Formable Object - A New Haptic Interface for Shape Rendering

Stefan Klare∗

Institute of Automatic Control Engineering

Technische Universitat Munchen

Dmitrij Forssilow†

Institute of Automatic Control Engineering

Technische Universitat Munchen

Angelika Peer‡

Institute of Automatic Control Engineering

Technische Universitat Munchen

ABSTRACT

Interacting with 3D-shape objects using bare hands represents avery intuitive way to explore object shapes and offers lots of newopportunities in the field of virtual reality and design. Only a few3D-shape interfaces are known, but their resolution is rather lowand/or they are not actuated. Thus, a new design for an actuated3D-shape interface with a comparatively high resolution is pre-sented, which can be further extended to cover larger interactionareas. The kinematics of the device is analyzed and a numericalsolution for the inverse kinematics is presented. The ability to formpredefined shapes is analyzed. The presented interface can displaybasic shapes like cylinders or spheres, and due to its specific kine-matic design, can easily be mounted as end-effector to kinesthetichaptic interfaces.

1 INTRODUCTION

Haptic interfaces for shape rendering are either devices that canmorph their shape to form a surface which can be explored by auser, or devices that generate the illusion of experiencing a realshape. Haptic interfaces for shape rendering promise applicationsin the field of design and prototyping. By using a shape renderinginterface in the design process of e.g. cars or household aids, shapescan be visualized and haptically explored without costs for manu-facturing real parts. The shape/design of a product body highlycontributes to the commercial success of it. With a shape renderingdevice, shapes can be evaluated in a very intuitive way and modi-fications can be made with bare hands and directly applied to thedesign. Further, by using a shape rendering interface, the surfaceof objects can be explored with bare hands in contrast to state-of-the-art interfaces where only point-contacts can be simulated. How-ever, only few mechanical concepts have been developed up to now.Basically three design concepts can be distinguished: a) FormableBody Concepts, b) Formable Crust Concepts and c) Non-contactDisplays. These concepts will be described in the following para-graphs.

Formable Body Concepts: The Claytronics project [5] dealswith a very preliminary formable body concept. The main idea is,that 3D-shapes are generated by using programmable manner. Themanner consists of catoms (claytronic atoms) which can move inthree dimensions in relation to others or adhere to other catoms tomaintain a 3D shape. With the claytronic concept very complexshapes are possible (holes in the object, etc.). The main drawback,however, is that at present the catoms are bulky (45mm in diameter),thus the resolution is unsatisfying.

Formable Crust Concepts: Apart from the Claytronics-project there is the FEELEX mechanism [8], a 2.5D-formable crustconcept. The FEELEX uses a linear actuator array. Each actuatordrives a rod which is located underneath a rubber membrane, which

∗e-mail:stefan.klare@tum.de†e-mail:dmitrij@mytum.de‡e-mail:angelika.peer@tum.de

is deformed by the rods. A drawback of this concept is that it isequipped with a bulky actuator arrangement and it is not possibleto display shapes with undercuts.

In [3] multiple formable crust concepts for deforming a mem-brane or strip by bending it with actuators located directly under-neath the membrane/strip are discussed. However, these conceptsare only theoretical.

A preliminary concept is Digital Clay developed at Georgia In-stitute of Technology [10]. The principle item of Digital Clay is amultiple collocated spherical joint developed by Bosscher et al. [2],which can easily be manufactured in a very small scale. By com-bining the spherical joints to an array, a formable crust is obtained.However, the actuation of the Digital Clay is an unsolved problem.

Bordegoni et al. [1] developed a Self-Deformable Haptic Strip,which uses bending and torsion modules to deform a plastic strip. Aprototype of the mechanism exists. A drawback of the Haptic Stripis the missing extension of the mechanism. The Haptic Strip candisplay a narrow band of the surface only and exploration of largerobjects is only possible if the Haptic Strip is moved or rotated.

Finally, Mazzone [9] developed a parallel kinematics where mul-tiple nodes are connected to a network of end-effectors to displayuniversal shapes. The mechanism is not actuated and has a ratherlow resolution (average node distance: 195mm).

Non-contact Displays: Non-contact displays are often classi-fied as tactile displays. Like shape rendering interfaces they createhaptic stimuli in 3D-space at multiple points of the users hand andare therefore comparable to them to a certain extent. Such displaysuse air-flow or ultrasonic transducers to provide haptic sensations.Hoshi et al. [6] developed an array of ultrasonic transducers, whichare able to provide haptic feedback in space above the array, butgrasping or manipulation of virtual objects is not possible.

In Table 1 a comparison of [8], [10], [1] and [9] is shown. Theother concepts are not considered in the comparison, because theyare either to premature or too different from the design presented inthis paper.

Table 1: Comparison of existing analoguesFEELEX Digital Haptic Deformable

[8] Clay [10] Strip [1] Structure [9]

Average 4.8cm 1.3cm 10cm 19.5cm

node distance (estimated)

Number of 36 > 100 6 (only one 16

nodes direction)

Undercuts no yes yes yes

Actuated yes no yes no

In this paper a new design for a formable crust, in the followingcalled FO (Formable Object), is presented. The FO is not only atheoretical concept, but, compared to several concepts presentedabove, is designed to build a prototype with a comparatively highresolution. The FO can be mounted at the end-effector of a roboticarm, which is important when the FO is to be moved to differentpositions in space. The FO has 24 DoF which allows displayingbasic shapes like cylinders or spheres.

In Section 2 the mechanical construction will be presented fol-lowed by Section 3 that derives the kinematic equations. Two in-verse kinematic solutions are introduced that either minimize posi-

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IEEE World Haptics Conference 201314-18 April, Daejeon, Korea978-1-4799-0088-6/13/$31.00 ©2013 IEEE

tion errors only or position and orientation errors simultaneously.Simulation results for shape rendering are presented in Section 4.Finally, the paper concludes with a summary and outlook to futurework.

2 MECHANICAL CONSTRUCTION

In this section details on the kinematic design, actuators and sensorsare given. As the FO is to be used as end-effector of an encountered-type haptic interface (cf. [12]), it must be lightweight and mount-able at one point. In order to be able to render stiff objects, highstiffness of the mechanical structure is demanded (≈ 1 kN/m). Themaximal force of a pinch grasp is about 60 N [11]. Working againstsuch high forces, however, is not required, because most object ma-nipulations are not performed with maximal forces, so we decidedto set the maximal demanded counterforce to 10 N. The resolutionshould be as high and possible, guaranteeing also actuation of thewhole device. Simple shapes like cylinders or spheres (concave &convex) must be presentable by the interface.

2.1 Design

The FO is built of multiple nodes which represent the object to bedisplayed, see Fig.1. The nodes are connected by joints in multipleclosed loops forming a parallel kinematics. The FO is designedas a deformable plane and consists of multiple basic elements thatcan be connected to a mesh of nodes. An element contains twonodes and the connection between those nodes. A higher number ofnodes will increase the area to display, but at the same time increasethe complexity to control the interface. Figure 1 shows the CAD-drawing of an assembly of 9 nodes.

Figure 1: CAD-drawing of prototype with 9 nodes

2.1.1 Basic Element

A principle sketch of a basic element is shown in Fig. 2, while theCAD-drawing of it is shown in Fig. 3. The structures presentedin the following sections are assembled from such basic elements.Two nodes are connected by a telescopic rod with 2 axial bear-ings on its ends. The axial bearings deliver 2 degrees of freedom(DoF) and the telescopic rod, which can extend and rotate aboutits own axis, delivers another 2 DoF. Thus, the connection betweentwo nodes has 4 DoF. The two DoF of the axial bearings are ac-tuated and the two DoF of the telescopic rod are unactuated. Theheight of the node is h = 22 mm and the width is w = 18 mm. Thedistance between two nodes is d = 27 mm . . .44 mm, depending onthe length of the telescopic rod. The nodes are build from ABS.Cable lead-throughs are integrated into the nodes and the cables areled away below the surface of the FO ending at a motor module,where actuators (DC motors) are mounted. The actuation principleis described in more detail in Section 2.2.

2.1.2 Determinacy

One important design characteristics is the determinacy of the sys-tem. To gain determinacy, a variety of designs can be thought of.

NodeNode

Linear Bearing (2DoF, unactuated)

Axial Bearing (1DoF, actuated)

ps

pc

r

h

w d

Figure 2: Basic Element with 4DoF

NodeCable Fastener

Cable

Cable Lead-Through

Telescopic Rod

Encoder

MotorsMotor Drivers

Motor Module (scaled)Cable Sleeve

Figure 3: CAD-drawing of Motor Module and Basic Element

In the following two paragraphs, designs are presented, which arestatically determined and which can be arbitrarily expanded.

Determinacy can be proven with the well known Chebychev-Grubler-Kutzbach criterion [7]

M(s) = 6n(s)−j

∑i=1

(6− fi) = 6(N(s)−1− j(s))+j

∑i=1

fi (1)

where M determines the overall degrees of freedom (DoF), n is thenumber of rigid bodies, j the number of joints and fi the numberof DoF of the i-th joint. N is the number of rigid bodies n plusthe fixed base (N = n+1). In order to gain a statically determinedmechanism, the number of overall DoF M must be equal to thenumber of actuators a. In case of the FO each joint has 4 DoF( fi = 4), among them two actuated ones (a = 2 j).

Figure 4 and 5 show two design concepts and their possible ex-tensions, where s is the step of extension. It can be seen, that theFO can be arbitrarily extended to cover larger areas. Design 1 is adesign where the kinematics is changing with each extension, whilethe resolution remains the same. A new step of extension is addedto the previous step so that a mural structure is formed. By doing so,rectangular loops occur in vertical and horizontal direction whereassquare loops remain in the diagonal directions (cf. Fig. 4). Design2 has a recursive kinematic design, so that all knowledge gained atstep 1 can be transferred to all further steps. The recursive char-acteristic of design 2 becomes clearer when considering all lowersteps of the kinematics as one big center node: Each new step bringsin 4 new closed loops which have the same kinematic structure asthe loops of the previous steps. The drawback of the latter design,however, is that the resolution decreases with each additional layer.After analyzing the two designs the overall DoFs M of the FO cangenerally be specified as a function of s according to (1):

Design 1: Design 2:

N1(s1) = 4s21 +4s1 +1 N2(s2) = 8s2 +1

j1(s1) = 6s21 +6s1 j2(s2) = 12s2

fi,1 = 4 fi,2 = 4

n1(s1) = N1(s1)−1 n2(s2) = N2(s2)−1

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leading to:

M1(s1) = 12s21 +12s1 and M2(s2) = 24s2. (2)

Furthermore, the number of actuators a(s) is given by:

a1(s1) = 2 j1 = 12s21 +12s1 and a2(s2) = 2 j2 = 24s2. (3)

For each step the number of actuators a has to match the number

of overall DoF, so that a(s)!= M(s) and thus, both mechanism are

statically determined.

s = 1 s = 2 s = 3

Base node

Node

Link

Figure 4: Design 1: Changing kinematic design

s = 1 s = 2 s = 3

Base node

Node

Link

Figure 5: Design 2: Recursive kinematic design

2.2 Actuators

In order to display objects with fine contours the resolution shouldbe as high as possible and thus, the node distance should be min-imized. This, however, requires a very compact actuation princi-ple. In robotics electrical actuation is the most common actuationprinciple. Mounting electrical motors directly at the nodes, how-ever, would result in a very bulky design and consequently lead to arather low resolution. Alternative actuation principles are hydraulicor pneumatic actuation. These actuation principles have in commonthat large and heavy components like pumps or compressors areplaced at a distance and the power is transmitted to remote locationsby hoses, comparable to an electrical actuation combined with a ca-ble transmission. Main advantages and disadvantages of such actu-ation principles are listed in Table 2. When using a pneumatic ac-

Table 2: Comparison of transmission principles+ -

pneumatic medium always available compressible

hydraulic uncompressible leaking, tanks needed

cable transmission no medium needed limited stiffness of cables

tuation principle, high stiffness cannot be achieved, because of thecompressibility of air. This is unacceptable for haptic applications,where rendering of stiff objects plays an important role. Using ahydraulic actuation principle would imply the need of a heavy tankand a closed oil circuit. Furthermore, working with hydraulics/oil

always implicates leakage problems. Due to the impractical prop-erties of the hydraulic and pneumatic actuation, a cable-driven ac-tuation was chosen for the FO. Cable fasteners were designed andwere mounted on each end of the telescopic rods. Thus, cable pullscan be fixed on the fasteners and led through the nodes. Bowdencables were used to transmit motions from electrical motors to thenodes. In doing so, the 2 rotational DoF of the basic elements canbe controlled from distance.

2.3 Sensors

Like actuators also sensors must be very compact in order to fulfillthe requirement of a high resolution. As mentioned in Section 2.1.2the FO has M = a = 2 j DoF, which means that only motions about2 DoF per link have to be captured by sensors. The 2 DoF deliveredby the axial bearings can be easily measured by magnetic encoders(Austriamicrosystems, AS5040) which are compact and have a highresolution.

3 INVERSE KINEMATICS

In the following subsections the inverse kinematics of the FO with 9nodes will be discussed. The FO with 9 nodes is the smallest think-able mechanism (s = 1), but due to the expandability in case of de-sign 2 it is sufficient to discuss the properties of the FO without lossof generality. Expansions of design 1 have to be analyzed in detailfollowing the example of the 9 node mechanism, presented in thispaper. In order to display a specific shape of an object the inversekinematics of the mechanism has to be known. Each node repre-sents a point on the surface to display. Two strategies of displayinga surface are compared with each other, a method minimizing posi-tion errors only and a method minimizing position and orientationerrors simultaneously.

3.1 Constraints

The shape of the FO is constrained by 4 loops (L1 · · ·L4) that form aclosed kinematic chain. These 4 loops are illustrated in Fig. 6. Thehomogeneous transformations jTi are used to describe the relativeposition and orientation between node i and node j, whereas I is theidentity matrix and 0 is the zero matrix. The origins of nodes arelocated in the center point pci of each node (cf. Fig. 2). The closedloops are formulated as follows:

L1 : 1T2 ·2T3 ·

3T4 ·4T1 − I = 0, (4)

L2 : 1T6 ·6T5 ·

5T4 ·4T1 − I = 0, (5)

L3 : 1T6 ·6T7 ·

7T8 ·8T1 − I = 0, (6)

L4 : 1T2 ·2T9 ·

9T8 ·8T1 − I = 0. (7)

Each Transformation jTi contains 4 joint variables (αi j, βi j , τi j ,li j), whereas αi j and βi j define the angles of the two axial bearingsand τi j and li j define the rotation and the length of the telescopicrod between node i and node j. In the following paragraphs thevector of all joint variables is denoted as q. Throughout this paperhomogeneous transformations are used.

Each loop provides 6 independent equations (3 positions & 3orientations). This means that 24 equations have to be satisfied tomeet the given constraints. Assuming that node 1 is fixed in space,node 2 to 9 can be positioned/oriented within these constraints. Weassume that a virtual surface to be displayed by the FO is given by a3D-function z= f (x,y) and the orientation of the surface is given by

the normal of the surface n(x,y) =[

nx ny nz

]Twith |n|= 1.

In the following sections, two different strategies to determine theinverse kinematics are discussed.

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1

2 3

4

567

8

9

L1

L2L3

L4

x

y

z

Figure 6: Closed loops constraining the FO

3.2 Minimizing position errors of nodes

This section deals with the positioning of the free nodes (node 2to 9). When talking about the position of a node, the position ofthe upper surface of the node is meant. For positioning of all freenodes 8 ·3= 24 DoF are needed. This means that the free nodes canbe placed at arbitrary positions, if these positions are located in theworkspace of the device. The position of node i described in frame1 is described by (8), where the parameter h means the height of thenode (cf. Fig. 2). The constraints and desired positions provide 48equations for the 48 unknowns q.

p1si =

1Ti ·[

0 0 h2 1

]T=[

psi,x psi,y psi,z 1]T

(8)

3.3 Minimizing position and orientation errors of nodes

The above described method of placing the nodes at specific posi-tions without considering their orientations can lead to an unevensurface assuming that the nodes are connected by an elastic layer.Wrong orientations of the nodes can result in wrinkles and bumpson the surface. To overcome this problem we developed a methodwhich also considers the minimization of the orientation error ofthe single nodes.

In order to deform the FO, the z-component of the distance di,zof the single nodes to the surface has to satisfy:

di,z = f (psi,x, psi,y)− psi,z = 0, for i = 2, · · · ,9 (9)

whereby the vector of all distances is denoted by

d =[

d2,z, · · · ,d9,z

]T.

The normal vector of each node is given by ri =psi−pci

|psi−pci|where

pci describes the center point and psi the surface point of node i,with |ri|= 1 (see Fig. 2). To orient the nodes along the direction ofthe surface we further have to satisfy:

∡(ri,n(psi)) = ∡(ri,ni) = arccos

(

ri ·ni

|ri ·ni|

)

= 0 (10)

for i = 2, · · · ,9

In doing so, the orientation error can be interpreted very intuitively.Uniqueness of the solution is guaranteed by taking joint limits intoaccount. In the following the vector of all angles is denoted with

a = [∡(r2,n2), · · · ,∡(r9,n9)]T .

Equation (9) and (10) provide 8 equations each. These 16 equa-tions plus the 24 equations coming from the constraints can be for-mulated as constrained optimization problem and be solved numer-ically.

3.4 Optimization

For the optimization a cost function for the position error Fp(q) andthe orientation error Fo(q) are used:

Fp(q) = ‖d‖ (11)

Fo(q) = ‖a‖ (12)

The decision space of the optimization is defined by the four closedloops (4)-(7), which specify the nonlinear equality constraints andjoint limits of the linking elements which specify the inequalityconstraints. Each entry of the matrices (4)-(7) leads to one equa-tion hl(q) = 0. Note that only the first 3 rows of the homogeneoustransformations are considered, because the 4th row is trivial. Thejoint limits bk are set to

−0.436rad ≥αi j ≤ 0.436rad

−0.436rad ≥βi j ≤ 0.436rad

−0.524rad ≥τi j ≤ 0.524rad

22mm ≥li j ≤ 37mm

and are described by inequalities gk(q) ≤ 0. Thus, the optimizationproblem can be formulated as follows:

minq

F(q) = koFo(q)

π/2+ kp

Fp(q)

1m(13)

subject to gk(q)≤ bk, k = 1, . . . ,96,

hl(q) = 0, l = 1, . . . ,48,

where ko and kp are weighting factors to weight the orientationand position error of the nodes. When considering positions only,ko = 0 is chosen. In (13) the cost functions Fo and Fp were normal-ized by the angle π

2 and the distance 1m to facilitate interpretation.Please note that convexity of the optimization depends on the sur-face to display and the cost function which is highly nonlinear.

4 RESULTS

To analyze the performance of the FO, the optimization was simu-lated using Matlab. For optimization the ‘interior-point’-algorithm[4] was used. The optimization was performed on an ‘Intel Core i5-2500K Quad-Core’-Processor (3.3GHz/7.5GB). A maximum num-ber of 20.000 iterations and 500.000 function evaluations was se-lected. The function to display was chosen to be a 3D-parabola

z = f (x,y) = Ax2 +By2 + h2 with A and B parameters that allow to

change the shape to be displayed. Positive parameters A and B leadto a convex shape, whereas negative values lead to a concave shape.If one parameter is equal zero the surface is curved in one directiononly. Parameters with different signs lead to a saddle-like shapewith a simultaneously concave and convex curvature. Note that the

surface is shifted up by h2 . This shift is needed because the frame

of node 1 is located at position [0 0 0 1]T and the surface todisplay should contact the upper surface of node 1.

The base node (node 1) is placed at the center of the interac-tion area. When placing the base node at this point, the orientationaround it is not predetermined as it can be rotated around its z-axis.In order to find the best solution for the optimization, the base nodewas placed at the center of the interaction area and another DoF wasadded.

To analyze the possibility of the FO to display different shapes,surfaces with different parameters were tested in simulation. In Ta-ble 3 cost function values and the optimization time t are given.One can see that by increasing the weighting factor ko, Fo decreasesand Fp increases. This means that the orientation error reduceswhen choosing a higher weighting factor, while the position errorincreases. The same behavior can be observed for the maximum po-sition error dm and orientation error am, defined by the largest abso-lute values of d and a, respectively. This behavior is not mandatorybecause Fp and Fo are defined by the eucledian norm of d and a.Figure 7(a) - 7(c) visualize the FO fitting a virtual surface. Figure7(d) - 7(f) show a zoom into one node (node 8). The differences be-tween different weighting factors can be observed. As expected thedistance of the node to the surface is larger with a higher weight-ing factor ko, whereas the orientation error of the node is larger

64

with a lower weighting factor. The reason for the errors lies in theconstraints (kinematic constraints & joint limits) of the interface.Large errors can be observed, when large curvatures are to be ren-dered (A = 8,B = 2). The optimization converges to a minimumwhere one or multiple of the constraints become active.

Further, when choosing ko sufficiently high, saddle-like shapes(A = 4,B = −2) can be rendered better than convex shapes withsame absolute parameters (A = 4,B = 2). An explanation for thiswill be given in the next section.

Furthermore, one can see that bending in two directions(A = B = 4) is rendered worse than bending in one direction(A = 4,B = 2).

Simulation times lie between 39s and 161s, which is not accept-able for real-time applications. Thus, joint angles defining a specificshape, have to be determined offline.

Table 3: Parameters for shape reconstruction (A & B: coefficients ofparabola, ko: orientation weight, F : costfunction, Fp & Fo: norm ofposition and orientation error, dm & am: maximum error of positionand orientation, t: optimization time)

A 4 4 4 8

ko B 2 -2 4 2

0

F 1.1 ·10−9 2.5 ·10−9 1.6 ·10−9 2.5 ·10−9

Fp 1.1 ·10−9 2.5 ·10−9 1.6 ·10−9 2.5 ·10−9

Fo 0.4231 0.4131 0.6266 0.4271

dm[mm] 5.9 ·10−7 1.7 ·10−6 9.4 ·10−7 1.3 ·10−6

am[deg] 10.1 10.5 15.4 12.3

t[s] 39 56 52 156

0.01

F 0.0024 0.0025 0.0037 0.0024

Fp 1.2 ·10−9 1.7 ·10−9 2.5 ·10−9 1.5 ·10−9

Fo 0.3730 0.3994 0.5771 0.3803

dm[mm] 6.2 ·10−10 1.1 ·10−9 1.4 ·10−9 9.7 ·10−10

am[deg] 11.2 12.0 14.0 12.2

t[s] 63 104 32 162

0.1

F 0.0159 0.0064 0.0228 0.0218

Fp 0.0062 0.0064 0.0086 1.2 ·10−9

Fo 0.1528 3.4 ·10−7 0.2227 0.3419

dm[mm] 3.0 3.3 3.7 6.1 ·10−7

am[deg] 5.3 1.2 ·10−5 7.2 11.0

t[s] 62 49 91 161

4.1 Rendering Complexity

The ability of the mechanism to render complex shapes is analyzed.Since the mechanism has 9 nodes only, it is obvious that highlycomplex objects can not be rendered. Thus, the ability of the FOto display spherical and cylindrical shapes was analyzed. Theseshapes can be convex or concave. The bending radius was variedbetween R = 0 . . .− 0.06 m and R = 0 . . .0.06 m where a negativeradius denotes a concave shape and a positive radius denotes a con-vex shape and R = 0 m denotes a flat configuration. The inversekinematics described in Section 3.3 was used to calculate the joint-angles of the mechanism and thus, the position and orientation ofthe nodes. Weighting factors kp = 1 and ko = 0.05 were chosenand a shape was defined as ‘rendered’ if all position errors werebelow 1 mm and orientation errors below 10 deg. The maximumreachable curvatures ρ = 1/R within these constraints are shownin Table 4 and are visualized in Figs. 8 - 11. It can be seen, thata larger curvature can be rendered when bending in one directiononly (cylindrical) than bending in two directions (spherical). Thesame behavior can be observed when analyzing Table 3 and com-paring cases with A = 4,B = 2 and A = B = 4.

As mentioned before, we found that larger curvatures can berendered for concave shapes than for convex shapes. This circum-stance becomes clearer when taking into account that the node cen-ters pc are positioned on a parallel imaginary curve to the surface,if node surface points ps touch the surface to render. In the concavecase this parallel curve has a smaller curvature than the one of theconvex case with the same parameters.

Table 4: Maximal displayable curvatures ρmax

concave convex

Sperical 3.33 3.20

Cylindrical 25.00 16.67

Figure 8: Maximum bending radius (cylindrical/convex)

Figure 9: Maximum bending radius (cylindrical/concave)

Figure 10: Maximum bending radius (spherical/convex)

Figure 11: Maximum bending radius (spherical/concave)

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(a) A = 4,B = 4,ko = 0 (b) A = 4,B = 4,ko = 0.01 (c) A = 4,B = 4,ko = 0.1

(d) A = 4,B = 4,ko = 0, zoomed in (e) A = 4,B = 4,ko = 0.01, zoomed in (f) A = 4,B = 4,ko = 0.1, zoomed in

Figure 7: Formable Object fitting a virtual surface: (a)-(c) group of 9 nodes, (d)-(f) zoom into one node.

5 CONCLUSIONS AND FUTURE WORK

5.1 Conclusions

In this paper first ideas for a haptic interface for shape renderingwere presented. The interface can improve state-of-the-art kines-thetic haptic interfaces that typically allow for one interaction pointonly as it makes full-hand interaction possible. The interface hasa higher resolution than most comparable state-of-the-art conceptsand is fully actuated. The mechanical design as well as the kine-matics were described and two possibilities to extend the designwere highlighted. The display can be mounted as end-effector on arobotic arm as only one node of the interface has to be fixed with theenvironment. Two possibilities to fit the object to a desired shapewere introduced and its differences were highlighted. The simula-tions showed that by choosing different weighting factors the ori-entation and position errors of the nodes can be adjusted, but thatthey cannot be eliminated at the same time. This drawback can beovercome by introducing modifications in the kinematic design.

5.2 Future Work

In future the prototype of the FO with 9 nodes will be build andcontrolled. Minor adjustments in the design are required to fur-ther reduce position and orientation errors, especially when render-ing spherical surfaces. In order to use the FO for the rendering ofshapes with compliance the solution of the optimization problemhas to be realized in real-time, therefore an alternative differentialkinematic solution will be investigated. Furthermore, the mecha-nism has to be equipped with force sensing elements to measureinteraction forces. A further increase of the resolution is aimedbecause the average node distance of 36 mm is still too large torender every-day objects. Manufacturing the device with MEMS-Technology will be investigated.

6 ACKNOWLEDGMENTS

This work is supported in part by the BEAMING project within the7th Framework Programme of the European Union, Accessible andInclusive ICT, contract number ICT-2010-248620 and the Instituteof Advanced Studies of the Technische Universitat Munchen.

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