A Novel Layer Jamming Mechanism With Tunable Stiffness Capability for Minimally Invasive Surgery Yong-Jae Kim,Shanbao Cheng,Sangbae Kim,and Karl Iagnemma
Abstract—This paper presents a novel“layer jamming”mecha-nism that can achieve variable stiffness.The layer jamming mech-anism exploits the friction present between layers of thin material, which can be controlled by a confining pressure.Due to the mech-anism’s hollow geometry,compact size,and light weight,it is well suited for various minimally invasive surgery applications,where stiffness change is required.This paper describes the concept,the mathematical model,and a tubular snake-like manipulator proto-type.Various characteristics of layer jamming,such as stiffness and yield strength,are studied both theoretically and experimentally.
Index Terms—Layer jamming,minimally invasive surgery (MIS),snake-like manipulator,tunable stiffness.
I.I NTRODUCTION
M INIMALLY invasive surgery(MIS)has become widely used due to its clear clinical benefits compared with open surgery.MIS patients tend to have shorter and better recoveries, and less trauma and postoperative pain.A challenge to MIS is that the dexterity of the surgeon is greatly reduc
ed due to the use of smaller openings and long instruments,therefore, motivating the development of highly dexterous andflexible medical tools[13].
Snake-like manipulators have been investigated by many re-searchers for MIS applications due to their unique character-istics and advantages:highflexibility,increased safety,high dexterity,obstacle-avoidance capability,potential for miniatur-ization,and so on[1]–[4],[14].Several prototypes for robotic surgery and endoscopy based on snake-like manipulators have been developed and commercialized[1]–[3].Recently,new at-tempts to perform laparoscopic surgery through a single port or a natural orifice reveal that increasedflexibility can hinder pay-load operation,despite the advantages over multiport surgery in terms of traumatic movement[4].However,externally actuated snake-like ,those with actuators located away from the manipulator structure and driven by cables or linkages) typically have an inherent disadvantage compared with angled
Manuscript received October31,2012;revised December20,2012;accepted December27,2012.Date of publication April15,2013;date of current version August2,2013.This paper was recommended for publication by Associate Editor S.R´e gnier and Editor B.J.Nelson upon evaluation of the reviewers’comments.This work was supported in part by the Samsung Advanced Institute of Technology of Samsung Electronics.
Y.-J.Kim is with the Samsung Advanced Institute of Technology,Yongin si 446-712,Republic of Korea(e-mail:yj424.kim@samsung).
S.Cheng is with the Direct Drive Systems,FMC Technologies,Fullerton, CA92833USA(e-mail:chengshanbao@gmail).
S.Kim and K.Iagnemma are with the Massachusetts Institute of Technology, Cambridge,MA02139USA(e-mail:sangbae@mit.edu;kdi@mit.edu). Color versions of one or more of thefigures in this paper are available online at
Digital Object Identifier10.1109/TRO.2013.2256313joint ,those with actuators integrated with the structure):a substantial lack of stiffness and strength.
In general,externally actuated snake-like manipulators have an underactuated structure with a compliant“backbone”[5], which often results in low stiffness at the end effector.In order to overcome this drawback,various stiffening mechanisms have been developed.One popular approach is to amplify the control wire tension and exploit the natural friction between rigid links, to modulate stiffness[2].In practice,however,the wire tension must be high,and thus,the links must be large enough to sustain large loads.As a result,the links can occupy substantial space, and thus,it is often
difficult to create a compact,lightweight manipulator based on this approach.
Recent research in the robotics community has focused on the use of tunable-stiffness materials,such magnetorheologi-cal(MR)or electrorheologicalfluids,to achieve variable me-chanical properties.These materials can change their apparent viscosity through modulation of an externalfield.MRfluids have been successfully applied in robotic applications such as gripping[6]and exoskeleton actuation[7].These technologies are most commonly used for precise control of damping and have been applied in tunable automotive suspensions.However, these materials have often limitation in achieving high stiffness or yield strength required in MIS when activated.
Phase-change materials can also be used as tunable stiffness elements in robotic devices.Previous work has involved using thermally activated materials,such as wax or solder,to create locking mechanisms in soft robotic applications,since such ma-terials can transition between liquid and solid states[8],[9]. These methods have been shown to demonstrate large change of stiffness and strength.However,most phase-change ,thermorheological or photorheological materials)have long activation timescales(on the order of seconds)that are not ideal for practical manipulation applications.
Particle jamming technology using granular media has re-cently been researched as another way to achieve tunable stiff-ness[10].If each robotic joint is composed of a volume of granular ,dry sand or coffee),it can effectively transition between afluid-like,compliant state,and a solid-like, stiff state if,for instance,a vacuum is applied on the volume such that the grains pack together to“jam”and develop a yield stress[11].Particle jamming has interesting features such as high deformability in thefluid state and drastic stiffness in-crease in the solid state,without significant change in volume. However,it requires a substantial volume of granular material to achieve significant stiffness.In addition,the bulk mechanical properties of jamming are not yet well understood,and(perhaps for this reason)jamming has not yet been demonstrated as part of a practical engineering system.
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Fig.1.Application of layer jamming mechanism:flexible main stem used for
MIS.
Fig.2.(a)Prototype snake-like manipulator,including three linear actuators.(b)Closeup view of tubular shape of device with a large,central hollow section for tool passage shown on the left side,and the layer jamming scales shown on the right side.
In this paper,we propose a novel mechanism to achieve tun-able stiffness termed “layer jamming,”which made use of fric-tion in between layers with the negative air pressure,along with the design of a tunable stiffness manipulator.This thin-walled tubular mechanism with tunable stiffness has several desirable properties for MIS applications,one of which is shown in Fig.1,where the variable stiffness tubular mechanism can be used as main stem for other snake-like manipulators in MIS.Fig.2shows the thin-walled,tubular shape of the layer jamming mech-anism.First,due to its hollow form,it can be used as a guide tube to deliver one or multiple MIS tools inside the human body.Second,during insertion of the manipulator into the body,it can assume a very flexible/low stiffness state to achieve a desired configuration and avoid accidental injury.Third,after insertion,it can be assumed that it is in a very rigid/high stiffness state to maintain a desired configuration while guiding insertion of MIS tools inside the body.A preliminary introduction of this device is published in [16],and more detailed and comprehensive study and analysis of its properties and its manufacturing process and application are presented herein as a journal article for the first time.
There are some researchers who have already made use of friction to realize the state transition between “flexible”and “rigid”of devices [17]–[19].Our design was invented
totally
Fig.3.
Concept of layer jamming element.
independently.Our design and implementation are totally dif-ferent from others.We designed and developed a thin-wall,tubular manipulator consisted of a spiral form of thin plastic layer shown in Fig.2.This spiral plastic layer [see Fig.1(b)]is wrapped by latex rubbers to apply vacuum pressure so that friction between layers can modulate the overall stiffness of the device.Due to its unique topology of the structure,it has the desired characteristics of 1)minimum volume,2)light weight,3)fast state transition,and 4)high payload.The combination of these characteristics is suitable for a guiding channel in MIS.Another key difference from [19]is that Bureau et al.[19]only described empirical results,whereas we are presenting a rigor-ous analytical model with experimental validation.
Section II briefly introduces one-degree-of-freedom (1-DOF)layer jamming joint including its concept,
analysis,modeling,manufacturing process,and experimental results.In Section III,the tubular snake-like manipulator is presented,and its design,actuator implementation,and experimental results and MIS application are described and discussed in detail.Section IV presents conclusions.
II.O NE -D EGREE -OF -F REEDOM L AYER J AMMING M ECHANISM A.Basic Concept of Layer Jamming
The basic concept of the layer jamming mechanism is illus-trated in Fig.3,where each overlapping plate represents a flap of flexible material (e.g.,paper or mylar),and p,w ,L ,and F denote,respectively,pressure onto the outer flap,the width and length of the flaps,and the maximum resisting tensile force.Defining the number of contact surfaces between flaps as n and the interflap frictional coefficient μ,F can be calculated as follows:
F =μnpwL.
(1)
The resisting force can,thus,be modified by changing the number,size,or frictional properties of the overlapping flaps.For instance,assuming that the pressure p and the size of the contacting surface of
flaps wL are fixed,the resisting force can be increased by increasing the number of contact surfaces n or frictional coefficient μ.In other words,if an appropriately thin,rough material is selected,a high resisting tensile force could potentially be achieved in a compact volume.This suggests that a simple,compact mechanism could provide a significant tunable stiffness capability.
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Fig.4.(a)Layer jamming joint design.(b)Flap patterns with
joint.
Fig.5.Section view of assembled layer jamming joint.
B.1-DOF Layer Jamming Joint
1)Design of 1-DOF Layer Jamming Joint:Based on the layer jamming concept,a 1-DOF joint can be designed.Fig.3shows a design of a 1-DOF rotational joint based on layer jam-ming.This is a simple pin joint,with both the upper link and lower link in Fig.4(a)having 15mm inner diameter and 24mm out
er diameter.A 20-mm diameter surface on both the upper and lower joint serves as a mounting surface to attach two iden-tical patterned flaps of flexible material.These two links form a 1-DOF revolute joint that is constrained by a central tension wire (see the dotted green line in Fig.5).
The upper flap pattern and lower flap pattern in Fig.4(b)both have 15mm length and 5mm width,and a “toothed”pattern to minimize creasing or buckling during individual flap deforma-tion.Matte surfaced Mylar film (polyethyleneterephthalate)is used for the flaps,with a thickness of 0.12mm and measured frictional coefficient is 0.6.The stiffness of the flap material is important because the layered flaps can be subjected to com-pressive and bending forces according to the direction of an external applied load and can potentially fail in buckling (in-stead of applying a resisting force).Increasing the flap
material
Fig.6.Parameters of a flap at arbitrary position.
stiffness thus increases the external load that can be tolerated before material failure.
2)Manufacturing of 1-DOF Layer Jamming Joint:Fig.5shows a sectional view of the assembled joint.The joint is assembled by hand.The flaps are cut via a laser cutting process.The upper and lowe
r links are made of ABS plastic by a 3-D printing process.As shown in Fig.4(b),there exist holes on two sides of the links where two fishing wires are passed through and tightened on both sides,therefore,pressing the upper links against the lower links to keep the two in contact.The flaps are glued together on each link and overlapped on top of each other with the pattern shown in Fig.3.An elastomeric membrane is wrapped around the inside and outside of the assembled joint.The membrane is a latex rubber tube with a thickness of 0.2mm.Flexible tubing is admitted into the membrane and connects to an external pump in order to supply a vacuum.O rings are used to fit the latex rubber onto the flexible tubing and the rigid links to achieve a vacuum seal.When vacuum pressure is applied,the air inside the membrane is drawn away,and the membrane applies a confining pressure to the outside flap surface.The pressure can be 101.3kPA (1atm)at maximum.
The process of making the customized latex rubber tube is as follows.The raw material that was employed was an abrasion-resistant natural latex film rubber with the desired thickness (0.2mm),which is commonly available.Liquid latex rubber was also employed in a diluted form (with an equal volume of water).Flat cardboard was used as a mold.The width of the cardboard was determined based on the required diameter of the tube.A mold release was applied to the cardboard to prevent the latex film from sticking to the cardboard.The latex film was then wrapped around the c
ardboard.Afterward,the latex film was brushed with the diluted liquid latex on the overlapping sections of the film,to form a closed tube.Weight was placed on top of the overlapping film region,and then,a heat gun was used to heat the glued,overlapping area.The tube was left to dry for 24h,and after that,the weight was removed,and the finished tube was rolled off of the cardboard.
3)Modeling of 1-DOF Layer Jamming Joint:The effect of a given flap at an arbitrary position on the rotational joint stiffness can be analyzed with the diagram shown in Fig.6(a).For a 1-DOF rotational joint,the motion of a “side flap”(with the flap
1034IEEE TRANSACTIONS ON ROBOTICS,VOL.29,NO.4,AUGUST 2013
face oriented normal to the axis of joint rotation)is rotational along the axis of the pivot,whereas motion of a “front flap”(with the flap face oriented parallel to the axis of joint rotation)is purely translational,as in Fig.3.Intermediate flaps have combined motion of rotation and translation.
Considering two arbitrary points P 1and P 2on a flap face that have nonzero separation distance w ,the amount of motion of the points caused by rotation θof the joint can be calculated as follows:
Δm 1=r sin φ1ΔθΔm 2=r sin φ2Δθ
(2)
where φ1and φ2denote the angles from the joint axis to each point,and r is the radius of the cylinder formed by the flaps.If w is sufficiently small,it can be expressed as
w ∼=r (φ2−φ1).
(3)
From (2)and (3),and by converting φ1and φ2to φ,which
is the angle from the joint axis to a point on the flap,the rota-tional motion component Δψand translational motion compo-nent Δm are obtained as follows:
Δψ∼=lim
φ1,φ2→φΔm 2−Δm 1
w
=cos φΔθ(4)Δm ∼=
lim
φ1,φ2→φ
Δm 2+Δm 1
2
=r sin φΔθ.
The relationship between the frictional force of the flaps and the resisting torque on the joint can be calculated by using the virtual work method.If a flap is sufficiently long,the motion Δv of an infinitesimal part of the flaps in Fig.6(b)is as follows:
|Δv |=
(l Δψ)2+Δm 2= (l cos φ)2+(r sin φ)2Δθ.
(5)
In order to satisfy energy conservation,the following equation should hold:
τΔθ=
L
2−L 2
|Δv |p μwdl =2 L 2
|Δv |p μwdl.(6)Substituting Δv into (6)with (5),the resisting torque τ(φ)
can be obtained as follows:
τ(φ)=2p μw
L 2
(l cos φ)2+(r sin φ)2dl (7)=p μw L 4 (L cos φ)2+(2r sin φ)2
+
(r sin φ)2|cos φ|×ln ⎛⎝L
2r |cot φ|+
L 2r
cot φ 2
+1⎞⎠⎞⎠.From this equation,the total resisting torque of a 1-DOF layer
jamming joint can be calculated as follows:
τ1DOF =n
n f l a p
τ(φ).(8)
where n flap denotes the number of flaps around the cylindrical
frame.Fig.7shows the change in resisting force of one flap
as
Fig.7.
Resisting torque comparison of three representative flaps
geometries.
Fig.8.Resisting torque variation according to the number of flaps around the
frame.
a function of the change of the angle φ,as computed from (7),where the radius of the cylinder r is 10mm.All of the flaps of Fig.7(a)–(c)have an identical size of 40mm,although with widely varying aspect ratios.Note that φ=0◦represents the location of a front flap,and φ=90◦represents the location of a side flap.
When the length of the flap is four times longer than the radius of the cylinder [see Fig.7(b)],the resisting force of the front flap is exactly the same as the side flaps,and the intermediate flaps contribute slightly more than either the front or side flap.As shown in Fig.7(c),the greatest contribution to resisting force is derived from a relatively long flap at the front position,which agrees with intuition.Also,the contribution of the side flaps does not change as a function of aspect ratio,which also agrees with intuition.It should be noted that,in practice,there is a geometric constraint on flap length caused by overlapping and interference of adjacent flaps during joint bending.In addition,another practical constraint derives from the fact that long flaps can be prone to buckling or creasing.
Fig.8represents the resisting torque according to the number of flaps n flap ,where the size of total contact surface remains ,n flap w =constant.Considering the scale of the y -axis of the graph,we can notice that the resisting torque is not changed significantly,and it converges to a constant value.The torque in the region of lower numbers of n flap has small fluctuation.It is caused by the placement of the flaps around the frame.Fig.8was obtained assuming that the first flap is
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Fig.9.Flaps and rubber skin
movement.
Fig.10.Schematic of elastomeric membrane tension.
aligned with the pivot direction.If the position of the first flap is changed,the shape of fluctuation will be changed.Ideally,we can choose an arbitrary number of n flap without losing resisting torque performance.However,if n flap is extremely high,the width of the flaps w becomes too small to resist buckling and creasing,and in the opposite situation,an unnecessarily large flap width decreases the flexibility of the mechanism.Here,we have chosen n flap between 8and 12.
4)Modeling of Membrane Tension:Besides the friction be-tween flaps in the layer jamming mechanism,the tension be-tween the elastomeric membrane (here,latex rubber)and the flaps plays a
n important role in determining joint stiffness.The elastomeric membrane tends to resist relative movement when the flaps slide on top of one another.In order to better understand the mechanism,membrane tension was modeled analytically and validated by 3-D finite-element analysis (FEA)simulation.Fig.9shows a diagram of two flaps covered by an elastomeric membrane moving in opposite directions,while subject to a confining pressure.Let us assume that the friction acts only between the flap and the membrane and that there is no friction between the flaps,and then,the tension T 0of the membrane at the contacting edge between the two flaps (see black dotted line of Fig.7)is the same as pulling force of each flap.
The elastomeric membrane can be represented as a number of lumped elements connected by springs,as illustrated in Fig.10.Here,ΔF is the confining force on the membrane and flap caused by the pressure p ,and μΔF is the corresponding friction force between the membrane and flap.Thus
F =pw Δx
(9)T (x )=T (x )+ΔT +μF.
(10)
From (9)and (10),we can obtain
ΔT =−μF =−p μw Δx
(11)where ΔT is the difference in tension across a small section of membrane Δx ,and the boundary condition for this equation is T |x =0=T 0.Therefore,the tension along the entire membrane can be obtained by integrating over the length x :
T (x )=
x
ΔT = x 0
p μwdx,T (0)=T o .(12)Since the membrane cannot take compressive force,T (x )
always has a positive value.Thus,the tension distribution along the membrane is
T (x )=
⎧
⎪⎪⎨⎪⎪⎩T o
−p μwx,x <T o p μw
0,x ≥
T o p μw .(13)What we are interested in is the relationship between the displacement of the two flaps and the tensile force of the flaps T 0.If we assume that L t is the displacement of the two flaps,which is the same as total elongated length of the membrane,and based on Young’s modulus definition,we can obtain
EA
Δx
Δl t =T (14)
L t =2
T o p μw
dl t =2
T o p μw
T EA
dx (15)
where Δl t is infinitesimal elongation of the membrane in the region of Δx ,and A is the cross-sectional area of the membrane.The elongation of a membrane occurs at the both sides of the contacting edge,and thus,L t in (15)has a doubled value of the integral.Using (13)and (15)
L t =2 T o
p μw 0T EA dx =2 T o p μw 0
T o
−puwx EA dx
=2EA T o x −puw 2x 2 T o p μw
=2
EA T o
T o p μw −puw 2 T o p μw
modulate2
=T 2
o
EAp μw
.As a result,the membrane tension as a function of L t is obtained as follows:
T o =
EAp μwL t .(16)We can also calculate the length of the region of nonzero
tension by using (13)and (16):
x max =
T o
p μw =
EAL t p μw .(17)In order to better understand the tension distribution and
effect of membrane physical parameters on the layer jam-ming mechanism performance,the membrane tension was mod-eled analytically.This model was then validated by 3-D FEA simulation.
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