three-fingered robot hand with gripping force generating

Tanaka, J.

Paper:

Three-Fingered Robot Hand with Gripping ForceGenerating Mechanism Using Small Gas Springs

– Mechanical Design and Basic Experiments –Junya Tanaka

Corporate Research & Development Center, Toshiba Corporation1 Komukai Toshiba-cho, Saiwai-ku, Kawasaki-shi, Kanagawa 212-8582, Japan

E-mail: [email protected][Received March 1, 2018; accepted November 26, 2018]

This paper presents the mechanical design of a newthree-fingered robot hand for a robot designed to han-dle tableware. The finger mechanism has three jointsand consists of a pair of fourbar linkage mechanisms,one small gas spring, and one feed screw mechanism.As the feed screw moves, the finger mechanism per-forms flexion and extension operations with its jointsinterlocked. The gas spring generates gripping force,which is adjusted at the position of the moving partmoved by the feed screw. Therefore, the three-fingeredrobot hand can open and close synchronously, pow-ered by a single motor in the base of the hand. Thehand grips with mechanical flexibility. In addition, itcan maintain its grip with no power supply. Tests showthat the hand can successfully perform the movementsrequired to grasp various kinds of tableware.

Keywords: robot hand, tableware handling, servicerobot, hardware design, mechanism

1. Introduction

In Japan, a decreasing birthrate and aging populationhas caused a labor shortage that has encouraged the au-tomation of manual tasks. In food service facilities wherepeople and machines coexist, it would be useful to haverobots (Fig. 1(a)) that could handle tableware of variousshapes (Fig. 1(b)) in place of human workers. Robotsused in environments where people and machines coex-ist must be very safe because they are likely to come intophysical contact with people. In addition, if a battery isused as a drive power source in order to expand the activ-ity area of a robot, it is desirable for the energy consump-tion of each part of the robot to be low so that the robotmay continue to function for a long time. Furthermore,it is essential that a robot hand be capable of grippingtableware of various shapes and work efficiently. To becompatible with people in environments where the robotis introduced and to be able to use tableware optimized forease of use by human hands, it is possible to use a robothand with a multi-finger, multi-joint structure similar to

(a) (b)

Fig. 1. Various tableware items and tableware handling robot.

that of a human hand.Many excellent multi-fingered robot hands have al-

ready been developed [1–25]. For example, several hu-manoid hands have been developed in countries otherthan Japan, including the Salisbury Hand [1], Utah/M.I.T.Hand [2], DLR Hand I [3], DLR Hand II [4], andHIT/DLR Hand [5]. Other hands have been developedin Japan, such as the Gifu Hand I [6] and Gifu Hand II [7]developed by Kawasaki et al., the WENDY hand [8] de-veloped by Iwata et al., and a multi-fingered hand forlife-size humanoid robots [9] developed by Kaneko et al.In addition, many three-fingered robot hands have beendeveloped because the minimum number of fingers ca-pable of stably gripping an object is three. Such three-fingered robot hands include the BarrettHand [10] anda highspeed multi-fingered hand [11] by Namiki et al.Moreover, hands adaptable to various object shapes in-clude a soft gripper [12] and a hand for rescue robot HE-LIOS VIII [13] by Hirose et al. as well as a pneumatichand [14] by Tsukagoshi et al. Others include tendon-driven robotic hands [15–20] and link-interlock-drivenrobotic hands [21–24].

These robot hands are roughly grouped as follows interms of the arrangement of the joint-driven actuator: theinternal arrangement type, in which the actuator is directlyarranged in a joint, and the external arrangement type, inwhich a joint and the actuator are coupled via a powertransmission element, such as a wire and belt. In the in-ternal arrangement type, the joint is directly driven by theactuator, so it is expected to have high positioning repeata-bility and other precise controls. However, since many ac-

118 Journal of Robotics and Mechatronics Vol.31 No.1, 2019

Three-Fingered Robot Hand Using Small Gas Springs

tuators are used for the finger mechanism, increased sizeand weight as well as a risk of disconnection due to fric-tion in the wiring of the actuators when driven are con-cerns. On the other hand, in the external arrangementtype, the actuator and the joint to be driven are arrangedseparately, so the finger mechanism can have a simple,lightweight structure, and the wiring for each actuator canbe fixed to the base, thereby reducing the risk of discon-nection. However, for the external arrangement structurein which a wire and belt are used for the power transmis-sion element, regular maintenance is essential because offactors such as stretch and fracture caused by overload.A structure in which a link mechanism is used for thepower transmission element in the external arrangementis more complicated than a wire and belt structure, buthighly reliable power transmission can be expected sincestretching and fractures are unlikely to occur.

In addition, for the robot to come into widespread use,it is important for it to be low in cost, meaning that itis desirable for a robot hand to have the minimum num-ber of actuators. The link-interlock-driven hands [21–24],from which highly reliable power transmission can be ex-pected, are discussed with a focus on the number of ac-tuators. By using two motors and combining a planetarygear, a four-bar linkage mechanism, and an elastic ele-ment, Koganezawa et al. have developed an underactu-ated finger mechanism that enables adduction/abductionof the MP joint [21]. Furthermore, by combining an un-deractuated finger mechanism and a finger joint mecha-nism of variable stiffness, Koganezawa et al. have devel-oped a five-fingered robot hand driven by six motors [22].By using a single linear motion actuator and combininga four-bar linkage mechanism with an elastic element,Ueno et al. have developed an underactuated type fin-ger mechanism with a high gripping force [23]. How-ever, since there is an actuator in each finger mechanism,the multi-finger form requires several actuators, which in-creases the weight and cost of the robot hand. On theother hand, Fukaya et al. have developed the five-fingered“TUAT/Karlsruhe Humanoid Hand,” which is capable ofgripping various objects yet only uses a single motor witha cooperative link mechanism capable of applying equalforce to each joint [24]. Elaborating the link mechanismin this manner allows a robot hand to be configured withthe minimum number of actuators.

On the other hand, a robot hand that can grip with-out using electrical power should consume less energy.Non-back-drivable mechanism, such as a feed screw anda worm gear, can be used. Ueno et al. have developedan underactuated finger mechanism [23] that has a lin-ear motion actuator in which a motor, a harmonic gear,and a ball screw are integrated, realizing a large amountof backdrive torque. However, since this research targetsuse in environments in which people and machines coex-ist, the robot hand should be flexible so as to reduce therisk of human injury when the object gripped by the robothand comes in contact with a human being. This flexibil-ity cannot be realized by controls that use sensors if elec-trical power is lost, so any non-back-drivable mechanism

is problematic in terms of safety. Thus, a small mecha-nism that can maintain its grip in the absence of electricalpower, has flexibility, and can be incorporated into a robothand is necessary. In the load-sensitive continuously vari-able transmission mechanism [25, 26] developed for robothands, the reduction ratio is switched to a large reductionratio by an external force, giving the mechanism a lowflexibility even if it is back driven in the absence of elec-trical power. The use of an elastic element for the mech-anism of the robot hand is therefore considered. For in-stance, in the marine robot hand [20] developed by Stuartet al., an elastic element in the joint mechanism maintainsthe initial posture, which is a state in which the robot handis open and the joint mechanism has flexibility. It is easyto make the initial posture a closed state by changing thearrangement of the elastic element so that it maintains itsgrip in the absence of electrical power. However, simplyarranging the elastic element in the joint mechanism notonly increases the number of components but also allowsthe power generated by the elastic element to be used inboth the opening of and closing of the robot hand. Forthis reason, if the robot hand is caused to operate againstthe power of the elastic element, the energy consumptionof the actuator increases and the gripping force decreases.As a mechanism in which the power of the elastic elementis allowed to be used in both directions of the rotation ofthe joint, Uemura et al. have proposed a mechanism inwhich a linear spring and a feed screw are combined forthe joint of the link mechanism [27]. However, since thejoint mechanism is large but the operating range of thejoint is narrow, a structural elaboration is needed for it tobe incorporated into the robot hand.

Other studies related to grasping tableware include amethod suggested by Kosuge et al. in which a plate mem-ber of a rigid body that has a hook structure is combinedwith a multi-joint finger mechanism so as to grip an ob-ject as it hooks the edge of a piece of tableware [28, 29].This method works well when tableware is placed so thatthe edges are easily hooked. However, our target of thisresearch is the handling work in food facilities. It is a pos-sibility that tableware which is taller than a dish, for ex-ample, a cup, may be knocked over. Due to the restrictedrange of movement of the robot arm, it would then bedifficult to hook the edge of the cup with the hook struc-ture. For this reason, it is desirable that the robot hand forthe handling work targeted in this research be capable ofgripping any part of any piece of tableware, for examplea cup.

As the first step of research and development targetingthe realization of tableware handling done by the robot,this study is intended to develop a link-interlock-drivenrobot hand that has the minimum number of actuators,uses an elastic element to maintain its grip in the ab-sence of electrical power, has flexibility, and is capableof stably gripping various kinds of tableware with a sim-ple mechanism and control. The robot hand of this re-search has three-fingers, which is the minimum numbercapable of stably gripping an object. The hand is char-acterized by two things. One is the reduction of the total

Journal of Robotics and Mechatronics Vol.31 No.1, 2019 119

Tanaka, J.

number of actuators in it to one by interlocking the MP,PIP, and DIP joints of each finger mechanism so that theyperform flexion and extension. The other is that the grip-ping action has flexibility owing to an elaboration of thestructure of the mechanism. The mechanism is character-ized by the fact that the generating power of the elasticelement is applied to both directions of movement of therobot hand, opening and closing, using the singularity ofthe link mechanism to reduce the size of the robot handand expand the operating range of the finger joint. Thispaper includes the design principle, mechanism analyses,specific mechanism systems, and basic test results of thefinger mechanism and the three-fingered robot hand.

2. Development Concept of Three-FingeredRobot Hand

With the development concept of three-fingered robothand being “to have a mechanical flexibility and be ableto gripping tableware while employing only a single ac-tuator,” we examined the necessary requirements. Thework that the robot is required to do is to clear a table,moving tableware of various shapes from the table onto acart. Other requirements for the robot include removingany trash or waste from the table.

2.1. Gripping ObjectWe examined the tableware that is to be gripped. The

target environment into which the robot is to be intro-duced is assumed to be a commercial food court servingfood and beverages. Based on our classification of table-ware, we intended to develop a three-fingered robot handcapable of handling three types of the symmetrically-shaped tableware frequently used, as well as irregularly-shaped garbage bags. The tableware material we targetedwas the plastic frequently used in food courts. We tar-geted a robot hand capable of stably gripping tablewarehaving the following shapes:

• Tableware that is cylindrical and lower in height(dishes, bowls, etc.)

• Tableware that is cylindrical and taller in height(cups, etc.)

• Tableware that is elongated (chopsticks, spoons, etc.)

• Garbage bags

2.2. Design PrinciplesWe examined the performance and design principles

required for the three-fingered robot hand to be able togrip the tableware. As an actuator, we used one current-controllable DC motor. We developed the three-fingeredrobot hand based on the design principles detailed below.

(1) Dimension and Mass

The dimensions were determined to ensure compatibil-ity with human beings in environments in which peopleand machines coexist. More specifically, we aimed to de-velop a robot hand with average human hand dimensions.This means that the dorsal length (the straight-line dis-tance from the back of the middle finger metacarpal headto the end of the middle fingertip) of the middle fingerwas to be about 114 mm, the breadth of the hand (thewidth of the base of the fingers other than the thumb) wasto be about 83 mm, and the palm length to the middle fin-ger (the straight-line distance from the center of the wristcrease to the crease at the base of the middle finger) wasto be about 106 mm. The hand of a Japanese adult malewas used as a reference for these dimensions [a].

As for the mass, the weight capacity of the manipula-tor (TV800, Toshiba Machine) that supported the three-fingered robot hand at the time of the test of the grippingaction of tableware was 5 kg, so it was determined thatthe mass of the three-fingered robot hand was not to ex-ceed 5 kg. In addition, we reduced the weight of the three-fingered robot hand to the extent possible by removingany unnecessary structures, etc.

(2) Fingertip Forces

A sufficient fingertip force to prevent the tablewarefrom falling is needed for tableware to be held by thefingertips of the three fingers. On the assumption that theassumed maximum mass of the plastic tableware servingas the grip target is 150 g and the safety factor is 3, thegoal of the fingertip force was set to about 5 N. In ordernot to increase the size of robot hand, it was produced firstnot with a continuous force but with a maximum force. Inorder to grip heavier tableware, the fingertip force neededto be increased. Increasing the fingertip force requireschanging the DC motor, which in turn requires rewiringand readjusting the control system. We therefore tried adesign that would allow the fingertip force to be increasednot through a change in the DC motor but through the re-arrangement of the mechanism structure alone.

(3) Grip in the Absence of Electric Power

It is necessary for the robot hand to maintain the gripstate so as not to drop any tableware even if the DC motorloses power due to damage. In addition, a hand that cankeep its grip without any electrical power can be expectedto consume less energy. A typical DC motor will easilyrotate when power is lost and an external force momentacts on its output axis. However, an electromagnetic brakeset up in the DC motor in order to prevent rotation willincrease energy consumption and size. We tried to add adesign capable of maintaining the grip against the externalforce in the absence of electrical power by elaborating thestructure of the mechanism.

(4) Modularized Finger Mechanism

Since the finger mechanism comes into frequent con-tact with the tableware, the mechanism can be damaged.



It would then need to be replaced with a new finger mech-anism. This replacement can be made efficient by modu-larizing each finger mechanism through standardizing thedesign, and an improvement in the ease of maintenancecan be expected. In addition, the modularization of thefinger mechanism is expected to reduce the number ofcomponents and also the cost, owing to the reuse of com-ponents. We therefore tried to modularize the design ofthe finger mechanism.

(5) Finger Joint Structure

Determined the joint structure of the robot hand by re-ferring to human joint structure, we gave the finger mech-anism three joints: the metacarpophalangeal (MP) joint,the proximal interphalangeal (PIP) joint, and the distal in-terphalangeal (DIP) joint. In order to reduce the numberof DC motors, unlike a human finger, the finger mecha-nism we developed is a joint structure in which the MP,PIP and DIP joints interlock to enable the finger mech-anism flex and extend. This is an underactuated fingermechanism with 1 degree of freedom. In order to ensurethe safety of the people around the robot and to preventthe mechanism from being damaged due to contact withthe finger mechanism, we examined providing the fingerflexibility with only the mechanism element, and we pro-vided the finger mechanism with the elastic element.

(6) Object Sensing Sensor

In order to improve grip certainty, there must be a wayto confirm the state of the grip. In order to confirm theposition and posture of the tableware, the robot hand hasa wide-angle camera within it. In the sensing structure ofa common robot hand, contact with an object is detectedusing a contact sensor on the surface of the finger; thegripping force is detected using a force sensor. The useof a dedicated sensor allows the target physical quantityto be detected with high accuracy, but sensors increasethe wirings needed and therefore the cost. We thereforelooked into a method of easily detecting contact and esti-mating gripping force by using the interlocking and rota-tion of the finger mechanism.

3. Development of Underactuated FingerMechanism

This section outlines the finger mechanism developedon a basis of the concept presented in Section 2.

3.1. StructureFigure 2 presents the external appearance of the fin-

ger mechanism developed as a manual drive for the basicverification of mechanism operations. Fig. 2 presents thenames of the links used in this paper. Fig. 3 is a schematicdiagram of the operation of the finger mechanism. Fig. 4presents the structure view (X-Y plane) in which each linkis modeled in a state in which the finger mechanism is

30

30

50

50

23

MP

PIP

DIP

Feed Screw Mechanism

Moving Part

Proximal Link

Middle Link

Distal Link

Gas Spring

Fig. 2. Developed finger mechanism.

1 2 3

Moving Part

MechanicalStopper

Gas Spring

MP

PIP

DIP

(a) (b) (c)

Fig. 3. Outline of finger driving mechanism.

X-axisO

A

B

C

D

E

F

G

H

OA

OC

CH

AB

CDDE

BFBC

l

l

ll

lEGl

ll

lFG

lEF

CFl

l

θOC

θ

θOA

θD

H

θC

θF

θEinθ

αβ

θA

DIP PIP

MP

Y-axis

Fig. 4. Kinematic sketch of the finger mechanism.

closed. In Fig. 4, joint O denotes the MP joint, joint C de-notes the PIP joint, and joint F denotes the DIP joint. Allthe joint angles are positive in the counterclockwise direc-tion. As presented in Fig. 3(a), the initial posture is thestate in which the finger mechanism is stretched straight


Tanaka, J.

Table 1. Link length and joint angle in initial posture.

Link length [mm] Initial angle [deg]

lOA 10.00 θOC 45.00

lAB 45.84 θOA 0.00

lOC 50.00 θA 65.52

lBC 9.00 θH 45.00

lCD 9.00 θin 0.00

lBF 31.32 θC 0.00

lCF 30.00 θD 23.19

lEF 9.00 θE 336.80

lDE 22.85 θF 16.70

lEG 30.00 α 90.00

lFG 31.32 β 73.30

out. The length of each link and each joint angle in the ini-tial posture were determined by considering of the rangeof movement of the finger mechanism. Those parametersare presented in Table 1.

The finger mechanism consists of a pair of four-barlinkage mechanisms, a small gas spring, a feed screw, andthree joints, namely, the MP, PIP, and DIP, which inter-lock and rotate. By interlocking and rotating, the jointangle of the finger mechanism in operation is uniquely de-termined. To ensure the movable range of the finger joint,each four-bar linkage mechanism is a cross link mecha-nism. For mechanical flexibility, a gas spring is adoptedbecause it is small and lightweight, and a large initial loadcan be set. Also, the finger mechanism has a structuredriven by the reaction force of the gas spring. The reactionforce of the gas spring varies according to the amount ofexpansion and contraction. By adjusting the internal gaspressure in advance, the reaction force of the gas springcan be set over a wide range even with gas springs of thesame size. Since the dimensions of the gas spring do notchange, it is unnecessary to alter the gas spring mount-ing portion of the finger mechanism when replacing anexisting gas spring with one that has been adjusted to agiven internal gas pressure. For this reason, it is pos-sible to try various gas spring reaction forces with ease.Other than that, since the gas spring is componentized asa product, it has a resistant to dust and has a high reliabil-ity of operation. In the finger mechanism, we used a gasspring that increases its reaction force as it contracts. Weadopted a “FGS-8-20-AA-50” (Fujilatex Co. Ltd.), whichhas an expansion and contraction of 20 mm and an in-ternal gas pressure of 50 N. Both ends of the gas springare connected to make passive rotation possible. Morespecifically, one end of the gas spring is connected to themoving part (joint H) on the feed screw, and the otheris connected to the PIP joint (joint C). The shape of thesplicing fittings on either end of the gas spring was elab-orated, and the gas spring length lCH was determined tohave a minimum length of 72 mm and a maximum lengthof 92 mm. According to the product specifications, the

1 2 3

Fig. 5. Non-contact flexion of the finger mechanism.

gas spring reaction force Fgas [N] is expressed as follows.

Fgas = −1.4(lCH −72)+71 . . . . . . . . (1)

The flexion and extension operations of the fingermechanism were realized by switching the moment direc-tion around the MP joint (joint O) by using the gas springreaction force along with the movement of the movableportion of the feed screw (joint H). The gripping forceof the finger mechanism is generated using gas spring re-action force. In the position coordinates HHH = [HX HY ]Tof the moving part (joint H), the operating range of theX-axis position coordinates HX is set to a range from−30 mm to 20 mm, and the Y -axis position coordinatesHY are set to a constant value of −28 mm. The operationangle range of the finger mechanism was set with a me-chanical stopper, and the operating range of θOC was from45◦ to 105◦. If the feed screw is driven by the DC motor,this mechanism is structured so that even if an externalforce causes the finger mechanism to extend, that force istransmitted to the gas spring and the feed screw, not di-rectly to the DC motor. In addition, high reduction ratioof the feed screw allows the use of a DC motor of smallsize and low power. In this mechanism, the gripping forceis determined by the internal pressure of the gas springand the position of point H, so it is expected to gener-ate a gripping force that is greater than that generated bydirectly installing the small, low-power DC motor in thefinger joint. In addition, the grip can be maintained evenif the DC motor loses electrical power.

3.2. Flexion OperationFigure 5 presents the flexion operation of the finger

mechanism when it is not in contact with an object. Theoperation from the open state to the closed state is ex-plained using the symbols seen in Fig. 4. By manuallyrotating the feed screw, the moving part (joint H) moveslinearly along the screw axis, and the end of the gas spring(joint H) also moves. At this time, the gas spring reactionforce causes the link OC to rotate around the MP joint(joint O). Since the first-stage four-bar linkage mecha-nism consists of the joint OABC and the link OA is fixedon the base, the rotation of the link OC causes the links ABand BC to rotate at the same time. Due to this, the relativeangle of the links OA and BC in the four-bar linkage mech-anism changes. The second-stage four-bar linkage mech-



anism consists of the joint CDEF , but the rotation of thefirst-stage four-bar linkage mechanism causes links CFand DE to rotate at the same time. Due to this, the rela-tive angle of the links CD and EF in the four-bar linkagemechanism changes. Hence, the MP, PIP, and DIP jointsinterlock and rotate, and the finger mechanism takes aposture of flexion.

When the finger mechanism carries out a flexion opera-tion from an open state, as presented in Fig. 5, the flexionposture of the finger mechanism has points H, O, and Caligned in a straight line, and it moves point H. If the fin-ger mechanism contacts the mechanical stopper, the flex-ion operation of the finger mechanism stops. However,even after it stops, point H can move, and if point H iscaused to move further, θin (∠OCH) increases, and thegripping force can be increased gradually. For this rea-son, a more secure grip of tableware can be expected. Inaddition, for the purpose of gripping the tableware, a cer-tain level of stiffness can be expected. Hence, a sensitivecontrol of the gripping force is not altogether necessary,and it is expected that tableware can be gripped with thefinger mechanism without any problem. The relationshipbetween the position of point H and the gripping forceafter the flexion operation of the finger mechanism stopswill be described in detail in Section 4.3.

3.3. Mechanical FlexibilityThe effects of the gas spring on mechanical flexibility

will now be presented. Fig. 6 presents the finger mech-anism in contact with an object in a flexion operation.When the finger mechanism and the object make con-tact, the rotation of each joint is stopped. After the fingermechanism and the object make contact, through furthermovement of the feed screw, θin (∠OCH) in Fig. 4 be-comes large and the gripping force increases. This oper-ation indicates that the grip state can be generated even ifthe accuracy of the positioning control of the moving partis low and the movement of that part becomes consider-able. Next, Fig. 7 presents the MP, PIP, and DIP jointsinterlocking and rotating after an external force is appliedto the tip of the finger mechanism in the flexion posture.Each joint interlocks and is moved by the amount of ex-pansion and contraction of the gas spring against the mo-ment of the gas spring reaction force. As presented inFig. 7, when an external force is applied to the tip ofthe finger mechanism in the flexion posture, the fingermechanism behaves elastically with respect to the exter-nal force in a section where the gas spring expands andcontracts. When there is no expansion or contraction ofthe gas spring, however, it plays the role of a mechanicalstopper, and the finger mechanism does not open further.Accordingly, when the object being gripped should notdrop, point H should be positioned near the upper limit ofthe X-axis positive direction, and the amount of expansionand contraction of the gas spring should be reduced. Onthe other hand, in an environment where the object beinggripped may come into contact with a person, the amountof expansion and contraction of the gas spring is increased

1 2 3

Fig. 6. Contact flexion of the finger mechanism.

1 2 3

Fig. 7. Passive drive of the gas spring by external force.

Stainless Steel Wire

Fig. 8. Displacement sensor of gas spring.

through the adjustment of the position of point H. It isconsidered good that there is lower possibility of injury,owing to the flexibility of the finger mechanism, to anyonewho may come into contact with the object being gripped.The flexibility of the finger mechanism could also preventdamage to it.

3.4. Sensing Method Using the Expansion andContraction of the Gas Spring

Using the interlocking and rotating feature of the fingermechanism, we measured the expansion and contractionof the gas spring so as to find a way to easily detect a con-tact and estimate the gripping force. As can be seen inFig. 8, there is a displacement sensor (WP20, LEVEX) tomeasure the expansion and contraction of the gas spring.A stainless wire is inserted into a tubular member, moving


Tanaka, J.

50[mm]

(a) (b)

Fig. 9. Gripping motion for a plate.

a measurement region (12 mm) and changing the outputvoltage (1 to 5 V) of the displacement sensor. The deeperthe stainless wire is inserted into the tubular member, thegreater the output voltage becomes. Since the posture ofthe finger mechanism is uniquely determined due to in-terlocking and rotating, the posture of the finger mecha-nism can be estimated from the position and the gas springlength lCH of the moving part (joint H).

The contact detection method of the finger mechanismand the object using the interlocking and rotating of thefinger mechanism will be described first. First, a databaseis built by obtaining in advance the length lCH of the gasspring with respect to the position of joint H when thefinger mechanism is in the flexion operation in a state inwhich the finger mechanism is not in contact with the ob-ject, as in Fig. 5. Next, the measurement value and thedatabase value of the gas spring length lCH with respectto the position of joint H are sequentially compared whenthe finger mechanism is in operation. In the process inwhich the finger mechanism is in the flexion operation(Fig. 6), when the finger mechanism contacts the object,a difference is generated between the measurement valueand the database value in the gas spring length lCH withrespect to the position of joint H, and contact is detectedwhen this difference is detected. For instance, in the fingermechanism posture seen in Fig. 9, the difference betweenthe output voltage of the displacement sensor (a) whenthere is no contact and (b) when there is contact with aplate 50 mm high is about 1.06 V. Since the tablewarebeing considered has a certain degree of hardness, con-tact detection can be expected through the sensing of thismechanism. As described in detail in the Section 4, in es-timating the gripping force, the facts that the finger mech-anism interlocks and rotates and that the gripping forcedepends on the gas spring reaction force makes calcula-tion through mechanism analysis easy.

3.5. Gripping Force MeasurementWe measured the gripping force using the test device

presented in Figs. 10–12. In the test, the moving part waspositioned at the end in order to flex the finger mecha-nism, and the finger mechanism was in an open posture in

Fig. 10. Proximal link force evaluation test.

Fig. 11. Middle link force evaluation test.

Fig. 12. Distal link force evaluation test.

the position immediately before the amount of expansionand contraction of the gas spring becomes null. A digi-tal force gauge was caused to perpendicularly contact thesurface of each finger, and the gripping force producedby the gas spring reaction force was measured in thatstate. The proximal link finger surface had a maximumof 33.1 N (Fig. 10), the middle link finger surface had amaximum of 12.2 N (Fig. 11), and the fingertip surfacehad a maximum of 6.2 N (Fig. 12). It was confirmed that



Table 2. Formulas for calculating joint positions.

A AAA =

[lOA cos(θOA)lOA sin(θOA)

]

B BBB = AAA+

[lAB cos(θOA +θA)lAB sin(θOA +θA)

]

C CCC =

[lOC cos(θOC)lOC sin(θOC)

]

D DDD =

[(lOC + lCD)cos(θOC)(lOC + lCD)sin(θOC)

]

E EEE = DDD+

[lDE cos(θOC +θD)lDE sin(θOC +θD)

]

F FFF = CCC +

[lCF cos(θOC +θC)lCF sin(θOC +θC)

]

G GGG = FFF +

[lFG cos(θOC +θC +θF)lFG sin(θOC +θC +θF )

]

it was possible to ensure the target fingertip force of 5 N orgreater at the fingertip. It was also confirmed that the grip-ping force increased from the fingertip surface towardsthe base, from the middle link finger surface to that of theproximal link finger.

4. Kinematics Analysis

This section presents the derivation of force using statickinematics of the prototyped finger mechanism and theprinciple of virtual work. We used the values of the modeland each parameter presented in Fig. 4 and Table 1. Theoperating range of θOC was from 45◦ to 105◦, similar tothat of the prototyped finger mechanism. The prototypedfinger mechanism was limited to the two-dimensional op-eration of flexion and extension only, so the kinematicsand the gripping force were handled in two dimensions.

4.1. Kinematics of OperationsAs presented in Fig. 4, the joint position coordinates

were joint A to joint H (refer to Table 2 for the deriva-tion expression of the position of each joint). Since eachjoint of the finger mechanism interlocks and rotates dueto movement of the moving part (joint H), the posture ofthe finger mechanism is determined by the two angles θOAand θOC of the first-stage of the four-bar linkage mecha-nism consisting of the joint OABC. Since the link OA isfixed to the base, θOA takes on a constant value of zero.The gas spring reaction force pushes the PIP joint (joint C)out, changing θOC. After the flexion operation is stoppedby the finger mechanism coming into contact with themechanical stopper, when joint H is moved further, θin,which consists of link OC and the gas spring, increases.

The preconditions here are as follows. The momentaround the MP joint (joint O), caused by the gas springreaction force, is sufficiently great with respect to thefriction around the MP joint (joint O), and the link OCsmoothly rotates along with the movement of joint H.The values of θOC and the gas spring inclination angle θHare equal within the operating range of θOC. Accordingly,the following expressions are true for the relationship be-tween θOC and θH .

θOC = θH

(π4≤ θOC <

7π12

). . . . . . (2)

θOC = θH −θin

(θOC =

7π12

). . . . . . (3)

The distance from joint O to joint H is allowed to be lOH ,and θin is expressed as follows from the law of cosines.

θin = cos−1(

lOC2 + lHC

2 − lOH2

2 · lOC · lHC

). . . . . (4)

From the condition of constraint of the four-bar linkagemechanism that has two stages, the following equationsof constraint are true as they relate to the two joints Band E.[

j1j2

]=BBB−

(CCC + lBC

[cos(θOC +θC +α)sin(θOC +θC +α)

])= 0 . (5)

[j3j4

]=EEE −

(FFF + lEF

[cos(θOC +θC +θF +β )sin(θOC +θC +θF +β )

])=0 (6)

By partially differentiating the constraint conditions ofEqs. (5) and (6) with the angular variables θOA and θOC,the minute amount relationship of other joint angles is cal-culated as the following determinant.⎡

⎢⎣ΔθAΔθCΔθDΔθF

⎤⎥⎦= −QQQ−1RRR

[ΔθOAΔθOC

]. . . . . . . . (7)

However, QQQ and RRR are expressed as follows with Jacobiandeterminants.

QQQ =

⎡⎢⎢⎢⎣

∂ j1/∂ θA ∂ j1/∂ θC ∂ j1/∂ θD ∂ j1/∂ θF

∂ j2/∂ θA ∂ j2/∂ θC ∂ j2/∂ θD ∂ j2/∂ θF

∂ j3/∂ θA ∂ j3/∂ θC ∂ j3/∂ θD ∂ j3/∂ θF

∂ j4/∂ θA ∂ j4/∂ θC ∂ j4/∂ θD ∂ j4/∂ θF

⎤⎥⎥⎥⎦ (8)

RRR =

⎡⎢⎢⎢⎣

∂ j1/∂ θOA ∂ j1/∂ θOC

∂ j2/∂ θOA ∂ j2/∂ θOC

∂ j3/∂ θOA ∂ j3/∂ θOC

∂ j4/∂ θOA ∂ j4/∂ θOC

⎤⎥⎥⎥⎦ . . . . . . . . (9)

In addition, the minute amount relationship between theposition coordinates [ΔGX ΔGY ]T of the joint G of thefingertip and θOA and θOC is calculated from the followingexpression.[

ΔGX

ΔGY

]=−(PPPGQQQ−1RRR+SSSG)

[ΔθOA

ΔθOC

]= JJJG

[ΔθOA

ΔθOC

](10)


Tanaka, J.

However, PPPG and SSSG are expressed as follows.

PPPG =[

∂ GX/∂ θA ∂ GX/∂ θC

∂ GY /∂ θA ∂ GY /∂ θC

∂ GX/∂ θD ∂ GX/∂ θF

∂ GY /∂ θD ∂ GY/∂ θF

]. . . . . (11)

SSSG =[

∂ GX/∂ θOA ∂ GX/∂ θOC

∂ GY /∂ θOA ∂ GY /∂ θOC

]. . . . . (12)

JJJG is a Jacobian determinant of joint G. The posture of thefinger can be calculated by giving the value of the minuteangle [ΔθOA ΔθOC]T using Eqs. (7) and (10).

4.2. Derivation of Fingertip Force Usingthe Principle of Virtual Work

Fingertip force fff G is derived by using the Jacobiandeterminant JJJG calculated in the previous section. Asis well known, the relationship between the force fff G =[ fX

G fY G]T that acts on joint G of the fingertip and thetorque τττ = [τθOA τθOC]T that acts on θOA and θOC is cal-culated as follows, in accordance with the principle of vir-tual work.

fff G = JJJG−T · τττ . . . . . . . . . . . . . (13)

In addition, torque τττ is expressed as follows.

τττ =[

τθOA

τθOC

]=[

0loc ·Fgas sinθin

]. . . . . . (14)

Fgas: gas spring reaction force [N], θin: ∠OCH [rad].Similarly, force can be derived by using the principle

of virtual work for the other joints.

4.3. Mechanism Analysis Through SimulationUsing the calculated kinematics model, we simulated

the operation of the fingers and confirmed the operatingrange of the fingertips and the characteristics of the op-eration. The results of the simulation are presented inFigs. 13–15.

Figure 13 presents the results of a simulation of the or-bit of operation of each link in the flexion operation ofthe finger mechanism. It presents a change in the pos-ture of the finger when θH is changed by movement ofthe moving part (position coordinates HHH). Along withthe change in θH , each joint angle also interlocks andchanges. Fig. 13 indicates an operation in which, due toan increase in θH , the finger gradually flexes and falls.Since this flexion operation brings the finger into contactwith various large and small objects, it is useful for grip-ping objects. The posture 4© (θOC = 105.0◦) of Fig. 13is a state in which, after the finger mechanism contactsthe mechanical stopper and stops, the flexion operationand the position HX of the moving part is moved to theend portion (20 mm). The position HX of the moving partwhen the finger mechanism contacts the mechanical stop-per is about 8 mm.

X-axis[mm]

①H=[-30 -28]T

②H=[-9 -28] ③H=[0 -28]T

④H=[20 -28]T

T

①θ =45.0[deg]H

②θ =70.6[deg]H

③θ =90.0[deg]H

④θ =113.4[deg]H

20 40 60 800-20-40-60-80-40

-20

0

20

40

60

80

100

120

Y-a

xis[

mm

]

Fig. 13. Kinematic simulation of flexion.

H [mm]X

l

[mm

]C

H

-5-10-15-20-25-30 0 5 10 15 2076

78

80

82

84

86

88

90

92

Fig. 14. Relation between moving part position and gasspring length.

X-axis[mm]

H=[20 -28]T

③l =72.0[mm]CH

②l =78.1[mm]CH

①l =83.1[mm]CH

③θ =62.0[deg]OC

②θ =80.0[deg]OC

①θ =105.0[deg]OC

20 40 60 800-20-40-60-80-40

-20

0

20

40

60

80

100

120

Y-a

xis[

mm

]

Fig. 15. Kinematic simulation of extension.



In Fig. 14, the horizontal axis represents the posi-tion HX of the moving part, and the vertical axis repre-sents the gas spring length lCH . Fig. 14 shows the calcu-lation result of change in the gas spring length lCH whenthe finger mechanism is in a flexion operation as shown inFig. 13. As the selected gas spring length lCH has a mini-mum length of 72 mm and a maximum length of 92 mm, itis confirmed that all the postures of the finger mechanismare within the operating range of the gas spring lengthlCH . The amount of expansion and contraction of the gasspring due to the posture change from 1© to 4© in Fig. 13is about 13 mm, based on Fig. 14.

Figure 15 presents the results of a simulation of theoperation orbit of each link in the extension operation ofthe finger mechanism. The position coordinates HHH of themoving part are fixed. The finger mechanism shows aposture change from the state ( 1© in Fig. 15) in whichit comes into contact with the mechanical stopper to theposture ( 3© in Fig. 15) in which θOC is caused to rotatein the negative direction and the amount of expansionand contraction of the gas spring becomes null. It canbe confirmed that accompanied with the change in θOC,each joint of the finger mechanism interlocks and the gasspring lCH contracts and then gradually extends. This ex-tension operation corresponds to the posture change whenan external force acts on the finger mechanism in the flex-ion posture. Fig. 15 includes the gas spring length lCHin each posture, and the gas spring expands and contracts10.9 mm due to the change in posture from the one in 1©to that in 3© in Fig. 15.

Since the measurement area of the stainless wire usedto measure the expansion and contraction of the gas springis 12 mm, as indicated in Figs. 14 and 15, it is not possi-ble to measure the expansion and contraction of the gasspring with the finger mechanism in all postures. Wetherefore focus on measuring the expansion and contrac-tion of the gas spring when the hand is gripping, and weset the measurement range for the gas spring length lCHto about 72 to 84 mm. With the measurement range ofthe gas spring length lCH set, the operating range of theX-axis position coordinates HX of the moving part be-comes about −20 mm to 20 mm. The posture 3© shownin Fig. 15 is similar to those in Figs. 10–12. In these pos-tures, the gas spring reaction force Fgas becomes about71 N and the angle θin becomes about 25.5◦, and it iscalculated that the torque τττ = [0 1528.3]T [N·mm]. Onthe basis of the principle of virtual work, forces gener-ated in joints G, E, and B are calculated. In the stateshown in 3© in Fig. 15, it is calculated that joint G isfff G = [7.1 43.6]T [N], joint E is fff E = [12.5 31.6]T [N],and joint B is fff B = [31.8 5.2]T [N]. The force in the X-axisdirection increases from joint G toward the base side inthe order of the joints E and B.

Next is an explanation of the relationship between theposition HX of the moving part and the gripping forceafter the flexion operation of the finger mechanism isstopped. On coming into contact with an object or the me-chanical stopper, the flexion operation of the finger mech-anism stops, and even if the position HX of the movable

H [mm]

00 5

θ = 70.6[deg](Fig.13 ②)

10 15 20-5-10

200

400

600

800

1000

1200

1400oc

x

τ

[N

mm

]θo

c

θ = 90.0[deg](Fig.13 ③)ocθ = 105.0[deg](Fig.13 ④)oc

Fig. 16. Relation between moving part position and link-OCtorque.

portion is advanced after that, the posture of the fingermechanism does not change. For this reason, based onEq. (14), the gripping force depends on torque τθOC, cal-culated with the gas spring reaction force Fgas and theangle θin. In the development of a formula related totorque τθOC, Eqs. (1) and (4) are put into Eq. (14) andorganized as the following expression.

τθOC = loc(−1.4lCH +171.8)

× sin

(cos−1

(lOC

2 + lHC2 − lOH

2

2 · lOC · lHC

))(15)

As presented in Table 1, lOC is a constant value (50 mm).In Fig. 4, the relationship between the distance lOH fromjoint O to joint H and the position coordinates HHH =[HX HY ]T of the moving part (joint H) is calculated asfollows.

loc =√

HX2 +HY

2 . . . . . . . . . . . (16)

In addition, in Fig. 4, the relationship between the gasspring length lCH and the position coordinates H is calcu-lated as follows.

lCH =√

(loc · cosθOC −HX)2 +(loc · sinθOC −HY )2 (17)

Here, the operating range of the X-axis position coordi-nates HX is from −30 mm to 20 mm, and the Y -axis po-sition coordinates HY have a constant value of −28 mm.The relationship between the torque τθOC and the posi-tion HX of the moving part can be calculated by puttingEqs. (16) and (17) into Eq. (15). Postures 2©– 4© in Fig. 13are selected as the flexion posture of the finger mecha-nism, and the relationship between the position HX of themoving part and torque τθOC after the flexion operation ofthe finger mechanism is stopped is presented in Fig. 16.If the hand comes into contact with an object while it isin posture 2©, as shown in Fig. 13, the operating range ofthe position HX of the moving part is from about −9 mmto 20 mm. In the case of contact while in posture 3© inFig. 13, the operating range of the position HX of the mov-ing part is from about 0 mm to 20 mm. In the case ofcontact with the mechanical stopper while in posture 4©in Fig. 13, the operating range of position HX of the mov-


Tanaka, J.

Table 3. Results of calculation of fingertip force.

Fgas [N] τθOC [Nmm] fXG [N] fY G [N]

G20 1© 22.1 162.0 −1.7 −2.5G20 2© 24.9 394.3 −6.2 3.4G20 3© 28.4 611.3 −2.8 17.4G50 1© 55.4 405.0 −4.4 −6.4G50 2© 62.4 985.7 −15.6 8.6G50 3© 71.0 1528.3 −7.1 43.6G100 1© 110.9 810.1 −8.9 −12.8G100 2© 124.9 1971.5 −31.3 17.3G100 3© 142.0 3056.6 −14.3 87.1

ing part is from about 8 mm to 20 mm. In addition, theangle θOC of the posture 2© in Fig. 13 is 70.6◦, the angleθOC of the posture 3© in Fig. 13 is 90.0◦, and the angleθOC of posture 4© in Fig. 13 is 105.0◦. Fig. 16 indicatesthat in each posture, as the position HX of the moving partincreases, torque τθOC also increases. This is because thechange in the gas spring reaction force Fgas with respectto the change in the gas spring length lCH is small. Forthis reason, as angle θin increases, torque τθOC and thegripping force also increase.

4.4. Relationship Between the Internal GasPressure and Fingertip Force

In order to obtain a selection guide of the internal gaspressure of the gas spring, the relationship between theinternal gas pressure and the fingertip force (joint G) isexamined in each of postures 1©– 3© in Fig. 15, whichcomprise the grip posture. The internal gas pressure forthe selected gas spring can be adjusted in advance withina range of 20–100 N. For this reason, we compare thefingertip force in three states: when the internal gas pres-sure is at 20 N, which is its lower limit value, when it isa 50 N, which is half of its upper limit, and when it isat 100 N, which is its upper limit. As in Section 4.3, thefingertip force (joint G) is obtained, based on the princi-ple of virtual work, by calculating torque τττ from the gasspring reaction force Fgas and the angle θin. In posture 1©in Fig. 15, the angle θin is about 8.4◦. In posture 2© inFig. 15, the angle θin is about 18.4◦. In posture 3© inFig. 15, the angle θin is about 25.5◦. The gas spring reac-tion force in each of the postures 1©– 3© in Fig. 15 referredto the product specifications.

Table 3 presents fingertip force fff G calculated for eachof the postures 1©– 3© in Fig. 15 in each state of the inter-nal gas pressure of the gas springs. In Table 3, the stateof posture 1© in Fig. 15 while the internal gas pressure ofthe gas spring is set to 20 N is written as “G20 1©,” thestate of posture 2© is written as “G20 2©,” and the state ofthe posture 3© is written as “G20 3©.” Similarly, the stateof posture 1© in Fig. 15 while the internal gas pressure ofthe gas spring is set to 50 N is written as “G50 1©,” thestate of posture 2© in Fig. 15 is written as “G50 2©,” and

Fingertip force in X-axis direction [N]

Fing

ertip

forc

e in

Y-a

xis d

irect

ion[

N]

-20

0

20

40

60

80

100

0-5-10-15-20-25-30-35

Gas spring (50 N)Gas spring (100 N)

Gas spring (20 N) Fig.15③

Fig.15②

Fig.15①-40

Fig. 17. Relation between fingertip force in X- and Y -axesdirections.

the state of posture 3© in Fig. 15 is written as “G50 3©.”Also, the state of posture 1© in Fig. 15 while the internalgas pressure of the gas spring is set to 100 N is writtenas “G100 1©,” that of posture 2© is written as “G100 2©,”and that of posture 3© is written as “G100 3©.” Fig. 17presents the relationship between the internal gas pres-sure of the gas spring and the fingertip force (joint G) pre-sented in Table 3. Fig. 17 indicates that in the process oftransitioning from postures 1©– 3© in Fig. 15, the fingertipforces in X- and Y -axes directions change considerably.It also indicates that the greater the internal gas pressureis, the greater the fingertip force can be. However, a gasspring with a great internal pressure, as it is difficult tocontract manually, necessitates the use of a dedicated jigwhen the finger mechanism is assembled. In addition, inSection 2.2, the fingertip force is set to reach about 5 N,and it is thought that the target fingertip force can basi-cally be achieved with the internal gas pressure 50 N. Forthese reasons, the internal gas pressure 50 N was adoptedfor the gas spring of the three-fingered robot hand, as itwas for the finger mechanism in Section 3.

5. Development of Three-Fingered RobotHand

This section will describe in detail the mechanism ofthe developed three-fingered robot hand and the test re-sults. The test, from a practical point of view, verifiesthat the basic operation necessary for gripping tablewareis possible.

5.1. StructureFor basic verification of the mechanism operation,

Fig. 18 presents an external view of the developed three-fingered robot hand driven by a DC motor. As the inter-nal mechanism of the three-fingered robot hand, the mo-tor arrangement is presented in Fig. 19, the gear arrange-ment is presented in Fig. 20(a), and the pulley arrange-ment is presented in Fig. 20(b). Two fingers of the three-



30

23

10485

62

5030

Finger①

Finger② Finger③

Wide-angle Camera

170

Fig. 18. Three-fingered robot hand.

Spur Gear-A

Spur Gear-B

Spur Gear-C

Pully-C

DC-Motor

Transmission Shaft

Robot Hnad Base

Finger① Base

Fig. 19. Position of motor in the hand base.

fingered robot hand are arranged in opposite position ofthe remaining one. The three-fingered robot hand has amaximum open width of about 170 mm and a mass ofabout 650 g. The dimensions of the hand, based on the de-sign principles outlined in Section 2, were determined byreferencing the average dimensions of the hands of adultJapanese males. The finger mechanism has a structuresimilar to that of the finger mechanism in Section 3, andthe internal gas pressure of the gas spring is similarly setto 50 N. Owing to this, a gripping force similar to that ofthe finger mechanism in Section 3 was obtained.

Driving the three-fingered robot hand is just oneDC motor, which is mounted on the base of the handas presented in Fig. 19. On a basis of the findings ob-tained on the finger mechanism, detailed in Section 3,a small, low-power DC motor is adopted, the specifica-tions of which are presented in Table 4. As presented inFigs. 19 and 20(a), spur gear A is set up on the gear headoutput axis of the DC motor, and spur gear B is set up onthe input axis of the feed screw of finger mechanism 1©.As presented in Fig. 20(b), pulley A is set up on the in-put axis of the feed screw of finger mechanism 2©, and

Spur Gear-C Robot Hnad Base

Spur Gear-ASpur Gear-B

Finger① Finger②Finger③

(a)

Pully-C Robot Hnad Base

Pully-A Pully-B

Finger①Finger② Finger③

(b)

Fig. 20. Position of spur gears ABC and pulleys ABC.

pulley B is arranged on the input axis of the feed screwof finger mechanism 3©. As presented in Fig. 19, spurgear C is set up at one end of the transmission shaft, andpulley C is at the other end. Each of spur gears A–C isengaged. In addition, the pulleys A–C are connected viaa belt. The driving power from the DC motor is transmit-


Tanaka, J.

Table 4. Specifications of DC motor.

DC motorWattage [W] 4.5Maximum torque [m·Nm] 4.5Maximum speed [rpm] 12200Reduction ratio 84

D/A Board

Counter Board

A/D Board

Moter Drive DC Moter

Rotary Encoder

Displacement Sensor

Voltage Current

Rotation Angle

Voltage

USB Board CameraImage

Three-fingered handPC

Fig. 21. Drive control system.

ted to the feed screw of each finger mechanism via a spurgear and belt pulley. The lead of the feed screw is 2 mm.

A magnetic rotary encoder is mounted on the DC motoras a sensor measuring the number of rotations, and thereis a wide-angle camera mounted in the center of the baseof the three-fingered robot hand for object recognition. Adisplacement sensor that is similar to that detailed in Sec-tion 3 is set up at the location of the gas spring of eachfinger mechanism to measure expansion and contraction.

Figure 21 presents the drive control system for carry-ing out the test. In this test, a determined voltage to pro-duce the target speed was output to the motor driver, caus-ing a current to flow through the DC motor and producingdrive. For control, the magnetic rotary encoder detects therotation speed of the DC motor, inputs it to the counterboard, and gives feedback. Owing to the position con-trol of the DC motor, after the finger mechanism contactsthe mechanical stopper or the target object, as stated inSection 3.2. The gripping force can be adjusted, and theamount the finger mechanism opens can be adjusted usingthe amount of expansion and contraction of the gas spring,as stated in Section 3.3. For purposes that do not requirethose adjustments, the use of the DC motor is not neces-sarily required, and using an actuator such as a solenoidmay be a lower-cost option.

5.2. Gripping ActionFigure 22 presents the gripping action of the three-

fingered robot hand. It required about 15 s at the high-est rotational speed of the DC motor from the maximumopen state to the closed state of the finger mechanism. Theaction speed can be adjusted by selecting the gear head re-duction ratio of the DC motor that is suitable for the workbeing done. In addition, in Fig. 22, the measurements thatthe displacement sensor takes of the expansion and con-traction of the gas spring when the hand grips something

1

2

3

4

5

6 0:15

0:00

0:03

0:12

0:06

0:09

Fig. 22. Grip test.

are output to the display screen. The horizontal axis of thedisplay screen represents the time; the vertical axis repre-sents the output voltage. It was confirmed that the outputvoltage of the displacement sensor changes in accordancewith the gripping action.

5.3. Grip Posture of Typical TablewareWe selected tableware typical of what the robot hand is

being developed to handle in order to verify whether thethree-fingered robot hand was capable of gripping it. Thegrip test is presented in Fig. 23. The tableware we choseto represent that used in eating and drinking facilities ispresented in Fig. 23: (a) a dish (56 g), (b) a dish (70 g),(c) a bowl (142 g), (d) a cup (110 g), (e) a bowl (79 g),(f) a cup with a handle (147 g), (g) a spoon (10 g), (h) achopstick (12 g), and (i) a fork (10 g). (j) A garbage bag(17 g) was also included. In the test, after the movingpart was in turn moved by the DC motor and each jointof the three-fingered robot hand was flexed so that it sup-ported the target tableware item, the electrical power tothe DC motor was cut and hand sustained its grip using amechanical constraint of the mechanism.

As is made clear in Fig. 23, it is confirmed that thethree-fingered robot hand can grip cylindrical tableware,such as a dish and a cup, as well as tableware with anelongated shape, such as a spoon, by supporting it at threepoints. Fig. 23(j) makes it clear that each finger mech-anism of the three-fingered robot hand is flexed and cangrip a garbage bag, which is a soft object. In addition,since each finger mechanism has a lot of holding powereven if the power to the DC motor is lost, it is confirmedthat the grip can sustain the weight of the tableware. Sinceeach finger mechanism of the three-fingered robot handhas mechanical flexibility, it is clear that even a singleDC motor is capable of successfully gripping the outeredges of the tableware.



(a) Dish (ϕ 160×45) (b) Dish (ϕ 200×23)

(c) Bowl (ϕ 182×72) (d) Cup (ϕ 90×140)

(e) Bowl (ϕ 110×65) (f) Cup (ϕ 75×126)

(g) Spoon (length: 195) (h) Chopsticks (length: 227)

(i) Folk (length: 190) (j) Garbage (260×180×30)

Fig. 23. Different grasping actions (unit: [mm]).

5.4. Stiffness Evaluation

Figure 24 presents a stiffness evaluation test of thethree-fingered robot hand without electrical power. In thetest, a weight (3 kg) was suspended on the surface of themiddle link of the finger 3© to verify whether it could bemaintained. Since the weight capacity of the manipula-tor (TV800, Toshiba Machine) that supported the hand atthe time of the tableware grip test was 5 kg, the weighttested was 3 kg in consideration of the 650 g mass of thethree-fingered robot hand. The test confirmed that even ifthe weight of 3 kg is suspended on the middle link fin-ger surface as an external force, the finger mechanismis not damaged and maintains sufficient stiffness. Thisis because the gas spring plays the role of a mechanicalstopper when there is no expansion or contraction of the

Weight: about 3[kg]

Finger③

Fig. 24. Stiffness evaluation test.

Open Close

Non-Contact

Contact State

State

78[mm]

Finger

Finger

Finger

Fig. 25. Contact sensing evaluation test.

gas spring. In addition, it was confirmed that due to themechanical flexibility, the finger mechanisms of fingersother than the finger 3© on which the weight was sus-pended maintained their grip. It was confirmed that thefinger mechanisms having elastic mechanical flexibilitycarry out flexion operations in the range of the expansionand contraction of the gas spring, and the extension oper-ation is stopped when there is no expansion or contractionof the gas spring with respect to the external force in thedirection of extension of the finger mechanism.

5.5. Contact Detection OperationAs presented in Fig. 25, as a basic test of contact detec-

tion of the three-fingered robot hand, a grip test involvinga plate with a height of 78 mm was conducted. We com-pared the output voltage of the displacement sensors ineach finger mechanism when there was no contact withthe plate member with when there was contact. In the


Tanaka, J.

Fig. 26. Relation between position of moving part and out-put voltage of displacement sensor.

test, the moving part was moved at a constant speed by theDC motor. As presented in Fig. 26, it was confirmed that,in the finger mechanisms, there is a difference appearingin the output voltage between when there is no contact andwhen there is when the X-axis position coordinates HX ofthe moving part is near 0 mm. The difference in the out-put voltage orbit of the displacement sensors between thefinger mechanisms is thought to be an effect of the mount-ing accuracy of the displacement sensor and the assemblyaccuracy of the finger mechanism.

5.6. Gripping Action of TablewareWe conducted a basic test of a gripping action of the

developed three-fingered robot hand combined with a ma-nipulator (TV800, Toshiba Machine). Originally, theshape, position, and posture of tableware were detectedusing an external sensor or similar. However, since we areconfirming the operation of the mechanism this time, thatinformation was given in advance, and the grip posturecontrol was carried out on the basis of this information.As the test procedure, the three-fingered robot hand wasfirst moved to the grip position by the manipulator. Next,the moving part was moved so that the finger mechanismcarried out a flexion operation and gripped the tableware.Finally, the tableware being gripped was lifted by the ma-nipulator.

As Figs. 27–29 present a series of gripping actions, thethree-fingered robot hand moved down to the tablewarefrom above and carried out the gripping action. The dishin Fig. 27 is identical to that in Fig. 23(a), and the cupin Figs. 28 and 29 is identical to that of Fig. 23(d). It isconfirmed that when the edge of the dish is gripped as inFig. 27, the first finger of the three-fingered robot handsupports the inside of the dish and the second finger sup-ports the outside, making it possible to grip the dish. Itis confirmed that when the upper edge of the cup is as inFig. 28, gripping is possible by putting the fingertip out-side the rim of the cup and closing the finger mechanism.It is confirmed that when the open and close direction ofthe finger mechanism is not appropriate in the initial statewith respect to the arrangement of the cup, as in Fig. 29,the lateral surface of the cup can be gripped after a pos-ture change operation of the three-fingered robot hand bythe manipulator.

1

2

3

4

5

6 0:18

0:00

0:05

0:17

0:09

0:11

Fig. 27. Experiment of grasping a dish.

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Fig. 28. Experiment of grasping a cup by its rim.

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Fig. 29. Experiment of grasping a cup by its sides.



This test indicates that the developed three-fingeredrobot hand is capable of grasping the target tableware,such as dishes and cups. There is no need to use a differenthand for each piece of tableware. Based on these results,it is thought that the task of handling tableware can be re-alized by using the three-fingered robot hand developedin this study as an end effector of a robot and having anappropriate control. However, it will still be necessary toexamine a gripping action plan combined with a manipu-lator. For example, the hand should be able to push a pieceof tableware, such as a thin dish or a chopstick, with a fin-gertip to make the object easier to grasp, as such items areextremely low in height with respect to the fingertip.

6. Conclusion

This paper has proposed a three-fingered robot hand forhandling tableware. The hand is intended to enable robotsin eating and drinking facilities to do manual tasks suchas clearing tables. The three-fingered robot hand has amodularized finger mechanism, the usefulness of whichwas demonstrated by its ability to grasp different piecesof tableware. With each finger being made up of a pairof four-bar linkage mechanisms, a small gas spring, and afeed screw, the hand is a unique mechanism in which threejoints, namely, the MP, PIP, and the DIP, interlock and ro-tate. Owing to this, the three-fingered robot hand is ableto function with just one DC motor, and it is able to gripwith mechanical flexibility. The developed three-fingeredrobot hand, with a mass of about 650 g, was designedwith reference to the average hand dimensions of a adultJapanese males. The gas spring generates its grippingforce, which is adjusted in position by the moving part.This allows the gripping force of the hand to be generatedeven if the DC motor loses electrical power, and a grip testhas indicated that the grip state of tableware can be main-tained. In addition, the operation characteristics of thefinger mechanism are understood on a basis of an anal-ysis of the mechanism, and a stiffness evaluation has in-dicated that the finger mechanism has sufficient stiffness.In terms of sensing, it has been presented that contact de-tection and gripping force estimation of the finger mecha-nism can easily be realized through measuring the expan-sion and contraction of the gas spring. To test its practi-cal use, we conducted a basic test of the hand’s tablewaregripping action after it was combined with a manipulator,and we confirmed that a gripping action having mechani-cal flexibility enhances tableware handling. This mechan-ical flexibility can be expected to decrease the possibilityof injury to any people an object being gripped may comein contact with, and it can also help prevent damage to thefinger mechanism itself. In addition, since the test resultsof the basic operation suggest that the proposed mech-anism has a certain level of versatility, the hand can beexpected to be used for other purposes beyond tablewarehandling, purposes such as commercial product handlingin logistic sites and component handling in factories.

In the future, we plan to automate handling by using a

mounted wide-angle camera and a displacement sensor tomeasure the expansion and contraction of the gas spring.In addition, we intend to combine the three-fingered robothand with a mobile robot having a manipulator and havethe robot actually carry out tableware handling work.

AcknowledgementsThis work was supported in part by the New Energy and IndustrialTechnology Development Organization (NEDO) of Japan, underthe Development Project of Intelligent Technology for Next Gen-eration Robots.

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Tanaka, J.

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Supporting Online Materials:[a] Digital Human Research Center, AIST. https://www.dh.aist.go.jp/

database/hand/data/list.html [Accessed February 6, 2018]

Name:Junya Tanaka

Affiliation:Research Scientist, Corporate Research & De-velopment Center, Toshiba Corporation

Address:1 Komukai-Toshiba-cho, Saiwai-ku, Kawasaki, Kanagawa 212-8582,JapanBrief Biographical History:2008 Joined Toshiba Corporation2016- Research Scientist, Corporate R&D Center, Toshiba CorporationMain Works:• J. Tanaka, A. Sugahara, and H. Ogawa, “Four-Fingered Robot Hand withMechanism to Change the Direction of Movement – Mechanical Designand Basic Experiments –,” J. Robot. Mechatron, Vol.30, No.4,pp. 624-637, 2018.Membership in Academic Societies:• The Robotics Society of Japan (RSJ)• The Japan Society of Mechanical Engineers (JSME)


three-fingered robot hand with gripping force generating

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