needed for evaluation of product properties.


The kinematic structure is the basis for the analysis of any roboticsystem. Once the kinematic structure is developed, the designercan evaluate the performance of the system. The kinematic modelis based on the inverse kinematic model; where one needs to findthe position/orientation of the active joints given position and ori-entation of the TCP. The inverse kinematic model is developedbased on the constrain equation of a kinematic chain in Fig. 7b,as shown in Eq. (2),

ðCix � BixÞ2 þ ðCiy � BiyÞ2 þ ðCiz � BizÞ2 ¼ L2i ð2Þ

_l ¼ J _qi ð3Þ

where Bi and Ci are coordinates of spherical and universal joint,whereas J is the Jacobian matrix, while _q ¼ px; py;pz;a; b; c

� �are

generalized coordinates, where a;b; c½ � are the Euler angles, while_l and _q correspond to active joints and Cartesian space velocities.

The dynamic model describes the inherent property like inertiaof system. The Lagrange dynamic formulation is used to developequation of motion of the form as in (4),

MðlÞ€lVðl; _lÞ þ GðlÞ þ Ff ð_lÞ ¼ Fl ð4Þ

where MðlÞ;Vðl; _lÞ;GðlÞ and Ff ð_lÞ are the inertial, centrifugal, Coriolis,gravitational and frictional force matrices, while Fl is force vector,which represent the dynamic force.

We use the methodology for stiffness modeling by Ahmad et al.[38], this methodology is based on transformation of forces andmoments from platform to individual links, thereafter calculatingthe deflection of each link, and finally transforming the displace-ments back to the platform. The stiffness is calculated based onthe simplified analytical model, where compliance of linear-guide-ways and proximal links are considered, where passive and activejoints are assumed to be rigid without clearance. The stiffness of asingle kinematic chain of the selected kinematic structure is givenin Eq. (5).

Kchaini¼ U

C RB;dispðURAASB

URTAÞUB RC;force þ URB

BSCBRU

� ��1ð5Þ

where UC RB;disp and U

B RC;force are displacement and force transformationmatrices, while ASB and BSC are compliance matrices of linear guide-way and proximal link, whereas URA and URB are the rotation matri-ces of linear guideway and proximal link. The overall stiffness is thesum of the stiffness of the kinematic chains given in Eq. (6).

KTotal ¼X6

i

Kchainið6Þ


The simplified analytical model was validated by a simplifiedparametric model in Ansys APDL [39]. The inverse kinematic modelis developed based on the constraint Eq. (2), and was used tocalculate the length of linear guideway for positioning of TCP ofplatform at different locations in the workspace. The lower endof the linear guideways were constrained in, X;Y and Z directions.The linear guideways and proximal links were modeled as solidand beam elements respectively, while multipoint constraint(MPC) equations were used to satisfy the compatibility conditionbetween joints (both spherical and universal) and links (linearguideways and proximal links). At different configurations in theworkspace a maximum load of 50 N was applied in each, X;Yand Z directions, and the corresponding deformation wasmeasured.

3.3.1.2. Definition of performance evaluation criteria. Optimal designis one of the most important issues in the development of a hapticdevice because of its complex set of requirements. A brief discus-sion on the performance evaluation criteria and their significanceis given. Important criteria that are based on kinematics and kine-tostatic are discussed below.

The kinematic performance criteria are based on workspace vol-ume, kinematic isotropy, and quasi-static torque requirements onthe actuators.

First, the volume index VI is based on workspace volume. Theworkspace volume V is one of the most important kinematic prop-erties of manipulators, because of its impact on manipulator designand shape of the workspace. The workspace volume is definedbased on dexterous workspace, which considers orientation reach-ability of the workspace, a workspace that is reachable by all therequired maximum and minimum orientations at that point.

To calculate dexterous workspace, the manipulator is traversedin the workspace shown in Fig. 9, and at each grid point in theworkspace the prescribed rotations are applied. If any of the con-straints for active and passive joints, and kinematic, stiffness anddynamic singularities are not satisfied between the bounds of plat-form orientation aa;amð Þ; bb; bnð Þ and cc; coð Þ, then that grid point isnot within the dexterous workspace. A numerical procedure wasused to find the boundaries of the workspace by scanning gridpoints Puvw at a cross-section of the workspace, as shown inFig. 9. The volume index VI is defined as the orientation reachableworkspace volume which is given in Eq. (7), where a binary flagNuvw was defined at each grid point on the section defined in Eq.(7); a grid pixel is a reachable point when Nuvw ¼ 1; but not whenNuvw ¼ 0.



dz

dz

X

d

rdr

Y

Z

d

dr

r

I,j

I,j-1

i-1,j-1

i-1,j

Nij

Nij

Fig. 9. Workspace of a 6 DOF haptic device.


VI ¼ V ¼Z Zmax

Zmin

Z rmax

rmin

Z 2p

0Nuvwðr; h; ZÞrdhdrdZ ð7Þ

The integral in Eq. (7) is approximated by a summation over acorresponding grid by taking the flag value at the grid point andvolume of that cell. The approximation can be defined as

VI ¼X

u

Xv

Xw

NuvwDVuvw ð8Þ

where DVuvw ¼ ðru � ru�1Þðhv � hv�1ÞðXw � Xw�1Þ ruþru�12

While value of the binary flag Nuvw depends on the conditiongiven in Eq. (9).

Nuvw ¼1 if Puvw 2W X; Y; Z;a; b; cð Þ0 if Puvw R W X;Y ; Z;a;b; cð Þ

�ð9Þ

Here W are the grid points traversed by tool center point (TCP)in the NX ;NY and NZ directions with the platform orientationsa; b; c with a total of n3 rotations at each grid point, where n isthe number of rotations in one direction.

Second, the kinematic isotropy index II indicates how evenly thesystem moves in all generalized workspace directions. Physically,kinematic isotropy implies that the manipulator end-effector cantranslate and/or rotate with equal ease in all spatial directions. Inthe present paper, the isotropy index proposed by Gao and Gruver[40] has been used. The isotropy index is defined as in Eq. (10):

II ¼ 1

Jdk k J�1d

�� ; 0 6 II 6 1 ð10Þ

where Jdk k ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffitr J 1

n ½I�JT

� �rHere Jdk k is the frame-invariant Euclidian norm of Jacobian

matrix, while d is the dimension of the Jacobian matrix, and ½I� isthe identity matrix.

Third, the quasi-static force requirement index is defined as themaximum magnitude of generalized force on the actuator per unitof force and torque applied to the TCP. The force requirement indexðFRIÞ is expressed as:

FRI ¼ffiffiffiffiffiffiffiffiffiffikTmax

pð11Þ

Where kTmax ¼maxð½Jd�T ½Jd�Þ

Fourth, the kinetostatic performance is based on the stiffnessmatrix defined in the stiffness model. If we denote rminðKÞ as theminimum singular value of stiffness matrix K, then the stiffnessindex can be expressed as follow:

KI ¼ rminðKÞ ð12Þ


In the dexterous workspace, the isotropy, force requirement,and stiffness dexterity indices is based on the average of all therotations applied at the grid point. This is defined in Eq. (13):

II ¼Pm

a¼0

Pnb¼0

Poc¼0 IIaabbcc

m� n� o

;

FRI ¼Pm

a¼0

Pnb¼0

Poc¼0 FRIaabbcc

m� n� o

;

KI ¼Pm

a¼0

Pnb¼0

Poc¼0 KIaabbcc

m� n� o

ð13Þ

The above defined indices depend on the configuration and thegeometrical parameters of the manipulator. To describe it on thewhole accessible workspace, we use the global indices GII;GFRIand GKI, which are defined by the average of the local indices overthe entire workspace, as in Eq. (14):

GII ¼R

V IIdVV

GFRI ¼R

V FRIdVV

GKI ¼R

V KIdVV

ð14Þ

3.3.2. Optimum concept designThe performance of haptic devices is highly sensitive to dimen-

sions and geometry of the device; in this regard design optimiza-tion is an important step in the design process. The goal of theoptimization process is to find optimum geometric and structuralshape parameter values for the links and the platform, in orderto maximize the workspace volume and the global isotropy, stiff-ness while minimize the quasi-static force requirements on theactuators. To achieve this, an optimization problem was formu-lated with an objective function based on the performance indicesdefined before: the objective function is defined in Eq. (15).

GDI ¼min VI;GII;1

GFRI;GKI

� �ð15Þ

The indices defined in Eq. (15) are not comparable numerically.This might lead to conditions where the optimization procedurewould not work properly. Therefore, a new concept for normaliza-tion of performance indices is introduced, such that all indices areequally active and contribute in the optimization process. Eachindex is divided by its mid value VImid;GIImid;GFRImid;GKImid½ �, whichcorrespond to the numerical performance index value evaluated atthe mid value xmid between the lower and upper bounds, xlb and xub

respectively, of the design parameter xj as in (16). The new normal-



(a) Variation of isotropy index (II)

(b) Variation of quasi static force requirements index (FRI)

(c)Variation of stiffness index index (KI)

Fig. 10. Variation of performance indices within workspace.


ized global design index is defined in (17). The design parametersxj consist of length of linear guideways L1, length of proximal linkL2, radius of base Rb, radius of platform Rp, angles of base and plat-form attachment points, hb and hp respectively as shown in Fig. 7b.

where xmid ¼xub þ xlb

2

VImid;GIImid;GFRImid;GKImid½ �¼ f ðL1;mid; L2;mid;Rb;mid;Rp;mid; hb;mid; hp;midÞ ð16Þ

GDIn ¼minVI

VImid;

GIIGIImid

;GFRImid

GFRI;

GKIGKImid

� �ð17Þ

The optimization problem is formulated such that, it minimizeinverse of the normalized global design index over a set of designparameters of size under constrains on active joints, passive spher-ical joint angles uxi;uyi;uzi

h i, passive universal joint angles

/xi;/yi;/zi

� �and bounds on the design parameters xj as defined in

(18). The described optimization problem is solved through Genet-ic Algorithm (GA).

minimizex1

GDInðxÞover x ¼ L1; L2;Rb;Rp; hb; hp

� �subject to minðhiiÞ 6 hii 6 maxðhiiÞ/xi;/yi;/zi

� �lb6 /xi;/yi;/zi

� �6 /xi;/yi;/zi

� �ub

uxi;uyi;uzi

h ilb6 uxi;uyi;uzi

h i6 uxi;uyi;uzi

h iub

xlb 6 xj 6 xub

ð18Þ

Furthermore, the set of optimal design parameter values,obtained from the genetic algorithm was used to evaluate the per-formance of the device. In order to visualize the variation of theisotropy and the quasi-static force requirements indices in theoptimized workspace, the TCP is moved in a circular path in theX–Y plane (see Figs. 9 and 10) with small incremental changes ofthe radius. At each grid point, isotropy, quasi-static force require-ments, and stiffness indices are calculated. The variations of theisotropic index shown in Fig. 10a indicates that the device has agood isotropic behavior around the workspace center. The forcerequirement index is small for an applied unit force around thecenter of the workspace while it increases as the TCP moves awayfrom the central point as in Fig. 10b. The variation within the work-space of the stiffness index KI, as presented in Fig. 10c, shows thatthe structure is stiffer when the actuator stroke is at its minimumand less stiff when the actuator reaches its maximum stroke.

3.3.3. Control designIn parallel to a mechanical optimization we also perform a con-

trol design optimization in the conceptual design phase. The syner-getic goal is to find a structure that is optimal from kinematic,dynamic, and actuation points of views. Here, the transparencyand stability of the device are the most important performanceparameters to consider. The transparency requirement means thatmotion in free space should feel free while motion in contact witha virtual or remote object should result in feedback forces and tor-ques as close as possible to those appearing in the real world.

In free space motion, transparency is affected by the dynamics(inertia, friction) of the device and the dynamics of the operator.Keeping the device inertia as low as possible as well as compen-sating for it in the control design will increase the transparencyof the device. The task here is to investigate optimal control strat-egies and different approaches to compensate for these effects. Inthis regard different control strategies based on impedance con-trol, admittance control and hybrid control were investigated,and due to ease in implementation and computational efficiency,


model-based feedforward impedance control strategy with openloop is chosen as shown in Fig. 11. The aim of this feed-forwardis to increase the transparency of the device, i.e. the user shouldnot feel the inertia and friction of the device itself, only of the tool.The dynamic model was simplified by considering the inertialMðlÞ, gravitational GðlÞ and frictional terms Ff ð_lÞ of Eq. (4), whileneglecting the Coriolis force Vðl; _lÞ due less contributions accordingto [41]. The inertial and friction model parameters were identifiedusing Matlab identification toolbox. The stiffness model was used



Fig. 11. Control strategy of 6-DOF haptic device.

Fig. 12. Prototype of 6-DOF haptic device.


to compensate the small deformation of the TCP due tocompliance of linear guideway, proximal link and actuation sys-tem. The force applied from the human operator Fh is an inputto the haptic device, which is subtracted from the total force.The force produced by the haptic device was estimated by themeasuring current in each motor, motor torque constant and Jaco-bian matrix J.

Referring to the block diagram in Fig. 11, the encoders aremounted on the motor shafts to read the angles of the motors,which are then converted to joint angles and further onto thechange in length of the linear guideways through a gear ratio Rg .The lengths of linear guideways are then sent to a forward kine-matics module to determine the position/orientation of the tooltip in the virtual environment; the virtual model uses the posi-tion/orientation and desired physical properties to generate adesired force/torque response. The desired force/torque is thenmapped using a Jacobian matrix J to set of desired torques on theactuators to be produced by the motors in the haptic device. Tocompensate for inertial, gravitational and friction forces a compen-sation torque based on dynamic and friction model is added usingfeed-forward control. In order to compensate for elastic deforma-tion a stiffness model is used in the feedback loop. This compensa-tion is active only when the tool point is in contact with the virtualmodel.

3.4. Detail design

A prototype was developed based on the final set of optimaldesign parameter values and sensitivities [42] from the GA, andthe tuned control model [41]. The developed prototype with a sizeof 250 � 250 � 300 mm is shown in Fig. 12. Six DC Maxon motorswere fixed at the base and a cable transmission mechanism with apulley was used to convert the angular motion to the linear actua-tor motion. The cable transmission makes the system back driv-able. The developed 6-DOF haptic device shown in Fig. 12 isconnected to a personal computer using a dSpace 1103 board [32].

The proposed control structure, as shown in Fig. 11, is imple-mented in Simulink on that PC and the target controller code isexecuted on the dSpace board with a 1 kHz sampling rate. The hap-tic collision detection and force torque feedback program is imple-mented on the same computer. The position measurementresolution in each linear actuator is 0.01 mm and the update rateof the controller is 1 kHz.

In order to investigate the performance of the device, experi-ments were performed with different device control strategies:open loop; computed torque with dynamic compensation; andcomputed torque plus force feedback. The device was connectedto a virtual environment, with the user trying to move the virtualtool in free space and in contact with a virtual object (wall) havingstiffness of 50 N/mm. The reference force from the virtual objectcontact and the forces produced by the device (calculated frommotor currents) were recorded, as given in Fig. 13a–c. It has been


observed that the tuned controller and device structure satisfiesthe 6-DOF device performance requirements.

3.4.1. Further performance improvementsThere are many areas where we can make small improvements

in the detail design phase, e.g. alignment of linear actuators, selec-tion, and arrangement of joints to reduce their friction. In the com-ing sections, we will discuss friction and stiffness compensationimprovements.

3.4.1.1. Friction estimation and compensation. When moving thetool of the device in free space one should feel the mass of the tooland not any inertia of the structure or joint friction. This is corre-sponding to the requirement on transparency of the device andhas partly been addressed in the evaluation and selection of candi-date structure in the architecting and conceptual design phases.Eliminating or at least reducing the effects from joint friction bycompensation in the control of the device can improve its transpar-ency. This requires a compact and computationally efficient modelfor friction estimation such that it can be used for real time frictioncompensation. Our initial approach to model and estimate jointfriction is to use a multi-state Smoothed Generalized Maxwell Slipmodel (S-GMS) [43]. The S-GMS friction model, which is a multi-state dynamic friction model, is an extension of the GeneralizedMaxwell-Slip (GMS) friction model [44]. This friction model imple-ments all friction phenomena and behavior present in the GMSmodel, such as stick–slip motion, pre-sliding displacement, Stri-beck effects, frictional lag, and transitions between the slidingand pre-sliding regimes, while maintaining simplicity appropriatefor control purposes. The S-GMS model consists of a set of differen-tial equation in an analytical form, which preserve the benefits of



0 2000 4000 6000 8000 10000−20

−15

−10

−5

0

5

10

15

20

25

30

Forc

e in

z−d

irect

ion

[N]

Time [ms]

FeFm

(a) Open loop

0 2000 4000 6000 8000 10000−40

−30

−20

−10

0

10

20

30

40

Forc

e in

z−d

irect

ion

[N]

Time [ms]

FeFm

(b) Dynamic compensation

0 2000 4000 6000 8000 10000−100

−80

−60

−40

−20

0

20

40

60

80

Forc

e in

z−d

irect

ion

[N]

Time [ms]

FeFm

(c) Compensation with a PI controller [42]

Fig. 13. Comparison of reference and measured forces of the device.

Fig. 14. Friction estimation and compensation framework.


the GMS model while combining the state equations of pre-slidingand sliding into a single state equation. This model treats the fric-tion force as a sum of N parallel elementary friction interface ele-ment Fe. The analytical expression for an elementary frictionforce according to [43] is given as;


dFe

dt¼ ke

_l� geðFe;_lÞ _l Fe

aisð_lÞ

!ð19Þ

where geðFe;_lÞ is a smoothed transition function between presiding

ðge ’ 0Þ and sliding ðge ’ 1Þ regime, while keis the stiffness of ele-ment e. The transition function geðFe;

_lÞ consists of two multiplica-tive terms given in Eq. (20), the transition function (21) and thereset function (22)

geðFe;_lÞ ¼ gAe

ðFe;_lÞgBeðFe;

_lÞ ð20Þ

gAeðFe;

_lÞ ¼ 1� 12

tanh

kFl

aesð_lÞþ 1

!" #þ 1

2tanh k

Fe

aesð_lÞ� 1

!" #ð21Þ

gBeðze;

_lÞ ¼ 12þ 1

2tanh c

Fe

aesð_lÞ

_lms

!" #ð22Þ

where 1 2 0:9;1½ � is a factor to avoid ringing in sliding regime andset the frictional lag, the factor k sets the transition sharpness of(21). The reset function (22) vanishes at the velocity reverse itsdirection. The factor c sets the transition sharpness of (22). Thefunction sð_lÞ describes the Stribeck effect, which is defined as

sð_lÞ ¼ fC þ ðfS � fCÞe�_lms

2� �

where fS and fC are static and Coulomb friction force, ms the Stribeckvelocity, while

ae ¼FePNe¼1Fe

The resulting friction force is the summation of N number ofstiffness forces Fe plus a viscous rv

_l term is given as in Eq. (23).

Ff ¼XN

e¼1

Fe þ rv_l ð23Þ

3.4.1.1.1. Friction estimation. In this section the friction state esti-mation framework is presented. The estimation problem is basedon a discrete version of Eq. (19) and (23), discretized at timeinstant tk given in Eq. (24) and (25).

Fk ¼ f ðFk�g ; _qk�gÞ þwk�1;wk � Nð0;Q kÞ ð24ÞFfk¼ hðFk; _qkÞ þ vk; vk � Nð0;RkÞ ð25Þ

Here Fk and Ffk represent the state and measurement vectors attime instant tk, while f ð�Þ and hð�Þ are non-linear functions repre-senting the process model (friction state Eq. (19) and the observa-tion model (total friction Eq. (23))). Where wk and vk are theprocess model noise and the observation model noise with covari-ance Qk and Rk, respectively.

In order to compensate for friction, the observer-based frictioncompensation strategy proposed in [43,45], as shown in Fig. 14, hasbeen used, where the objective is to estimate the friction state Ff of



0 0.5 1 1.5 2−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

Time [s]

Post

ion

[mm

]

MeasuredReference

(a) Without compensation

0 0.5 1 1.5 2−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

Time [s]

Post

ion

[mm

]

MeasuredReference

(b) With compensation

Fig. 15. Comparison of reference and measured position without and with frictioncompensation using IEKF.

Table 1Position tracking error.

DOF Root mean square error withoutcompensation

Root mean square error withcompensation

X 0.02 0.01Y 0.018 0.01Z 0.06 0.03a 0.008 0.0062b 0.0065 0.0064c 0.0096 0.008


Eq. (23), while minimizing the error between estimated friction bF fk

and the measured friction eF fk based on the control input uk and theinertia M of the system.

The above estimation framework, which is based on the S-GMSmodel, is implemented with the Iterated Extended Kalman filter(IEKF) [46]. A brief description of this filter is given as follow.

The Iterated Extended Kalman filter (IEKF) is a recursive filter likeExtended Kalman filter (EKF) [46], that consists of time update andmeasurement update steps. Since the EKF linearize the state andmeasurement equations about the predicted state at an operatingpoint, this prediction is often inaccurate in practice. The IEKFreduces the linearization error in EKF. The estimate can be refinedby re-evaluating the filter around the new estimated state operat-ing point. This refinement procedure can be iterated until littleextra improvement is obtained. The IEKF predicts the future stateof friction bF�k based on the available system model f ð�Þ and projectsahead the state error covariance matrix P�k using the time updateequations to compute the predicted measurement from the pre-dicted state using function hð�Þ. The predictor step (time update)equations are as follow,bF�k ¼ f ðFk�g ;

_lk�1Þ ð26ÞP�k ¼ Ak�gPþk AT

k�1 þ Q k�1 ð27Þ

The corrector step (measurement-update equations) incorpo-rates the measurement eF fk into an estimated state bF fk

using theKalman gain matrix Kk. The corrector step (measurement update)is performed by initializing the iterated EKF estimate to the stan-dard EKF estimate:bFþk;0 ¼ bF�kPþk;0 ¼ P�k

ð28Þ

For i ¼ 0;1; . . . ;N, evaluate the following equations (where N isthe desired number of measurement-update iterations) [46]:

Kk;i ¼ P�k HTk;gðHk;iP

�k HT

k;g þ RkÞ�1 ð29Þ

Pþk;gþ1 ¼ ðI � Kk;gHk;gÞP�k ð30ÞbFþk;gþ1 ¼ bF�k þ Kk;geF fk� hðbF�k ; _lkÞ � Hk;gðbF�k � bFþk;gÞh i

ð31Þ

where I the identity matrix, while the state transition matrix Ak andobservation matrix Hk are defined by first order Taylor seriesapproximation of friction state Eq. (19), and observation Eq. (23)using the following Jacobian matrices Ak�1 and Hk.

Ak�1 ¼@f@F

bF k�1

and Hk ¼@h@F

bF k�1

The final a posteriori state estimate and estimation error covari-ance are as follows:bFþk ¼ bFþk;Nþ1

Pþk ¼ Pþk;Nþ1

ð32Þ

3.4.1.1.2. An experimental partial verification. The effects of frictioncompensation on the transparency of the device had to be verified.As a first initial step of the validation, we made an experimentalcomparative study of the effects on position accuracy. This studycompared the position error of the complete system without fric-tion compensation with the case when friction compensationbased on the compensation strategy shown in Fig. 14 was used.The comparison criteria are based on platform position and orien-tation. A sinusoidal trajectory of 0:5 sinð2ptÞ was applied to sixactuated joints in order to move the platform along the z-directionwith constant TCP orientation ða ¼ b ¼ c ¼ 0Þ. A comparison of thereference and measured positions along z-direction for the casewithout and with compensation are shown in Fig. 15a and b.


The tracking errors without and with compensation for thetranslational and rotational degrees of freedoms are presented inTable 1.

This first initial step of validate the friction compensation strat-egy gives the results shown in Table 1, which indicate improvedposition accuracy in terms of a reduced the root mean square errorfor 6-DOF motions of the TCP. The reduction is most significant inthe z-direction which is natural since the TCP motion was to moveback and forth in this direction only. The results from this first ver-ification step is quite promising, and the next step is to measurethe force at TCP when moving the tool in free space and comparethe force with and without friction compensation.



Table 2Performance mapping between requirements and prototype.

Required values Prototype

DOF 6 6Device size 250 � 250 � 300 mm 6 250 � 250 � 300 mm

Workspace Translation 50 � 50 � 50 mm 75 � 75 � 100 mmRotation Roll �40 �45

Pitch �40 �45

Yaw �40 �45

Minimum stiffness 45 N/mm 60 N/mm

Peak force/torque Force 50 N 54 NTorque 1 Nm 1.2 Nm


3.4.1.2. Stiffness estimation and compensation. When interactingwith a stiff tissue such as bone it is important to achieve a realistichaptic feedback of forces and torques that mimic a real surgical sit-uation. It is also vital to achieve an accurate position of the TCP tosimulate precision surgery. The structural stiffness requirement isaddressed with kinetostatic optimization in the conceptual designphase, while the requirement on position accuracy when interact-ing with the virtual reality demands stiffness compensation in thecontrol of the device. Thus we need an analytical stiffness modelthat is compact and computationally efficient, so it can be usedfor real time compensation by the control system of the device. Asystematic procedure has been developed in order to supportdevelopment of an analytical stiffness model [38]. This approachis using a combination of analytical models and physical experi-ments in order to validate the analytical model. This work is stillongoing and future work will focus on using the analytical stiffnessmodel for estimation of deflections in the structure and use this inthe control strategy in Fig. 11 for elastic deformationcompensation.

4. Discussion

Design of a haptic device is a complex task due to its multi-cri-teria and conflicting functional and performance requirements. Aneed for a methodology which can facilitate evaluation of require-ments has been addressed through a model-based and simulation-driven design approach. This approach enables usage of coarsemodels in early estimations of product behavior, which later canbe replaced or complemented with more detailed models duringthe detail design phase. As a test case, a haptic device based on aparallel kinematic structure was chosen, which have severaladvantages as compared to serial ones, e.g. high stiffness and lowinertia of the moving parts, and placement of the motors on thefixed base of the device. The proposed methodology was appliedon the test case for both conceptual and detail design of the device.A prototype was designed, manufactured and evaluated in thedetail design phase. Further performance improvement of theprototype was made through model-based friction compensation.We believe that this approach will support design of haptic deviceswith high performance, which can be observed through the perfor-mance mapping between requirements stated in Section 3 and ini-tial measured performance/characteristics of the prototype assummarized in Table 2.

5. Conclusions

A systematic step-by-step model-based and simulation-drivendesign methodology for the development of high performing hap-tic devices has been developed. To treat technical complexity andproject risk, the methodology is based on the V-process model aswell as the stage-gate model. The initial phase is a collaborative


effort between mechanical, electronics, and control domainspecialists, with conceptual system architecture and a detailedrequirements specification as its main deliverables. From thatstage, the development of the mechanical, electronics, and controlsystem could proceed as parallel conceptual and detail designactivities, until the system can be integrated, verified, prototyped,and validated.

The methodology was exemplified with a case to design a hap-tic device, based on a Stewart platform, to be used as surgical sim-ulators for training on hard tissues including bones and teeth. Suchdevices must have high stiffness, low inertia; large workspace, highmanipulability, low friction, high transparency, as well as theymust satisfy cost constraints. The multi-criteria and conflictingcharacter of the functional and performance requirements createa complex design space, which ask for a careful treatment duringthe design process. Based on the functional requirement a designconcept was developed by a systematic usage of kinematic,dynamic, stiffness, friction and control models. In the model-basedand simulation-driven design approach, the design starts from anabstract top-level model, which is extended via stepwise refine-ments through a design space exploration phase into a completerealization of the system. The transparency performance of thedevice was improved with a friction compensation strategy.We can conclude both from simulations and results from physicalexperiments that the performance of the designed haptic devicesatisfies the stated requirements.

The presented methodology is not restricted to a specific hapticdevice structure, and we strongly believe that it is applicable forany type of kinematic system haptic device with 5 or 6 DOFs justby changing the control strategy. All steps in this methodologyand the suggested set of tools to use are of a general nature andindependent of the test case that we selected for evaluating themethodology.

The initial architecting phase and some important tasks indetail design, such as robustification, and the industrializationaspects were not covered by the presented case. Furthermore,more cases are needed to validate the general character of themethodology.

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http://www.amazon.com/Winning-New-Products-Accelerating-Process/dp/0738204633

http://www.amazon.com/Winning-New-Products-Accelerating-Process/dp/0738204633

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http://www.mscsoftware.com

http://www.mathworks.com





http://www.dspaceinc.com







http://www.mscsoftware.com




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http://dx.doi.org/10.1109/TMECH.2013.2288944

http://dx.doi.org/10.1109/TMECH.2013.2288944




http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6197042

http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6197042




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A model-based and simulation-driven methodology for design of haptic devices