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Haptic function evaluation of multi-material part design
Computer-Aided Design 37 (2005) 727–736 www.elsevier.com/locate/cad
Haptic function evaluation of multi-material part design Zhengyi Yang, Lili Lian, Yonghua Chen* Mechanical Engineering Department, The University of Hong Kong, Pokfulam Road, Hong Kong, China Received 2 May 2004; received in revised form 23 August 2004; accepted 25 August 2004
Abstract Recently haptic shape modeling has got a momentum in industrial and conceptual design. In this paper, a real-time haptic interface of synthesized shape modeling and haptic function evaluation of product design for multi-material part is presented. Due to the advancement of manufacturing technologies, multi-material is increasingly employed by industrial designers as a means for increasing the appeals of a product while also adding functional capability. Multi-material part manufacturing processes allow designers to select different materials for different portions of a product in order to improve the material-function compatibility for the overall product. For quick design verification, the shape design and function evaluation are implemented in the same haptic environment where a load can be applied to a part design using a haptic device and at the same time the combined reaction of the part in terms of displacement and reaction can be visualized and felt by the user. The intuitive correlation between the applied force and incurred displacement (or deflection) provides an instant evaluation of the stiffness of a part design. The proposed methodology is illustrated through a case study: the design of a toothbrush. q 2004 Elsevier Ltd. All rights reserved. Keywords: Product design; Multi-materials; Function evaluation; Haptic shape modeling
1. Introduction Multi-material is commonly seen in today’s product design. This paper will mainly focus on soft touch materials that can be deformed when subjected to a load. Due to superior properties in many aspects of product aesthetics, ergonomics and functionalities, soft touch multi-material has found wide spread uses in product design. Examples of such product range from toothbrush, power grip to automotive dashboard and bathtub. The major advantages of such design are attractive and durable color, slip prevention and vibration absorption, impact and scuff resistance, etc. Since the addition of soft touch materials changes the stiffness of a part, it is desirable to have a quick evaluation of such a change. By analyzing the mechanical properties of a design at the early design stage, designers can not only minimize the probability of failure, but also can leverage analysis results to design better products faster at a lower cost. * Corresponding author. Tel: C852 2859 7910; fax: C852 2858 5415. E-mail addresses: [email protected] (Z. Yang), lianlili@ hkusua.hku.hk (L. Lian), [email protected] (Y. Chen). 0010-4485//$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.cad.2004.08.010
Mechanical property is just one aspect of the function of a product. The term of function is an abstracted description of work that a product must perform to meet customer needs. Functional requirements capture the intended behavior of the product. Function driven design is a methodology of focusing on those functions that are valuable to customers and delivering them at the lowest possible cost. Functional analysis determines whether the design is an answer to the problem statement written during the ideation phase. In this research, the product function considered is the stiffness. The traditional way of displaying analysis results is visual, such as data sheet, rendered charts, and animation. However, some of the physical properties, such as stress and strain, cannot be intuitively displayed via visual feedback only. In the proposed system, direct force feedback for analysis results is possible. Coupled with visual display, the haptic based analysis system allows designers or final users to feel the force they are applying, and at the same time, see the displacements or deflection that is happening due to the applied force. The proposed system provides an intuitive interaction with virtual object and a quick mechanics evaluation for designers in the early stage of product design.
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In product design, there are two related yet distinctively studied aspects: industrial design and engineering design. In industrial design, the functionality is considered from the perspectives of the user. User related factors or ergonomics, aesthetics, and the style of visible surfaces are of primary interests in industrial design [1]. While in engineering design, functionality is considered from the view point of manufacturers. Manufacturability, cost, physical properties, etc. are the main considerations. Generally speaking, industrial design is biased towards visualization, while engineering design is focused on performance. The efforts of industrial and engineering designers are often at odds, while the successful design of consumer products requires good interaction between the industrial designer and the engineer. Roy et al. [2] suggested that many unappealing and difficult to manufacture products evident in today’s market place may be partially attributed to the separation of function and form design. In this paper, a haptic system is developed to showcase the advantage of bridging the visualoriented design and function-oriented design. In our system, the haptic device is not only used as a sculpting tool for shape modeling, but also used as the tool for instant load simulation by allowing the user to easily add and feel a force and meanwhile observe the engineering effects (deformation, displacement or deflection). This system has been demonstrated with examples in product design of soft-touch materials.
2. Haptic shape modeling Designing complex three-dimensional shapes is one of the most challenging problems in computer art and computer-aided design. Traditional CAD systems in shape modeling are difficult to use and need a long learning time. Traditional CAD models only define the geometry of the objects. In physically based shape modeling, geometry is not the only piece of information defining an object, but aspects concerning physical characteristics of the object have to be considered and included into the model. In recent years, haptic modeling has been used in the fields of medicine, education, entertainment, computer arts, and engineering design and manufacturing. Using haptic modeling in a virtual design environment, designers are able to feel and deform virtual objects in a natural 3D setting, rather than being restricted to 2D projections for input and output. In haptic modeling, force feedback provides additional sensory cues, enabling designers to gain a richer understanding of the 3D environment. Computer haptics and graphics share the same goal of evoking the sensation of objects by appropriate sensory stimulation. A commercially available physics based shape modeling system is FreeFormw from SensAblew Technologies. Instead of forming clay with hands and then using a 3D digitizing device such as a touch probe or laser scanner to create a 3D model, the FreeFormw Modeling System allows
Fig. 1. FreeFormw modeling system.
for the shaping of virtual clay in physical space as shown in Fig. 1. Virtual models are built using a physical device. Users can create digital models in a similar intuitive and direct manner as physical modeling with clay or wax while taking advantage of the flexibility and efficiency provided by a digital environment [3]. FreeFormw’s haptic functionality provides designers with a level of interactive shape creation and evaluation that up until now has not been possible with commercialized CAD packages [4]. A critical issue in virtual haptic design is the development of a mechanics model for different materials and shaping methods. Jansson and Vergeest proposed a discrete mechanics model for deformable bodies based on interatomic interaction, and recursive resolution reduction [5]. Dachille et al. [6] reported a haptic B-spline deformation method where point, normal, and curvature constraints of B-spline surfaces are interactively specified and modified. Since haptic devices are designed to simulate physical processes, haptic modeling technologies have become an integral part of virtual prototyping systems in which realistic process modeling is required [7]. Using haptic modeling, a user can not only view the objects designed in the CAD environment, but also touch, grasp and move them in the virtual space to detect possible collisions with other objects [8]. To reflect the force in plastic deformation, a volumebased haptic rendering of milling process was developed for the proposed haptic shape modeling system [9]. Fig. 2 shows a part under modeling. Both the object and the milling tool are represented by a volumetric data structure called Spatial Run-Length Encoding (S-RLE) developed by the authors [10]. S-RLE consists of two cross-referenced database: one is a stack of lists in geometrical domain, recording the runs describing the spatial occupation of the object; the other is a table in physical domain, describing the physical properties of each element. The former is called position array and the latter property list. The property list is
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Fig. 2. Shape modeling based on simulated haptic material removal.
extendable to include more physical properties and to represent heterogeneous objects. The haptic response is implemented with a PHANToMw haptic arm. In the authors’ previous research, haptic rendering techniques for object contact and plastic deformation were reported. This paper is focused on the discussion of haptic shape modeling of multi-material models and haptic rendering for stiffness evaluation. A volume permutation method is proposed to model multi-material object.
3. Soft touch multi-material object modeling In industrial design, the shape of the product is constrained by: aesthetic requirements, such as stability, rhythm, balance, and organization; ergonomic requirements, such as ergonomic dimension, ergonomic haptics, and ergonomic physical properties. In some circumstances, these requirements are difficult to or even cannot be satisfied simultaneously. A design of multi-material product could be an alternative. The toothbrush shown in Fig. 3 is a good example of multi-materials product, which is manufactured with multi-shot molding processes. The blue (dark) color represents soft-touch material. Traditional material selection of these hygiene products are mainly based on healthy considerations. But now considerations also include the ergonomic (stiffness, soft-touch, anti-slip) and aesthetic (color, surface texture, etc.) factors. Here the distribution of soft touch material makes great impact to these two factors. Multi-shot molding processes allow designers to select different materials for different portions of a design, thus help to improve material-function compatibility for the overall object [11,12]. Moreover, a multi-material object is
Fig. 3. A toothbrush made of multi-materials.
produced as an integrated piece, thus it eliminates the assembly process. Although geometric algorithms for automated design of multi-shot molds for manufacturing multi-material product are reported, the methodology of multi-material product design is not fully discussed. Multi-material models are significantly more complex than the traditional CAD models. Currently available software tools for product design cannot assist in the design of multi-material product efficiently, not to mention about functional evaluation. For example, modeling the toothbrush as shown in Fig. 3 using an existing CAD system is not a trivial task. A possible solution is to model it as one part with multiple solids or as an assembly of several parts. Based on the proposed volume based haptic shape modeling, a volume permutation methodology is proposed to model multi-material object. The method is very straightforward: the object is modeled as a single part first with the substrate material; and then, the volumes of interest (VOI) are substituted with the secondary materials. This is a top-down design method. Thus, it’s easier to understand the design intention. Fig. 4 shows the design as a single piece on the left, secondary material distribution pattern is defined in the middle and the permutation of secondary material (shown as dark color) in the right. Permutation for more volume patterns is still an ongoing research by the authors.
4. Function evaluation Product functional evaluation is one of the most important design engineering activities. Testing and
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Fig. 4. Volume permutation for multi-material design.
monitoring of the product behavior, intended design performance and other product design parameters need to be performed. Such testing may be time-consuming and very costly. Therefore, engineering simulation methods are proposed to reduce the cycle time and cost on functional evaluation. The primary tool for mechanics simulation in engineering analysis is called Finite Element Analysis (FEA) [13]. FEA is very time-consuming and difficult to satisfy the high update rate of around 1 kHz in haptic rendering unless dramatic simplification is done. The 1 kHz rate required in haptic rendering rules out the use of previous FEA algorithms. Fig. 5 shows the finite elements at the ‘neck’ area of a toothbrush (a) and the visual display of the analysis result (b) which is obtained off-line after minutes of computation. A mass-spring model is inaccurate in its mathematical formulation. However, it is easier to solve because it is a diagonal system from the very beginning, and it does not introduce any geometric distortion. Despite its inaccuracy, it does not have visual distortion and it is computationally cheap to integrate over time because the system is, by its
Fig. 6. Haptic aided functional analysis of a toothbrush. (a) Testing elasticity of the toothbrush ‘neck’, (b) testing the button’s performance.
very nature, a set of independent algebraic equations, which requires no matrix inversions. In the traditional applications of FEA, the user is provided with some input/output facilities for specifying the forces applied to the object. As the reader can imagine, for a user to specify applied forces and boundary conditions textually requires that the user maintain in his/her mind the associations between the different nodal indices and the physical locations of those nodes on the object. All these make the use of FEA a daunting task, especially so for the non-specialist. In order to conform to a theory of elasticity, the deformations produced must be in response to forces applied to the object. In other words, the user must specify what forces to apply to where. The force–input interface is a four-sensor plate reported in [14]. In our system, the applied force is specified with the help of a PHANToMw stylus as shown in Fig. 6(a) where a force is haptically applied to a toothbrush. While applying the force, the user can feel the amplitude of the force and observe the deformation of the toothbrush. In another case as shown in Fig. 6(b), the user can test the switch button of an electrical toothbrush by pushing the button with the haptic stylus and evaluate its performance: is it too hard to push or too soft to be triggered accidentally? The button is a mechanical spring button covered with a soft-touch material volume for waterproofing purpose.
5. Haptic rendering
Fig. 5. FEA of the toothbrush as a homogeneous part. (a) Meshes generated for FEM, (b) the results of FEM on a single part: the displacement and stress distribution.
Haptic rendering systems simulate the contact forces between virtual models and reflect those forces to a user through a haptic device. This interaction is dependent on the geometric representation of the dataset and the haptic contact model. The major task of the haptic rendering
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algorithms is to calculate feedback forces from the information about the interaction of the haptic interface point (HIP) and the model. HIP is allowed to move freely until it collides with the model. A local point on the surface closest to the haptic interface point is found as the proxy point, and the relationship between the penetration direction and the surface normal at the closest point determines the forces to be applied. Therefore, two sub-tasks of haptic rendering are collision detection and feedback force computation. In this research, the collision detection task is accomplished with the GHOSTw API provided by SensAblew Technologies. A touchable model is maintained for each sample parts in the form of an instance of the ‘gstTriPolyMeshHaptic’ class. The following is focused on the development of force models. 5.1. Haptic rendering of multi-material beam In the early stage of product design, the force and displacement correlation is instructive and indicative. With the assumption that the deformations at the interfaces of different materials are the same, the multi-material
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toothbrush neck is simplified as a beam. An equivalent torsion spring model is developed to calculate the relationship between the external force and displacement. The deformation of an object depends on its geometry, on the mechanical properties of the material, and on the applied force. Stress represents the intensity of force while strain represents the intensity of deformation. Usually, stress, strain, and displacement are related. Two designs with different material distribution patterns are studies in this research. Fig. 7(a) is the alternating material element pattern and Fig. 7(b) is the sandwiched soft touch material pattern. 5.1.1. Design a As shown in Fig. 7(c), the beam consists of n elements of different materials. Assume the handle of the beam be constrained, the toothbrush neck is simplified as a cantilever. The length, deflection angle, Young’s modulus, and moment of inertia of the i-th element are denoted as li, gi, Ei, and Ii, respectively. The force applied with haptic device is F and the moment caused is M. For each material element, we have
Fig. 7. Multi-material beam. (a) Design a: transverse soft material pattern, (b) design b: longitudinal soft material pattern, (c) simplified model of multi-material beam, (d) simplified model of multi-material beam, (e) calculation of q.
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M ZF
n X
li and M Z ki $gi 0 gi Z F
iZ1
n X
! li =ki ;
(1)
iZ1
where ki Z
2Ei Ii ; l2i
(2) 5.1.2. Design b The only difference of the two models is the equation to calculate the global stiffness k. In design b,
and from the geometrical relationship, we get ! n i X X ! jAO j Z li $cos gj ; and ! j AB j Z
position of the HIP, respectively. Point O is the fixed end of the multi-material beam. q is calculated as, ! ! ! OP $OP K1 (9) q Z :POP Z cos ! : ! j OP j !jOP j
iZ1
jZ1
n X
i X
li $sin
iZ1
MZ
! gj ;
ð3Þ
therefore, :BOA Z tan
Pi Pn ! j AB j iZ1 li $sin jZ1 gj K1 ! Z tan Pn l $cos Pi g ; jAO j iZ1 i jZ1 j (4)
when g i is very small, the angle :BOA can be approximated by Pn Pi iZ1 li $ jZ1 gj K1 Pn :BOA ztan ; (5) iZ1 li If one torsion spring is used to simulate the whole beam, then F Z k :BOA0 k P F F niZ1 li Z Pn Pi z Pn Pi li $ g iZ1 li $ jZ1 gj iZ1 P jZ1 j K1 tan n
ki gi :
(6)
Since the deflection angles of each material block are the same, we have ! n 1X F Z M=l Z k $g; (11) l iZ1 i kZ
n n 1X 2 X ki Z 3 ðEi Ii Þ l iZ1 l iZ1
Some consumer products such as cameras, cell phones and electrical toothbrush have their push buttons embedded in a soft touch material volume. In Fig. 8, the push button of the battery powered toothbrush is covered with a soft-touch material volume. The major advantages of using soft-touch material here are comfortable and non-slip grip, waterproof and vibration absorption.
where k is the equivalent stiffness of the torsion spring, which is called global stiffness of the beam. And then, substitute (1) and (2) to (6), we get P F niZ1 li P kZ Pi F$ ijZ1 lj Pn l $ i iZ1 jZ1 ki Pn
Z
l iZ1 i Pi Pi l jZ1 j iZ1 li $ jZ1 ki
Pn
Pn iZ1 li P Pi l2j $ ijZ1 lj Pn iZ1 li $ jZ1 2Ej Ij
(7)
The displacement caused by the force exerted on the beam is then calculated as n .X li ; (8) F Z k$q iZ1
where q is calculated from the position of the PHANToMw HIP. As shown in Fig. 7(d), P and P* are the current and previous
(12)
5.2. Haptic rendering of soft touch resilient button
l iZ1 i
Z
(10)
iZ1
jZ1
K1
n X
Fig. 8. Soft-touch material covered button of a toothbrush.
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Fig. 9. The deformable mesh of button. (a) Button is in normal state. (b) Button is pressed.
Experiment on traditional push-buttons simulation using a haptic display is reported in [15]. In this paper, the softtouch material covered resilient button is modeled as a mass-spring mesh, beneath which there is an additional supporting spring, as shown in Fig. 9. The original status of the button mesh is shown in Fig. 9(a), and the pressed mesh in Fig. 9(b). The elasticity of the soft-touch material mesh is simplified as the springs drawn in dashed lines. Based on the mass-spring model in Fig. 9, the applied force F is a sum of the force Ft caused by the deformed soft-touch material layer and the force Fs caused by the compressed supporting spring of the switch, i.e.
where mj, vj, and hj are the mass, velocity, and current height of the jth mass point, respectively. From Eqs. (14)–(17), the force Ft can be derived and represented as the following:
F Z Ft C Fs ;
Ft Z
(13)
where Fs is set to zero when F is larger than a threshold value f to cause a sudden change of the feedback force, at which point the button is turned on. In order to calculate Ft, an energy based force model is developed. In any servo loop, the work done by the external force Ft corresponds to the increment of the energy of the mesh, which consists of the incremental elastic energy of all springs Ee, the kinetic energy Ek and potential energy Ep of all mass points. Ft $Dl Z DEe C DEP C DEk ;
(14)
where Dl is the displacement increment along the force direction. These energies are represented by the following three equations, Ee Z
n 1X k ðx K xi0 Þ2 ; 2 iZ1 i i
(15)
where ki is the stiffness coefficient of the ith spring, xi and xi0 are the current length and resting length of the spring, respectively; 1 Ek Z mj v2j ; 2
(16)
EP Z mj ghj ;
(17)
Ft Z
DEe C DEP C DEk ; Dl
(18)
To speed up the computation, we assume the mesh deforms under the quasi-static situation, which means the mesh deforms slowly so that it remains near static equilibrium at each instant. Therefore, DEkZ0 for any servo loop. Eq. (18) is simplified to, DEe C DEP Dl
(19)
6. Prototype implementation A prototype system is implemented using a PC controlled PHANToMw device for real time haptic simulations. The functional requirement here is the stiffness. A hard toothbrush may hurt the denture especially when used by children; while a too soft toothbrush may bend too much to be controlled. In order to have different stiffness while keeping the same ‘neck’ geometry of the toothbrush, soft-materials can be added to replace part of the hard material at the ‘neck’. Fig. 7(a) and (b) illustrate two alternative soft-material patterns. The designers can feel the different stiffness and deformation while applying a force at the head of the toothbrush. Fig. 10(a) shows the screen shots of the testing process. The bar next to the toothbrush is a force indicator where the yellow (light) color shows the magnitude of the applied force. Two designs, design a with stiffer neck and design b with softer neck are tested. It can be observed from the pictures that much smaller force is needed to achieve the same deflection for the softer toothbrush than that for the stiffer one. Fig. 10(b) show the recorded forces applied via the haptic device within a time span, in which the toothbrush is pushed and released three times. The desired neck stiffness can be found by repeatedly changing the soft-material pattern or volume and doing the haptic force-deflection simulation. Through this kind of trial-and-error, a typical process in product design,
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Fig. 10. Test the stiffness of the toothbrush neck. (a) Feeling the force while watching the deflection. (b) Force exerted via haptic device.
Fig. 11. Press the soft-touch material covered button. (a) Released. (b) Pressing. (c) Force varies with time.
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designers can get the right stiffness from which the best perceived correlation between the force and deflection is achieved. In this simulation, the physical attributes of the substrate (hard) material and secondary (soft) material are set as listed below: E1 Z 8:3e C 009 N=m2 ; v1 Z 0:28; r1 Z 1200 kg=m3 ; E2 Z 2e C 009 N=m2 ; v2 Z 0:394; r2 Z 1020 kg=m3 : Fig. 11 shows a similar analysis process for the soft-touch material clad push button: use the haptic stylus to push the button and feel the force feedback. Fig. 11(a) shows a toothbrush button without any load. Fig. 11(b) is the button subjected to a force. The relative magnitude of the force is shown through an indicator as in the light color scale. The recorded force–time curve is shown in Fig. 11(c). The sudden change of the force is due to the status change of the switch: the switch is turned on. By doing such evaluation, designers can tell whether the push button trigger force is appropriate or not with the current soft touch material volume. If not, the designer has to change the soft touch material volume or stiffness value and do the evaluation again until a comfortable design trigger force is found.
7. Conclusion and future works Haptic modeling is introduced into the early product design and function evaluation process. It is used as both a geometry modeling tool on the product design platform and a force-input/feedback interface in functional evaluation. A preliminary method based on volume permutation of multimaterial product design is discussed. A simplified torsion spring model is developed for haptic rendering of multimaterial objects. The proposed design system can help to improve the design efficiency by providing intuitive functional evaluation in the early stage of design. Functional analysis could be used by designers to gain insight into the likely performance and behavior of a proposed design. In the future, more generalized force models need to be developed to deal with complex objects. The product itself can be modeled and simulated as a deformable tool. Thus, the designer may feel like holding a true toothbrush when holding the PHANToMw stylus and brush it on a virtual tooth model that is modeled as a static rigid body to simulate the tooth brushing process. Such cases also exist in testing a badminton racket smashing a shuttlecock, which is modeled as a dynamic body. Other ergonomics performance should be added to the simulation, such as the vibration when the automatic toothbrush is turned on.
Acknowledgements This research is supported by a grant from Hong Kong Research Grants Council under the code HKU 7073/02E.
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References [1] Brunetti G, Golob B. A feature-based approach towards an integrated product model including conceptual design information. Comput Aided Des 2000;32(14):877–87. [2] Roy U, Pramanik N, Sudarsan R, Sriram RD, Lyons KW. Function-toform mapping: model, representation and applications in design synthesis. Comput Aided Des 2001;33(10):699–719. [3] http://www.sensable.com. [4] Sener B, Pedgley O, Wormald P, Campbell I. Incorporating the freeform haptic modelling system into new product development. In: Proceeding of EuroHaptics 2003, Dublin, Ireland, July 6–9; 2003, p. 26–38. [5] Jansson J, Vergeest JSM. A discrete mechanics model for deformable bodies. Comput Aided Des 2002;34(12):913–28. [6] Dachille IX, Qin H, Kaufman A. A novel haptics-based interface and sculpting system for physics-based geometric design. Comput Aided Des 2001;33(5):403–20. [7] Chen E. Six degree-of-freedom haptic system for desktop virtual prototyping applications. In: Proceedings of the first international workshop on virtual reality and prototyping, Laval, France; 1999, p. 97–106. [8] Gutierrez T, Barabero JI, Aizpitarte M, Cariilo AR, Eguidazu A. Assembly simulation through haptic virtual prototypes. In: Proceedings of third PHANToMw users group workshop, Dedham, MA, USA; 1998. [9] Yang ZY, Chen YH. Haptic rendering of milling. In: Proceeding of EuroHaptics 2003, Dublin, Ireland, July 6–9; 2003, p. 206–17. [10] Chen YH, Yang ZY. Haptic rendering based on spatial run-length encoding. J Robotics Comput Integrated Manufacturing 2003 [in press]. [11] Li XJ, Gupta SK. Geometric algorithms for automated design of rotary-platen multi-shot molds. Comput Aided Des 2004 [in press]. [12] Kumar M, Gupta SK. A geometric algorithm for automated design of multi-stage molds for manufacturing multi-material objects. In: Proceedings of symposium on solid modeling and applications 2001, Ann Arbor, Michigan, USA; 2001, p. 278–88. [13] Desai CS, Kundu T. Introductory finite element method. Boca Raton: CRC Press; 2001. [14] Kang H, Kak A. Deforming virtual objects interactively in accordance with an elastic model. Comput Aided Des 1996;28(4):251–62. [15] Doerrer C, Werthschuetzky R. Simulating push-buttons using a haptic display: requirements on force resolution and force-displacement curve. In: Proceedings of EuroHaptics, 2002, Edinburgh, UK; 2002.
Dr Chen Yonghua is now an associate professor. After obtaining a BSc degree in Mechanical Engineering from the Southwest Jiaotong University, he furthered his education in the UK and obtained his PhD in 1991 from the University of Liverpool. Before joining the department, Dr Chen had worked in Motorola Electronics Pvt., Ltd (Singapore), Asia Matsushita Electronics Pvt., Ltd (Singapore) and Swire Technologies Pvt., Ltd (Hong Kong) where he had accumulated enormous experiences in automation, robotics, engineering design and quality management. Dr Chen has filed one patent, co-authored a book and published over 60 referred papers in international journals and conferences. His current research interests include engineering design, reverse engineering, rapid prototyping and haptic modeling. Dr Chen is a Chartered Engineer and a member of the Institution of Mechanical Engineer.
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Z. Yang et al. / Computer-Aided Design 37 (2005) 727–736 Dr Yang Zhengyi is working as a research associate in the Mechanical Engineering Department at The University of Hong Kong, after obtaining a PhD degree from the same department. He obtained both his Bachelor and Master degrees in the Mechanical Engineering Department at Sichuan University, People’s Republic of China. His current research interests include haptic rendering, haptic modeling, CAD/CAM, advanced manufacturing technologies, rapid prototyping, and robot machining.
Miss Lian Lili is a PhD student at the Department of Mechanical Engineering of the University of Hong Kong. She received her Bachelor and Master degrees in the Department of Mechatronics Engineering at Harbin Institute of Technology, People’s Republic of China. Her current research interest includes haptic modeling and haptic rendering.
Haptic function evaluation of multi-material part design Zhengyi Yang, Lili Lian, Yonghua Chen* Mechanical Engineering Department, The University of Hong Kong, Pokfulam Road, Hong Kong, China Received 2 May 2004; received in revised form 23 August 2004; accepted 25 August 2004
Abstract Recently haptic shape modeling has got a momentum in industrial and conceptual design. In this paper, a real-time haptic interface of synthesized shape modeling and haptic function evaluation of product design for multi-material part is presented. Due to the advancement of manufacturing technologies, multi-material is increasingly employed by industrial designers as a means for increasing the appeals of a product while also adding functional capability. Multi-material part manufacturing processes allow designers to select different materials for different portions of a product in order to improve the material-function compatibility for the overall product. For quick design verification, the shape design and function evaluation are implemented in the same haptic environment where a load can be applied to a part design using a haptic device and at the same time the combined reaction of the part in terms of displacement and reaction can be visualized and felt by the user. The intuitive correlation between the applied force and incurred displacement (or deflection) provides an instant evaluation of the stiffness of a part design. The proposed methodology is illustrated through a case study: the design of a toothbrush. q 2004 Elsevier Ltd. All rights reserved. Keywords: Product design; Multi-materials; Function evaluation; Haptic shape modeling
1. Introduction Multi-material is commonly seen in today’s product design. This paper will mainly focus on soft touch materials that can be deformed when subjected to a load. Due to superior properties in many aspects of product aesthetics, ergonomics and functionalities, soft touch multi-material has found wide spread uses in product design. Examples of such product range from toothbrush, power grip to automotive dashboard and bathtub. The major advantages of such design are attractive and durable color, slip prevention and vibration absorption, impact and scuff resistance, etc. Since the addition of soft touch materials changes the stiffness of a part, it is desirable to have a quick evaluation of such a change. By analyzing the mechanical properties of a design at the early design stage, designers can not only minimize the probability of failure, but also can leverage analysis results to design better products faster at a lower cost. * Corresponding author. Tel: C852 2859 7910; fax: C852 2858 5415. E-mail addresses: [email protected] (Z. Yang), lianlili@ hkusua.hku.hk (L. Lian), [email protected] (Y. Chen). 0010-4485//$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.cad.2004.08.010
Mechanical property is just one aspect of the function of a product. The term of function is an abstracted description of work that a product must perform to meet customer needs. Functional requirements capture the intended behavior of the product. Function driven design is a methodology of focusing on those functions that are valuable to customers and delivering them at the lowest possible cost. Functional analysis determines whether the design is an answer to the problem statement written during the ideation phase. In this research, the product function considered is the stiffness. The traditional way of displaying analysis results is visual, such as data sheet, rendered charts, and animation. However, some of the physical properties, such as stress and strain, cannot be intuitively displayed via visual feedback only. In the proposed system, direct force feedback for analysis results is possible. Coupled with visual display, the haptic based analysis system allows designers or final users to feel the force they are applying, and at the same time, see the displacements or deflection that is happening due to the applied force. The proposed system provides an intuitive interaction with virtual object and a quick mechanics evaluation for designers in the early stage of product design.
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In product design, there are two related yet distinctively studied aspects: industrial design and engineering design. In industrial design, the functionality is considered from the perspectives of the user. User related factors or ergonomics, aesthetics, and the style of visible surfaces are of primary interests in industrial design [1]. While in engineering design, functionality is considered from the view point of manufacturers. Manufacturability, cost, physical properties, etc. are the main considerations. Generally speaking, industrial design is biased towards visualization, while engineering design is focused on performance. The efforts of industrial and engineering designers are often at odds, while the successful design of consumer products requires good interaction between the industrial designer and the engineer. Roy et al. [2] suggested that many unappealing and difficult to manufacture products evident in today’s market place may be partially attributed to the separation of function and form design. In this paper, a haptic system is developed to showcase the advantage of bridging the visualoriented design and function-oriented design. In our system, the haptic device is not only used as a sculpting tool for shape modeling, but also used as the tool for instant load simulation by allowing the user to easily add and feel a force and meanwhile observe the engineering effects (deformation, displacement or deflection). This system has been demonstrated with examples in product design of soft-touch materials.
2. Haptic shape modeling Designing complex three-dimensional shapes is one of the most challenging problems in computer art and computer-aided design. Traditional CAD systems in shape modeling are difficult to use and need a long learning time. Traditional CAD models only define the geometry of the objects. In physically based shape modeling, geometry is not the only piece of information defining an object, but aspects concerning physical characteristics of the object have to be considered and included into the model. In recent years, haptic modeling has been used in the fields of medicine, education, entertainment, computer arts, and engineering design and manufacturing. Using haptic modeling in a virtual design environment, designers are able to feel and deform virtual objects in a natural 3D setting, rather than being restricted to 2D projections for input and output. In haptic modeling, force feedback provides additional sensory cues, enabling designers to gain a richer understanding of the 3D environment. Computer haptics and graphics share the same goal of evoking the sensation of objects by appropriate sensory stimulation. A commercially available physics based shape modeling system is FreeFormw from SensAblew Technologies. Instead of forming clay with hands and then using a 3D digitizing device such as a touch probe or laser scanner to create a 3D model, the FreeFormw Modeling System allows
Fig. 1. FreeFormw modeling system.
for the shaping of virtual clay in physical space as shown in Fig. 1. Virtual models are built using a physical device. Users can create digital models in a similar intuitive and direct manner as physical modeling with clay or wax while taking advantage of the flexibility and efficiency provided by a digital environment [3]. FreeFormw’s haptic functionality provides designers with a level of interactive shape creation and evaluation that up until now has not been possible with commercialized CAD packages [4]. A critical issue in virtual haptic design is the development of a mechanics model for different materials and shaping methods. Jansson and Vergeest proposed a discrete mechanics model for deformable bodies based on interatomic interaction, and recursive resolution reduction [5]. Dachille et al. [6] reported a haptic B-spline deformation method where point, normal, and curvature constraints of B-spline surfaces are interactively specified and modified. Since haptic devices are designed to simulate physical processes, haptic modeling technologies have become an integral part of virtual prototyping systems in which realistic process modeling is required [7]. Using haptic modeling, a user can not only view the objects designed in the CAD environment, but also touch, grasp and move them in the virtual space to detect possible collisions with other objects [8]. To reflect the force in plastic deformation, a volumebased haptic rendering of milling process was developed for the proposed haptic shape modeling system [9]. Fig. 2 shows a part under modeling. Both the object and the milling tool are represented by a volumetric data structure called Spatial Run-Length Encoding (S-RLE) developed by the authors [10]. S-RLE consists of two cross-referenced database: one is a stack of lists in geometrical domain, recording the runs describing the spatial occupation of the object; the other is a table in physical domain, describing the physical properties of each element. The former is called position array and the latter property list. The property list is
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Fig. 2. Shape modeling based on simulated haptic material removal.
extendable to include more physical properties and to represent heterogeneous objects. The haptic response is implemented with a PHANToMw haptic arm. In the authors’ previous research, haptic rendering techniques for object contact and plastic deformation were reported. This paper is focused on the discussion of haptic shape modeling of multi-material models and haptic rendering for stiffness evaluation. A volume permutation method is proposed to model multi-material object.
3. Soft touch multi-material object modeling In industrial design, the shape of the product is constrained by: aesthetic requirements, such as stability, rhythm, balance, and organization; ergonomic requirements, such as ergonomic dimension, ergonomic haptics, and ergonomic physical properties. In some circumstances, these requirements are difficult to or even cannot be satisfied simultaneously. A design of multi-material product could be an alternative. The toothbrush shown in Fig. 3 is a good example of multi-materials product, which is manufactured with multi-shot molding processes. The blue (dark) color represents soft-touch material. Traditional material selection of these hygiene products are mainly based on healthy considerations. But now considerations also include the ergonomic (stiffness, soft-touch, anti-slip) and aesthetic (color, surface texture, etc.) factors. Here the distribution of soft touch material makes great impact to these two factors. Multi-shot molding processes allow designers to select different materials for different portions of a design, thus help to improve material-function compatibility for the overall object [11,12]. Moreover, a multi-material object is
Fig. 3. A toothbrush made of multi-materials.
produced as an integrated piece, thus it eliminates the assembly process. Although geometric algorithms for automated design of multi-shot molds for manufacturing multi-material product are reported, the methodology of multi-material product design is not fully discussed. Multi-material models are significantly more complex than the traditional CAD models. Currently available software tools for product design cannot assist in the design of multi-material product efficiently, not to mention about functional evaluation. For example, modeling the toothbrush as shown in Fig. 3 using an existing CAD system is not a trivial task. A possible solution is to model it as one part with multiple solids or as an assembly of several parts. Based on the proposed volume based haptic shape modeling, a volume permutation methodology is proposed to model multi-material object. The method is very straightforward: the object is modeled as a single part first with the substrate material; and then, the volumes of interest (VOI) are substituted with the secondary materials. This is a top-down design method. Thus, it’s easier to understand the design intention. Fig. 4 shows the design as a single piece on the left, secondary material distribution pattern is defined in the middle and the permutation of secondary material (shown as dark color) in the right. Permutation for more volume patterns is still an ongoing research by the authors.
4. Function evaluation Product functional evaluation is one of the most important design engineering activities. Testing and
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Fig. 4. Volume permutation for multi-material design.
monitoring of the product behavior, intended design performance and other product design parameters need to be performed. Such testing may be time-consuming and very costly. Therefore, engineering simulation methods are proposed to reduce the cycle time and cost on functional evaluation. The primary tool for mechanics simulation in engineering analysis is called Finite Element Analysis (FEA) [13]. FEA is very time-consuming and difficult to satisfy the high update rate of around 1 kHz in haptic rendering unless dramatic simplification is done. The 1 kHz rate required in haptic rendering rules out the use of previous FEA algorithms. Fig. 5 shows the finite elements at the ‘neck’ area of a toothbrush (a) and the visual display of the analysis result (b) which is obtained off-line after minutes of computation. A mass-spring model is inaccurate in its mathematical formulation. However, it is easier to solve because it is a diagonal system from the very beginning, and it does not introduce any geometric distortion. Despite its inaccuracy, it does not have visual distortion and it is computationally cheap to integrate over time because the system is, by its
Fig. 6. Haptic aided functional analysis of a toothbrush. (a) Testing elasticity of the toothbrush ‘neck’, (b) testing the button’s performance.
very nature, a set of independent algebraic equations, which requires no matrix inversions. In the traditional applications of FEA, the user is provided with some input/output facilities for specifying the forces applied to the object. As the reader can imagine, for a user to specify applied forces and boundary conditions textually requires that the user maintain in his/her mind the associations between the different nodal indices and the physical locations of those nodes on the object. All these make the use of FEA a daunting task, especially so for the non-specialist. In order to conform to a theory of elasticity, the deformations produced must be in response to forces applied to the object. In other words, the user must specify what forces to apply to where. The force–input interface is a four-sensor plate reported in [14]. In our system, the applied force is specified with the help of a PHANToMw stylus as shown in Fig. 6(a) where a force is haptically applied to a toothbrush. While applying the force, the user can feel the amplitude of the force and observe the deformation of the toothbrush. In another case as shown in Fig. 6(b), the user can test the switch button of an electrical toothbrush by pushing the button with the haptic stylus and evaluate its performance: is it too hard to push or too soft to be triggered accidentally? The button is a mechanical spring button covered with a soft-touch material volume for waterproofing purpose.
5. Haptic rendering
Fig. 5. FEA of the toothbrush as a homogeneous part. (a) Meshes generated for FEM, (b) the results of FEM on a single part: the displacement and stress distribution.
Haptic rendering systems simulate the contact forces between virtual models and reflect those forces to a user through a haptic device. This interaction is dependent on the geometric representation of the dataset and the haptic contact model. The major task of the haptic rendering
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algorithms is to calculate feedback forces from the information about the interaction of the haptic interface point (HIP) and the model. HIP is allowed to move freely until it collides with the model. A local point on the surface closest to the haptic interface point is found as the proxy point, and the relationship between the penetration direction and the surface normal at the closest point determines the forces to be applied. Therefore, two sub-tasks of haptic rendering are collision detection and feedback force computation. In this research, the collision detection task is accomplished with the GHOSTw API provided by SensAblew Technologies. A touchable model is maintained for each sample parts in the form of an instance of the ‘gstTriPolyMeshHaptic’ class. The following is focused on the development of force models. 5.1. Haptic rendering of multi-material beam In the early stage of product design, the force and displacement correlation is instructive and indicative. With the assumption that the deformations at the interfaces of different materials are the same, the multi-material
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toothbrush neck is simplified as a beam. An equivalent torsion spring model is developed to calculate the relationship between the external force and displacement. The deformation of an object depends on its geometry, on the mechanical properties of the material, and on the applied force. Stress represents the intensity of force while strain represents the intensity of deformation. Usually, stress, strain, and displacement are related. Two designs with different material distribution patterns are studies in this research. Fig. 7(a) is the alternating material element pattern and Fig. 7(b) is the sandwiched soft touch material pattern. 5.1.1. Design a As shown in Fig. 7(c), the beam consists of n elements of different materials. Assume the handle of the beam be constrained, the toothbrush neck is simplified as a cantilever. The length, deflection angle, Young’s modulus, and moment of inertia of the i-th element are denoted as li, gi, Ei, and Ii, respectively. The force applied with haptic device is F and the moment caused is M. For each material element, we have
Fig. 7. Multi-material beam. (a) Design a: transverse soft material pattern, (b) design b: longitudinal soft material pattern, (c) simplified model of multi-material beam, (d) simplified model of multi-material beam, (e) calculation of q.
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M ZF
n X
li and M Z ki $gi 0 gi Z F
iZ1
n X
! li =ki ;
(1)
iZ1
where ki Z
2Ei Ii ; l2i
(2) 5.1.2. Design b The only difference of the two models is the equation to calculate the global stiffness k. In design b,
and from the geometrical relationship, we get ! n i X X ! jAO j Z li $cos gj ; and ! j AB j Z
position of the HIP, respectively. Point O is the fixed end of the multi-material beam. q is calculated as, ! ! ! OP $OP K1 (9) q Z :POP Z cos ! : ! j OP j !jOP j
iZ1
jZ1
n X
i X
li $sin
iZ1
MZ
! gj ;
ð3Þ
therefore, :BOA Z tan
Pi Pn ! j AB j iZ1 li $sin jZ1 gj K1 ! Z tan Pn l $cos Pi g ; jAO j iZ1 i jZ1 j (4)
when g i is very small, the angle :BOA can be approximated by Pn Pi iZ1 li $ jZ1 gj K1 Pn :BOA ztan ; (5) iZ1 li If one torsion spring is used to simulate the whole beam, then F Z k :BOA0 k P F F niZ1 li Z Pn Pi z Pn Pi li $ g iZ1 li $ jZ1 gj iZ1 P jZ1 j K1 tan n
ki gi :
(6)
Since the deflection angles of each material block are the same, we have ! n 1X F Z M=l Z k $g; (11) l iZ1 i kZ
n n 1X 2 X ki Z 3 ðEi Ii Þ l iZ1 l iZ1
Some consumer products such as cameras, cell phones and electrical toothbrush have their push buttons embedded in a soft touch material volume. In Fig. 8, the push button of the battery powered toothbrush is covered with a soft-touch material volume. The major advantages of using soft-touch material here are comfortable and non-slip grip, waterproof and vibration absorption.
where k is the equivalent stiffness of the torsion spring, which is called global stiffness of the beam. And then, substitute (1) and (2) to (6), we get P F niZ1 li P kZ Pi F$ ijZ1 lj Pn l $ i iZ1 jZ1 ki Pn
Z
l iZ1 i Pi Pi l jZ1 j iZ1 li $ jZ1 ki
Pn
Pn iZ1 li P Pi l2j $ ijZ1 lj Pn iZ1 li $ jZ1 2Ej Ij
(7)
The displacement caused by the force exerted on the beam is then calculated as n .X li ; (8) F Z k$q iZ1
where q is calculated from the position of the PHANToMw HIP. As shown in Fig. 7(d), P and P* are the current and previous
(12)
5.2. Haptic rendering of soft touch resilient button
l iZ1 i
Z
(10)
iZ1
jZ1
K1
n X
Fig. 8. Soft-touch material covered button of a toothbrush.
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Fig. 9. The deformable mesh of button. (a) Button is in normal state. (b) Button is pressed.
Experiment on traditional push-buttons simulation using a haptic display is reported in [15]. In this paper, the softtouch material covered resilient button is modeled as a mass-spring mesh, beneath which there is an additional supporting spring, as shown in Fig. 9. The original status of the button mesh is shown in Fig. 9(a), and the pressed mesh in Fig. 9(b). The elasticity of the soft-touch material mesh is simplified as the springs drawn in dashed lines. Based on the mass-spring model in Fig. 9, the applied force F is a sum of the force Ft caused by the deformed soft-touch material layer and the force Fs caused by the compressed supporting spring of the switch, i.e.
where mj, vj, and hj are the mass, velocity, and current height of the jth mass point, respectively. From Eqs. (14)–(17), the force Ft can be derived and represented as the following:
F Z Ft C Fs ;
Ft Z
(13)
where Fs is set to zero when F is larger than a threshold value f to cause a sudden change of the feedback force, at which point the button is turned on. In order to calculate Ft, an energy based force model is developed. In any servo loop, the work done by the external force Ft corresponds to the increment of the energy of the mesh, which consists of the incremental elastic energy of all springs Ee, the kinetic energy Ek and potential energy Ep of all mass points. Ft $Dl Z DEe C DEP C DEk ;
(14)
where Dl is the displacement increment along the force direction. These energies are represented by the following three equations, Ee Z
n 1X k ðx K xi0 Þ2 ; 2 iZ1 i i
(15)
where ki is the stiffness coefficient of the ith spring, xi and xi0 are the current length and resting length of the spring, respectively; 1 Ek Z mj v2j ; 2
(16)
EP Z mj ghj ;
(17)
Ft Z
DEe C DEP C DEk ; Dl
(18)
To speed up the computation, we assume the mesh deforms under the quasi-static situation, which means the mesh deforms slowly so that it remains near static equilibrium at each instant. Therefore, DEkZ0 for any servo loop. Eq. (18) is simplified to, DEe C DEP Dl
(19)
6. Prototype implementation A prototype system is implemented using a PC controlled PHANToMw device for real time haptic simulations. The functional requirement here is the stiffness. A hard toothbrush may hurt the denture especially when used by children; while a too soft toothbrush may bend too much to be controlled. In order to have different stiffness while keeping the same ‘neck’ geometry of the toothbrush, soft-materials can be added to replace part of the hard material at the ‘neck’. Fig. 7(a) and (b) illustrate two alternative soft-material patterns. The designers can feel the different stiffness and deformation while applying a force at the head of the toothbrush. Fig. 10(a) shows the screen shots of the testing process. The bar next to the toothbrush is a force indicator where the yellow (light) color shows the magnitude of the applied force. Two designs, design a with stiffer neck and design b with softer neck are tested. It can be observed from the pictures that much smaller force is needed to achieve the same deflection for the softer toothbrush than that for the stiffer one. Fig. 10(b) show the recorded forces applied via the haptic device within a time span, in which the toothbrush is pushed and released three times. The desired neck stiffness can be found by repeatedly changing the soft-material pattern or volume and doing the haptic force-deflection simulation. Through this kind of trial-and-error, a typical process in product design,
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Fig. 10. Test the stiffness of the toothbrush neck. (a) Feeling the force while watching the deflection. (b) Force exerted via haptic device.
Fig. 11. Press the soft-touch material covered button. (a) Released. (b) Pressing. (c) Force varies with time.
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designers can get the right stiffness from which the best perceived correlation between the force and deflection is achieved. In this simulation, the physical attributes of the substrate (hard) material and secondary (soft) material are set as listed below: E1 Z 8:3e C 009 N=m2 ; v1 Z 0:28; r1 Z 1200 kg=m3 ; E2 Z 2e C 009 N=m2 ; v2 Z 0:394; r2 Z 1020 kg=m3 : Fig. 11 shows a similar analysis process for the soft-touch material clad push button: use the haptic stylus to push the button and feel the force feedback. Fig. 11(a) shows a toothbrush button without any load. Fig. 11(b) is the button subjected to a force. The relative magnitude of the force is shown through an indicator as in the light color scale. The recorded force–time curve is shown in Fig. 11(c). The sudden change of the force is due to the status change of the switch: the switch is turned on. By doing such evaluation, designers can tell whether the push button trigger force is appropriate or not with the current soft touch material volume. If not, the designer has to change the soft touch material volume or stiffness value and do the evaluation again until a comfortable design trigger force is found.
7. Conclusion and future works Haptic modeling is introduced into the early product design and function evaluation process. It is used as both a geometry modeling tool on the product design platform and a force-input/feedback interface in functional evaluation. A preliminary method based on volume permutation of multimaterial product design is discussed. A simplified torsion spring model is developed for haptic rendering of multimaterial objects. The proposed design system can help to improve the design efficiency by providing intuitive functional evaluation in the early stage of design. Functional analysis could be used by designers to gain insight into the likely performance and behavior of a proposed design. In the future, more generalized force models need to be developed to deal with complex objects. The product itself can be modeled and simulated as a deformable tool. Thus, the designer may feel like holding a true toothbrush when holding the PHANToMw stylus and brush it on a virtual tooth model that is modeled as a static rigid body to simulate the tooth brushing process. Such cases also exist in testing a badminton racket smashing a shuttlecock, which is modeled as a dynamic body. Other ergonomics performance should be added to the simulation, such as the vibration when the automatic toothbrush is turned on.
Acknowledgements This research is supported by a grant from Hong Kong Research Grants Council under the code HKU 7073/02E.
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References [1] Brunetti G, Golob B. A feature-based approach towards an integrated product model including conceptual design information. Comput Aided Des 2000;32(14):877–87. [2] Roy U, Pramanik N, Sudarsan R, Sriram RD, Lyons KW. Function-toform mapping: model, representation and applications in design synthesis. Comput Aided Des 2001;33(10):699–719. [3] http://www.sensable.com. [4] Sener B, Pedgley O, Wormald P, Campbell I. Incorporating the freeform haptic modelling system into new product development. In: Proceeding of EuroHaptics 2003, Dublin, Ireland, July 6–9; 2003, p. 26–38. [5] Jansson J, Vergeest JSM. A discrete mechanics model for deformable bodies. Comput Aided Des 2002;34(12):913–28. [6] Dachille IX, Qin H, Kaufman A. A novel haptics-based interface and sculpting system for physics-based geometric design. Comput Aided Des 2001;33(5):403–20. [7] Chen E. Six degree-of-freedom haptic system for desktop virtual prototyping applications. In: Proceedings of the first international workshop on virtual reality and prototyping, Laval, France; 1999, p. 97–106. [8] Gutierrez T, Barabero JI, Aizpitarte M, Cariilo AR, Eguidazu A. Assembly simulation through haptic virtual prototypes. In: Proceedings of third PHANToMw users group workshop, Dedham, MA, USA; 1998. [9] Yang ZY, Chen YH. Haptic rendering of milling. In: Proceeding of EuroHaptics 2003, Dublin, Ireland, July 6–9; 2003, p. 206–17. [10] Chen YH, Yang ZY. Haptic rendering based on spatial run-length encoding. J Robotics Comput Integrated Manufacturing 2003 [in press]. [11] Li XJ, Gupta SK. Geometric algorithms for automated design of rotary-platen multi-shot molds. Comput Aided Des 2004 [in press]. [12] Kumar M, Gupta SK. A geometric algorithm for automated design of multi-stage molds for manufacturing multi-material objects. In: Proceedings of symposium on solid modeling and applications 2001, Ann Arbor, Michigan, USA; 2001, p. 278–88. [13] Desai CS, Kundu T. Introductory finite element method. Boca Raton: CRC Press; 2001. [14] Kang H, Kak A. Deforming virtual objects interactively in accordance with an elastic model. Comput Aided Des 1996;28(4):251–62. [15] Doerrer C, Werthschuetzky R. Simulating push-buttons using a haptic display: requirements on force resolution and force-displacement curve. In: Proceedings of EuroHaptics, 2002, Edinburgh, UK; 2002.
Dr Chen Yonghua is now an associate professor. After obtaining a BSc degree in Mechanical Engineering from the Southwest Jiaotong University, he furthered his education in the UK and obtained his PhD in 1991 from the University of Liverpool. Before joining the department, Dr Chen had worked in Motorola Electronics Pvt., Ltd (Singapore), Asia Matsushita Electronics Pvt., Ltd (Singapore) and Swire Technologies Pvt., Ltd (Hong Kong) where he had accumulated enormous experiences in automation, robotics, engineering design and quality management. Dr Chen has filed one patent, co-authored a book and published over 60 referred papers in international journals and conferences. His current research interests include engineering design, reverse engineering, rapid prototyping and haptic modeling. Dr Chen is a Chartered Engineer and a member of the Institution of Mechanical Engineer.
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Z. Yang et al. / Computer-Aided Design 37 (2005) 727–736 Dr Yang Zhengyi is working as a research associate in the Mechanical Engineering Department at The University of Hong Kong, after obtaining a PhD degree from the same department. He obtained both his Bachelor and Master degrees in the Mechanical Engineering Department at Sichuan University, People’s Republic of China. His current research interests include haptic rendering, haptic modeling, CAD/CAM, advanced manufacturing technologies, rapid prototyping, and robot machining.
Miss Lian Lili is a PhD student at the Department of Mechanical Engineering of the University of Hong Kong. She received her Bachelor and Master degrees in the Department of Mechatronics Engineering at Harbin Institute of Technology, People’s Republic of China. Her current research interest includes haptic modeling and haptic rendering.