Development of a Surgical Knife Device fora Multi-fingered Haptic Interface Robot ⋆

Takahiro Endo ∗ Satoshi Tanimura ∗ Haruhisa Kawasaki ∗

∗ Department of Human and Information Systems, Gifu University,Japan (e-mail: tendo@gifu-u.ac.jp, m3028038@edu.gifu-u.ac.jp,

h kawasa@gifu-u.ac.jp)

Abstract: This paper presents the design of a surgical knife device for a multi-fingered hapticinterface robot called HIRO, and summarizes the experimental results. HIRO consists of a robotarm and a five-fingered hand, and is able to handle the tool with fingers. A variety of tools canbe attached to HIRO, and the system is therefore able to present the force sensation of manytool-type devices. For example, in medical training, there are many different shape and usagetools, so a haptic interface that can present the force sensation for many tools will be importantfor virtual training systems. This paper particularly focuses on the connection between HIROand a tool-type device. By introducing a performance index, a tool-type device (a surgical knifedevice) for HIRO that satisfies a certain kind of optimal connection has been developed. Further,several experiments were carried out to investigate the performance of the developed surgicalknife device. These results correspond to a display of high-precision force.

Keywords: Haptic Interface; Virtual Reality; Surgical Knife; Robotics.

1. INTRODUCTION

It is possible to communicate with the virtual environmentvia a haptic interface. An operator of the haptic interfacecan feel force sensations from the virtual environment, andfurther, the operator can provide force and position infor-mation to the virtual environment. Unlike the traditionalinterface using visual and audio cues, the haptic interfaceis unique, as it provides a bidirectional interaction betweena human being and the virtual environment (Hale andStanney [2004], Hayward et al. [2004], Hannaford andOkamura [2008]). Therefore, the haptic interface is a keyinput/output device for communication with highly real-istic sensations and has been used in many applicationareas.

One of the application areas of the haptic interface ismedical training and evaluation. During surgical training,medical doctors use various surgical tools such as scissors,surgical knives, and syringes, and they must train withthese tools to master specific procedures or technique.However, it is neither easy nor safe for this training withsurgical tools to occur in the real environment. Because ofthese challenges, a training system that uses virtual realityand a haptic interface technology has been researchedaggressively. With the construction of a virtual trainingsystem, training can be safely carried out and a traineecan practice in various situations that might not be ableto be experienced in the real world. Further, the results ofsome studies indicate that such a system could increase theskill with which real surgery can be performed (Seymour

⋆ This paper was supported by the Ministry of Internal Affairs andCommunication R&D Promotion Programme (SCOPE), and by theArtificial Intelligence Research Promotion Foundation.

et al. [2002]) and contribute to the learning of real motorskills (Youngblood et al. [2005], Morris et al. [2007]).

Based on the above, many researchers have been devel-oping tool-type haptic interfaces, which involve scissors,surgical knives, syringes, and others, for use in some ob-jective task (Okamura et al. [2003], Greenish et al. [2002],Webster III et al. [2005], Wakamatsu et al. [1999], HonmaandWakamatsu [2004], Bielser and Gross [2000]). By usingthe tool-type haptic interface in the virtual environment,an operator is able to carry out virtual training whilefeeling force sensations through the tool-type haptic in-terface. However, these tool-type haptic interfaces presentthe force sensation of the corresponding single type of tool-device. To present the force sensations of a variety of sur-gical tools, many tool-type haptic interfaces are required.Providing many tool-type haptic interfaces requires instal-lation locations and costs a great deal. For this reason, wehave previously developed a haptic system that presentsthe force sensations of a variety of surgical tools (Kawasakiet al. [2007]). This system consists of a multi-fingeredhaptic interface named HIRO and numerous tool-typedevices, including a surgical knife, scissors, and syringe.HIRO has five haptic fingers and handles the tool-typedevices with the haptic fingers. Plural tool-type devicescan easily be attached to and removed from HIRO, andthe system is able to present the force sensations of manytool-type devices. HIRO does have five haptic fingers andthus it is a multi-degree-of-freedom system. We thereforemust consider how many haptic fingers are necessary to beconnected to the tool-type device with HIRO, and whichhaptic fingers should be used for the connection. In theconnection between HIRO and the tool-type device, wepreviously considered the working space, but we did not

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technically clarify the optimal connection between HIROand the tool-type device.

This paper introduces a performance index between HIROand the tool-type device, and, based on the performanceindex, a tool-type device that satisfies a certain kind of op-timal connection between HIRO and the tool-type devicehas been developed. More specifically, a surgical knife wasdeveloped as the tool-type device. Further, experimentalinvestigation of its performance was presented. This pa-per is organized as follows: In the next section a multi-fingered haptic interface robot, HIRO, and our previoustool-devices for HIRO are introduced. Section 3 presentsthe performance index and newly developed surgical knife,which was designed based on the performance index. Theexperimental results described in Section 4 demonstratethe high potential of our system. Finally, Section 5 presentsour conclusions.

2. FIVE-FINGERED HAPTIC INTERFACE ROBOTAND PREVIOUS TOOL-TYPE DEVICES

2.1 Five-Fingered Haptic Interface Robot

The authors have developed multi-fingered haptic interfacerobots that are placed opposite a human hand, includingHIRO (Kawasaki et al. [2003]), HIRO II+ (Kawasaki andMouri [2007]), and HIRO III (Endo et al. [2011]), whichis shown in Fig. 1. HIRO III can present three-directionalforces at an operator’s five fingertips. The specifications forHIRO III are shown in Table 1. HIRO III can be brieflysummarized as follows.

HIRO III consists of an interface arm and a five-fingeredhaptic hand. The interface arm consists of an upper arm,a lower arm, and a wrist. The interface arm has 3 degreesof freedom (DOF) at the arm joint and 3 DOF at thewrist joint. The interface arm, therefore, has 6 jointsallowing 6 DOF. The haptic hand is constructed of fivehaptic fingers. Each haptic finger has 3 joints, allowing3 DOF. The first joint relatice to the hand base allowsabduction/adduction, while the second and the third jointallow flexion/extension. The total DOF of HIRO III is21, and its working space covers VR manipulation on thespace of a desktop. Further, a three-axis force sensor isinstalled at the top of each haptic finger. To manipulateHIRO III, an operator wears a finger holder, which isshown in Fig. 1 (b), on each of his/her fingertips. The

(a) HIRO III (Haptic Interface RObot III). (b) Finger holder.

Fig. 1. Multi-fingered haptic interface robot: HIRO III,and a finger holder.

Table 1. Specifications of HIRO III

Degrees of FreedomHand:15 DOF (Number of haptic fingers:5)Arm:6 DOF

Performance

Output force of haptic finger: over 3.6 NMaximum displayable stiffness: 5 kN/mFrequency response: 8 HzSampling time of control: 1 kHz

finger holder has a steel sphere, and the haptic finger hasa permanent magnet at its fingertips. By means of themagnet force, the finger holder can be connected to HIROIII, as shown in Fig. 1 (a). Here note that the sphere,which, when attached to the permanent magnet at theforce sensor tip, forms a passive spherical joint. Its role is toadjust for differences between the human and haptic fingerorientations. Hereafter the multi-fingered haptic interfacerobot is described as HIRO.

2.2 Previous Tool-Type Devices for HIRO

Fig. 2 shows our previously developed haptic interface thatpresents the force sensation of plural tools using HIRO.As tool-type devices, a surgical knife, scissors, and syringedevices were developed. As an example, Fig. 3 shows thesurgical knife device. To connect a tool-type device toHIRO, the steel spheres are installed in the tool-typedevice as shown in Fig. 3 (b), and it is easy to exchangethe plural tool-type devices using the permanent magnet ofthe haptic fingertip of HIRO. HIRO has the force sensors,motors, and encoders, that are required to create the forcesensation, and thus the tool-type devices only require astructure similar to that of the real tool.

VR

HIRO

operator

various surgical tools

knife

scissors

syringe

Fig. 2. Concept of plural surgical tool device presentationusing HIRO.

(a) HIRO III handling surgical

knife.

(b) Tool-type device’s steel

sphere.

Fig. 3. HIRO III handling surgical knife, and the steelsphere in the tool-type device.

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3. NEWLY DEVELOPED SURGICAL KNIFE

HIRO has five haptic fingers and is a multi-degree-of-freedom system. It is therefore a big challenge to considerhow many haptic fingers are necessary to be connectedto the tool-type device with HIRO, and which hapticfingers should be used for the connections. Technicallyclarifying the optimal connection between HIRO and thetool-type device is important with regard to presentingthe operator the force feeling through the tool-type device.This section describes our development of a surgical knifedevice in relation to a mobility and performance index. Forsimplicity, the interface arm is not included in the analysis.

3.1 Connection Analysis by Mobility

We now analyze the number of haptic fingers necessaryfor HIRO to have connected to the tool-type device. Themobility index M is given by

M = 6n−5∑

m=1

(6−m)Jm, (1)

where n is the number of moving links,m is the class of thejoint, and Jm is the number of joints of class m. Further,for the typical joint, the class of the joint is defined asfollows: the class of the revolute joint is 1, the class of theprismatic joint is 1, and the class of the spherical joint is3. For more details, please see Megahed [1993].

Haptic fingers and a surgical knife make the closed-looplink mechanism, and thus the number of joints doesnot correspond to the degree of freedom of the overallsystem. In this case, the mobility index M implies thedegree of freedom of the overall system, and the followingfact is trivial: the active joints’ number D that requirescontrolling all degrees of freedom of the overall systemmust satisfy

D ≥ M. (2)

Further, the mobility indexM must satisfyM ≥ 6 becausethe surgical knife is 6 DOF. Haptic fingers and a surgicalknife device are connected through the passive sphericaljoint described in the above section. Therefore, to supportthe surgical knife with the haptic fingers, two or morehaptic fingers are necessary. When the surgical knife deviceis connected to HIRO with two haptic fingers, the mobilityindex is M = 6 because of n = 7, J1 = 6, J2 = 0,J3 = 2, J4 = J5 = 0. At this time, the active joints’number is D = 6 because two haptic fingers are usedto hold the device, and thus (2) is satisfied. However, todraw the virtual surgical knife in the VR environment,the position and orientation of the surgical knife deviceare required. The haptic finger has encoders at the joints,and the joint angles and the tip position are obtained.In this case (two haptic fingers are used), we cannot solvethe forward kinematics, which determines the position andorientation of the knife device from the positions of twohaptic fingertips. In contrast, when the device is connectedto HIRO with three haptic fingers, the mobility index isM = 6 because of n = 10, J1 = 9, J2 = 0, J3 = 3,J4 = J5 = 0. At this time, the active joints’ numberis D = 9, and thus (2) is satisfied. In this case, wecan also obtain the geometrically determined position andorientation of the surgical knife device from the position

of three haptic fingertips. Although (2) is satisfied whenthe haptic finger is 4 or more, this paper uses three hapticfingers, which is a minimal number, at the connection.

3.2 Kinematics

To consider the connection by introducing a performanceindex, we first consider the kinematics of the overallsystem, which is illustrated in Fig. 4. The system consistsof three haptic fingers and a surgical knife, in which the i-th haptic finger contacts the surgical knife at point Ci. Thecoordinate systems are defined as follows: Σb is the basecoordinate system, Σtool is the object coordinate systemfixed on the surgical knife, and ΣFi is the i-th fingertipcoordinate system fixed on the i-th haptic fingertip. Inaddition, the following notations are used: bpFi

∈ R3 is

the position vector of ΣFi with respect to Σb,bRFi ∈

R3×3 is the orientation matrix of ΣFi with respect to Σb,bptool ∈ R3 is the position vector of Σtool with respect toΣb,

bRtool ∈ R3×3 is the orientation matrix of Σtool withrespect to Σb.

Since the contact at Ci is fixed, the following constraintbetween the haptic fingertip position and the surgical knifeposition is obtained:

bptool +bRtool

toolpCi= bpFi

+ bRFi

FipCi, (3)

where toolpCi∈ R3 is the position vector of Ci with respect

to Σtool, andFipCi

∈ R3 is the position vector of Ci withrespect to ΣFi . Differentiating (3) yields

bptool − (bRtooltoolpCi

)× bωtool

= bpFi− (bRFi

FipCi)× bωFi , (4)

where bωtool ∈ R3 and bωFi ∈ R3 are the angular veloc-ities of the surgical knife and the i-th haptic fingertips,respectively, (p)× ∈ R3×3 is a skew-symmetric matrixexpressing the cross-product form of a vector p ∈ R3, andthe fact that toolpCi

and FipCiare constants was used in

the derivation of (4).

Now we define the following matrices:

Dtooli =

[I3×3, − (bRtool

toolpCi)×

]∈ R3×6, (5)

DFi =[I3×3, − (bRFi

FipCi)×

]∈ R3×6, (6)

where I3×3 ∈ R3×3 is an identity matrix. Further, the i-thhaptic fingertip velocity and the joint angle velocity arerelated by

Knife device

i-th haptic finger

i-th contact point: Ci

Fi tool

b

bpFi

,bRFi

bptool

,bRtool

Fig. 4. Haptic fingers and surgical knife device.

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[bpFibωFi

]= JFi qi, (7)

where JFi∈ R6×3 is a Jacobian and qi ∈ R3 is the joint

angle vector of the i-th haptic finger.

From (4)-(7), we can obtain the following kinematics:

Dtool vtool = JCF q, (8)

where Dtool = col[Dtool1 , Dtool

2 , Dtool3 ] ∈ R9×6, vtool =

col[ bptool,bωtool] ∈ R6 is the velocity vector of the surgi-

cal knife device, JCF = diag[DF1JF1 , DF2JF2 , DF3JF3 ] ∈R9×9, q = col[q1, q2, q3] ∈ R9.

On the other hand, from the principle of virtual work, thefollowing relation is obtained:

F tool = (Dtool)Tf c, (9)

where F tool = col[ f tool, ntool] ∈ R6 is the totalforce/moment vector applied to the surgical knife deviceby the haptic fingers, f c = col[f c1 , f c2 , f c3 ] ∈ R9, and

each haptic finger applies a force f ci ∈ R3 at the contactpoint Ci.

3.3 Performance index

In subsection 3.1, we determined that HIRO and thesurgical knife device should be connected by three hapticfingers. But we did not clarify which haptic fingers shouldbe used. Specifically, we must know the configuration(or state) of the haptic fingers in the connection andthe position relations between the three contact points.To determine these from a kinematic perspective, weintroduce a performance index that considers the well-known manipulability (Yoshikawa [1985]). Equation (8)can be rewritten as

vtool = Jq, J = (Dtool)+JCF . (10)

Thus, we can consider the following equation as a usualmanipulability:

w =

√det(JJT ). (11)

However, if the optimal connection points are derivedusing w, the value of w becomes maximum (infinity)when the three connection points between HIRO and thesurgical knife device form a straight line. As such, thematrix Dtool is rank-deficient, and this is a singularity.We therefore cannot use w as the measure.

From the above perspective, we consider the following tobe optimal: the connection points away from the singular-ity, and the haptic fingers are also not in the singularityconfiguration. And, as the performance index, we definethe following:

PI = αWDWF + βWA, (12)

WD =

√det((Dtool)TDtool), WF = | detJCF |, (13)

WA = −3∑

i=1

3∑j=1

γj

[e−µ(qij−aij) + eµ(qij−bij)

], (14)

where α, β, and γj are the weighting coefficient of WD,WF , and the j-th joint of the haptic finger, respectively,qij is the j-th joint angle of the i-th haptic finger, µ isthe parameter to adjust an exponential function, and aijand bij are the lower and upper limits of the j-th joint

angle of the i-th haptic finger, respectively. In WD, thematrix Dtool is determined only by the positions of thethree connection points, and WD itself means that if thevalue of WD becomes large, the positions of the connectionpoints are away from the singularity. Further, WF is well-known manipulability, and the manipulability of the hapticfinger becomes high and the configuration of the hapticfinger is away from the singularity configuration when thevalue of WF becomes large. Therefore, the value of WDWF

corresponds to the fact that the connection points andthe configurations of the haptic fingers are simultaneouslyaway from the singularities; in addition, it contains themanipulability of the haptic fingers. Here, note that whenwe consider the value ofWDWF only, it is possible that theconnection positions and the configuration of the hapticfingers are away from the singularities but the haptic fingergoes to the outside of the limit of the movable range. Wetherefore add the WA to the performance index, whichcorresponds to the limits of the joint angles of the hapticfingers.

3.4 Surgical Knife Device based on the Performance Index

Based on the performance index (12), a surgical knife de-vice for HIRO is developed. From the results of subsection3.1, three haptic fingers are used. For the combination ofall three haptic fingers, the joint angles that maximize thevalue of (12) are derived. In the derivation, the steepestdescent method and the following parameters were used:α = 1.0, β = 1.0 × 10−13 (this fits the largeness of WA

to the largeness of WDWF ), γ1 = 1.2, γ2 = 1.0, γ3 = 1.1,µ = 10, a11 = −0.61, a21 = a31 = −0.52, ai2 = −0.43,ai3 = 0.35, b11 = 0.61, b21 = b31 = 0.52, bi2 = 0.87, andbi3 = 1.84. In addition, it is easy to see that the positionand the orientation of the object coordinate system Σtool

are not related to the value of PI. Thus, in the derivation,Σtool was fixed on the blade edge of the surgical knifedevice, and furthermore Σtool was set on a centroid of atriangle formed by three haptic fingertips.

As a result, the value of (12) reaches a maximum when thefollowing combination of haptic fingers are used: thumb,the index finger, and the pinky finger. Further, in this case,WD = 1.85 × 10−2, WF = 1.91 × 10−11, βWA = 1.04 ×10−13, and PI = 2.51×10−13. The joint angles in this caseare shown in Table 2.

At the development of the surgical knife device thatmaximizes the performance index (12), we consider thefollowing guidelines: the device is connected the fingertippositions that maximize the value of (12), namely, thesurgical knife device is connected to HIRO in which theangles of the haptic fingers are in Table 2, HIRO and thedevice are connected by the passive spherical joints, thedevice is set to the direction which helps an operator’sgrasp, and the device keeps the appearance of the realsurgical knife. Based on the guidelines, the surgical knifedevice was developed. Fig. 5 shows the developed surgicalknife device that connects to HIRO. A handle of the

Table 2. Joint Angles

1st joint [deg] 2nd joint [deg] 3rd joint [deg]

Thumb 26.14 -14.41 62.25

Index finger 15.08 -15.77 57.13

Pinky finger -20.25 -12.66 61.46

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close up

Fig. 5. Developed surgical knife device that connects toHIRO.

surgical knife device is shaped to imitate the real surgicalknife.

4. EXPERIMENT

To evaluate the developed surgical knife device, two kindsof experiments were carried out. One was to manipulatethe device in free space, and the other was to manipulateit in constraint space. In each experiment, the result ofthe newly developed surgical knife device, which is shownin Fig. 5, was compared with the result of the previouslydeveloped surgical knife device, which is shown in Fig. 3.As the control law of HIRO, the manipulability-optimizedcontrol was used. For the control, please see Endo et al.[2011]. For the experiment, the control PC used a real-timeOS (ART-Linux) to guarantee a 1ms sampling time.

Fig. 6 shows the responses of the previously and newlydeveloped surgical knife devices in free space. In the figure,(a) and (b) show the responses of the force f tool of thepreviously and the newly developed surgical knife device,respectively. In both cases, the operator manipulated thesurgical knife device like he was drawing a circle. Sincethe manipulation in free space was considered, the desired

(a) Force f tool of the previously developed device.

(b) Force f tool of the newly developed device.

Fig. 6. Experimental results in free space.

Fig. 7. VR environment.

forces were set to zero. However, the responses of theforces show a slight force error. To consider this errorquantitatively, the average value of the absolute forceerror was considered. The average values of the previouslydeveloped device were as follows: 0.425N for the x-axis,0.354N for the y-axis, 0.503N for the z-axis, and a totalof 0.427N . The average values of the newly developeddevice were as follows: 0.193N for the x-axis, 0.228N forthe y-axis, 0.331N for the z-axis, and a total of 0.250N .Therefore, the responses of the newly developed device infree space were apparently improved, and the total averagevalue of the absolute force error was reduced to 60%.

Next, the manipulation in constraint space was considered.In the experiment, the virtual plane was made in the VRenvironment, as shown in Fig. 7. When the surgical knifedevice touches the virtual plane, the force is presentedto the operator through the surgical knife device. Thepresented force is calculated by the penetration depth ofthe blade edge of the surgical knife device, and we set theforce to work only in the vertical direction (z-axis). Fig. 8shows the experimental results in the constraint space. Inthe figure, (a) and (b) show the responses of the force f toolof the previously and newly developed surgical knives,while (c) shows the time response of the performance indexPI, where the following parameters were used: for thepreviously developed surgical knife device, β = 1.0×10−15

(this fits the largeness of WA to the largeness of WDWF ),and α, γj , µ, aij , bij were same values in subsetion 3.4,and for the newly developed surgical knife device, allparameters were same values in subsection 3.4. In thefigures, we only show the z-axis force because we set thedesired virtual force to work only in the z-axis. First,the operator moves the device towards the virtual plane,and then the operator touches the virtual plane throughthe device. The average values of the absolute force errorof the previously and newly developed surgical knivesduring the contact were 0.354N and 0.273N , respectively.Thus, the responses of the newly developed device inthe constraint space were apparently improved, and theaverage value of the absolute force error was reducedto 77%. On the other hand, from Fig. 8 (c), the newlydeveloped surgical knife device kept the high value of PI,and the good operability was obtained compared to thepreviously developed surgical knife device.

5. CONCLUSION

In the present study, a surgical knife device for a multi-fingered haptic interface robot: HIRO was developed. Todetermine a certain kind of optimal connection between

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(a) Force f tool of the previously developed device.

(b) Force f tool of the newly developed device.

(c) Time responses of PI.

Fig. 8. Experimental results in constraint space.

HIRO and the tool-type device, a performance index thatconsiders the singularity in the kinematics was introduced.The surgical knife device was then developed based onthe performance index. Then, the experimental tests werecarried out. Compared with the previous version of thesurgical knife device, the force errors in free space andin constraint space were reduced. This shows the high-precision force representation of our system. In this paper,we considered only a surgical knife device. However, hu-man beings work with many tools. For example, in themedical field, there are many tools of different shapes anduses like the surgical knife, scissors, syringe, and others,so a haptic interface that can create the force sensation ofmany different tools is important for the virtual trainingsystem. So, in addition to the surgical knife device, we willintroduce in the future a performance index and developmany other tool-type devices for the virtual training sys-tem.

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