Compliance effects in a parallel jaw gripper.pdf

Robots grasp and manipulate objects with the aid of a gripper. Usually the object is presentedCompliance can be introduced to the robot by using a compliant end-eector or gripper. Thiscan be done in dierent ways. In literature a variety of subjects on gripper compliance canbe found 1,3,4, these are mainly focussed on control theories for universal grippers and neMechanism and Machine Theory 38 (2003) 15091522*Corresponding author. Tel.: +31-15-278-3130; fax: +31-15-278-1397.at a predened pickup location where the robot can grasp and move it to another predenedlocation.Diculties arise when the pickup location and destination are part of a heavy rigid body thatcan move due to external disturbances. If the robot cannot adapt to this movement during pickupor release, the full force of the movement will be transferred into the robotC213s components, whichcan result in damage. Therefore the robot should be exible or compliant where the environmentis sti 3.Compliance eects in a parallel jaw gripperA.J.G. Nuttall, A.J. Klein Breteler*Faculty of Design, Construction and Production, Department of Transportation Technology, University of TechnologyDelft, Mekelweg 2, 2628CD Delft, The NetherlandsReceived 17April 2002; received in revised form 24 April 2003; accepted 30 June 2003AbstractThis paper discusses mechanical compliance eects in a gripper with parallel jaws. In it a case study of adedicated gripper design is presented to analyse two dierent design elements inuencing the compliantbehaviour: the exibility introduced by preloaded springs and the resistance caused by friction.The gripper manipulates semi-automatic twistlocks used for securing seagoing cargo containers. Thecompliance eects are eective to reduce misalignment and overload of the gripper.C211 2003 Elsevier Ltd. All rights reserved.Keywords: Mechanical compliance; Twistlock manipulator; Preloaded springs; Friction force1.I/locate/mechmtE-mail address: a.j.kleinbretelerwbmt.tudelft.nl (A.J. Klein Breteler).0094-114X/$ - see front matter C211 2003 Elsevier Ltd. All rights reserved.doi:10.1016/S0094-114X(03)00100-9manipulation. In 5,6 such a compliance is investigated using stiness models and in 7 a remotecompliance centre is introduced. These investigations integrate compliance into the control sys-tem, with the aid of special sensors and actuators making reliable force and position controlpossible. With this form of electronic control the universal gripper can manage many dierenttasks and objects.This is in contrast to the special-purpose end-eector that is to be designed for a specic taskand object. By making use of simple sensors and actuators combined with a mechanical form ofcompliancean eective, reliable androbustgripper canresult, whichwill also beable toadapt (allbeitinalimitedmanner)toamovingpickuppoint.Theadaptationofthisformofcomplianceforgripper congurations has proven hard to nd in literature.This paper gives an insight into the eects of mechanical compliance in a gripper. A case studyof a gripper design will aid as example to discuss two dierent modes of mechanical compliance.This example case consists of a parallel jaw gripper conguration intended for the manipulationof semi-automatic twistlocks.operation. If it is pulled the shaft rotates that connects the cones together.1510 A.J.G. Nuttall, A.J. Klein Breteler / Mechanism and Machine Theory 38(2003) 150915222.Backgroundtothe twistlockmanipulatorAmanipulatorwasrequiredto automaticallyconnectandremove semi-automatictwistlocks toand from a containerC213s bottom corner castings. In Fig. 1 a semi-automatic twistlock is shown onthe left. This type of twistlock is a lashing device that is used to secure sea-going cargo containersto the deck of a ship. It consists of a body, an upper and lower rotating cone and a handle formanual operation of the cone positions.Theupper cone can be insertedinto the bottomcorner casting depicted on the right sideof Fig.1 by unlocking it through rotating the lower cone. The top collar xes into the hole of the cornercasting,becauseitmatchestheshapeofthehole.Whentheconesarerotatedbacktotheiroriginalposition, the twistlock is secured to the bottom corner casting. The handle is intended for manualFig. 1. A semi-automatic twistlock and a corner casting of a container.For automation of this securing procedure and the reverse operation a gripper had to be de-signedthatcanholddierenttypesoftwistlocksbytheircollarswithsucientgraspingforce10.The jaws also have to open far enough, to prevent collisions with the cones while the manipulatoris positioning over the twistlock with open jaws.The container can move during the pickup or release operation due to external disturbances,because it will be hoisted up in the air by cables or resting on a rolling chassis with pneumatictyres. The wind is an example of a disturbance that can generate uctuating forces on the side ofthe container, which can result in an oscillating movement. Due to the possible movement of thelarge container mass (30 ton) and the robust construction of the twistlock the gripper will have tobe compliant to prevent damage to itself or other components of the robot. Mechanical com-pliancewillalsohelptackletheproblemofthemovingpickuppointonthecontainerandkeeptherequired control system simple.collar sizes had to be taken into account for a reliable operation of the gripper.IngeneratedA.J.G. Nuttall, A.J. Klein Breteler / Mechanism and Machine Theory 38(2003) 15091522 1511namic forces created on the twistlock. The total force (Ftot) that has to be compensated in a di-rection parallel to the collar surface is 200 N. This was calculated by determining the dynamicforces caused by movement of the manipulator and the static gravitational force. With a fric-tional coecient (l) of 0.125 the grasping force exerted by each jaw (Fjaw) can be calculated asfollows:Ftot 2C1 lFjaw) FjawFtot2l 800 NThis is the minimal force that has to be guaranteed during the manipulation of a twistlock, for allcollar sizes.Fig. 2b shows the open and closed positionof the jaws. It showshow far the jaws have to open,during the positioning of the open gripper. There has to be enough clearance between the coneFig. 2a the forces applied by the jaws during a grasp are presented. The frictional forceson the collar sides will have to be suciently large to compensate the static and dy-The collar was chosen as contact surface for the gripper, because it is the common element indierent twistlock designs. It has to t into the standardised hole of the corner casting, so theshapeandsizewillberoughlythesame.Althoughthewidthoftheholeisonlyallowedatoleranceof1.5mmthecollarwidthsfoundinpracticecanvarybetween57and62mm.This5mmrangeinFig. 2. Grasping forces on twistlock and the required jaw travel.and jaw to prevent a collision, because the cone diameter is larger then the collar width. To get aclearance of 15 mm the displacement of a jaw has to be 40 mm.3.Findingasuitablegripper congurationAn existing gripper that is capable of producing a rather large clamping force and large dis-placement is illustrated in Fig. 3a 2. It consists of two parallel jaws, actuated by a double actingpneumatic cylinder. Attached to the cylinderC213s piston rod is a dual rack gear, which drives twopartialsectorsofpinion gears.Two pairsofthe symmetrical arrangedparallelclosing linkagesaremounted directly on the partial sectors of the pinions and provide the clamping force.This design only features compliant behaviour with respect to the width of the grasped object.If the grasped object is larger then the distance between the closed jaws, they will come in contactwith the object before they are fully closed. Therefore the piston will not travel to its end positionduring this closing operation. This makes it possible to grasp dierent sized objects. It willhowever be more dicult to sense the closed position of the jaws. A special sensing method likeforce detection will be required to measure the closed position.1512 A.J.G. Nuttall, A.J. Klein Breteler / Mechanism and Machine Theory 38(2003) 15091522The gripper conguration of Fig. 3a can be given additional compliance as shown in Fig. 3b.Preloaded springs have been added to the jaws, to get compliant behaviour in the horizontaldirection. Preloading the springs gives two advantages. First of all the stroke required to build upsucient grasping force can be short. If the preload is set to the minimal required grasping force,after contact with the object the springs hardly need any travel for a secure grip. Secondly theminimal required grasping force can be guaranteed with the aid of a proximity sensor that candetect the end position of the pneumatic cylinder. If the cylinder reaches the end of the closingstroke with an object between the jaws, the springs will have been pressed in and the graspingforce would at least have to be equal to the set preload.Fig. 3. Parallel gripper congurations with compliance.analysed using the theory given below.A.J.G. Nuttall, A.J. Klein Breteler / Mechanism and Machine Theory 38(2003) 15091522 15134.Modelingthe gripper,FEMapproachWhen the frictional compliancy is in eect, the jaws will slip relatively to the twistlock surface.The friction forces under slip will be considered proportional to the contact force. This is areasonable assumption for the conceptual design phase of the gripper.The theory needed concerns just the equilibrium of static forces, as for instance can be de-scribed with the principle of virtual work. The spring forces and the friction in the grippermechanism are considered as internal forces. Their virtual work must be equal to the virtual workof the compliant force, which is considered as the driving force.To perform the actual calculations, a general computer program for kinematic and dynamicanalysis can be used in which this theory has been embedded. The portion of the theory used toperform the analysis calculations, is described below briey. The theory is also known as niteelement approach 8,9.From FEM the two maps displacements on deformations, and applied forces on internal forcesare known as dual maps, indicating that both relations can be described with the same matrix.Here it means that the contact forces of the jaws (internal forces) will be calculated with the sameThisgripperdesignwithspringsinthejawswasnotusedforthetwistlockmanipulator,becausethe springs take up too much space. Special measures would have to be taken to keep the jawconstruction suciently compact.An alternative conguration with spring elements can be seen in Fig. 3c. The preloaded springsare not directly connected to the jaws, but they have been placed between the actuator and thelever of the jaw parallelograms. The mechanism amplies the force of the cylinder, when the jawsare closing, if the springs would have been ordinary bars. The generated grasping force is largestwhen the jaws are nearly closed. The more they are opened the smaller the possible force, but thelarger their displacement versus the cylinder displacement.In this conguration another eect is introduced with respect to compliant behaviour. If ahorizontal force is applied, a resistance is generated by friction in the contact surfaces. Thehorizontal force has to be large enough to overcome this resistance and to move the jaws with theobject in between.The cause of this eect is illustrated in Fig. 3d. When the grasped object moves to the right theleft jaw swings up and the right jaw swings to a lower position while they both remain parallel toeach other. This causes the jaws to slide over the surface and generate frictional forces if thegrasped object does not change orientation. In the example case the object or twistlock will notchange orientation,because it is xed to the containerduring the grasping manoeuvre.It canonlymove with the container in the horizontal direction.The design in Fig. 3c will be considered further for the twistlock manipulator and will bematrix as used for kinematic motion analysis.In the FEM-concept a constant length is considered to have deformation zero. For kinematicsit concernselementThosenodespartial derivatives (the total amount of co-ordinates of moving nodes, vector x ). Following theFEM-approacgripperandc1514 A.J.G. Nuttall, A.J. Klein Breteler / Mechanism and Machine Theory 38(2003) 15091522more columnsin case of a multiple DOF mechanism) of the inverse of matrix D .Applied forces (vector fc) can be exerted at the co-ordinates. Their amount of virtual work willbe consumed by the internal forces (vector rp), which should be regarded as multipliers for theprescribed deformations. This equilibrium condition yieldsrpDcTC138C01C1 fc5known in the FEM for stress analysis of statically determined structures. Eqs. (4) and (5) showcclearlyoxoepDcC138C014this determines implicitly the kinematic transfer function of rst order as one column (orTo calculate all unknown partial derivatives, co-ordinates with respect to deformations, thematrix called Dc(the known coecients of the rst order continuity equations) can be invertedcC20C21h the mechanism input is also to be modelled as a prescribed deformation. In themechanism this concerns the elongation of the pneumatic cylinder.mechanism model there are as many equations (prescribed deformations, vector ep) as unknowncor a xed angle w between two truss elements.partial derivatives concerning xed nodes are known (zero); those concerning movingare the unknowns in a linear system of rst order continuity equations. In a correctMoving with deformation zero can be expressed in kinematics with a continuity equation of therst order, like here for constant lengthokoxkC12C12C12C12C12C12C12C12TC1oxkokC12C12C12C12C12C12C12C12 1 2Written out with the help of (1)C0cosbkC0sinbkcosbksinbkC12C12C12C12C1oxkokC12C12C12C12C12C12C12C12 1 3where b is the angle of the element that can be obtained from the given xkvector.Comparable continuity equations can be constructed to prescribe a xed angle of the trusskxkyQC0 yP2xQC0 xP2q1an internal force.The length itself is a continuous function of global co-ordinates (position vector x) of the el-ement. For a truss element, dened by the end-points P and Q and numbered k, the continuityequation can be written asxkjxPyPxQyQjTjust a mathematical variation of the length, for force analysis a normal force exists asAmodelofthegrippermechanismcanbebuiltwithtrusselementseachhavingconstantlength.thedualuseofthemaps:thematrix D canbeusedbothforpositionanalysisandforforcedetected with a simple on/o switch the required contact forces between jaws and twistlock can beguaranteed by (preloaded) springs.Forcediameter.diameter,A.J.G. Nuttall, A.J. Klein Breteler / Mechanism and Machine Theory 38(2003) 15091522 1515shorter. A second advantage is the decreased volume of the air supply.To investigate the force amplication, mainly intended to help to choose the driving cylinder, anumerical experiment has been performed. Having in mind the mechanism of Fig. 3c and springsat the jaws (like in Fig. 3b), the whole subsystem of the two springs and the twistlock can bereplaced by one spring (see Fig. 4). With d as the width of the twistlock the spring characteristiccould be chosen as follows: Length greater than d 22 mm (11 mm clearance at both sides): the applied forces are zero. From d 22 to d 20 mm the applied forces build up to 400 N (the preload). From d 20 to d mm the applied forces increase linearly to 800 N.The closing motion including force analysis according the FEM-theory has been performedusing the mechanism model in Fig. 4. Some trials have been made before the nal dimensions ofthe gripperamplication, such that the high forces apply only when needed, can reduce the cylinderThis is advantageous for space occupation of the moving end-eector. Not just thebut also the overall length decreases because the piston length, bearing and end cap areThejawsneedarelativelywideopening(seeFig.2b)andahighforceattheendofthestroketohold the twistlock. This combination tends to both a large cylinder diameter and a large stroke.analysis. The deformation modelled for input has a corresponding r, which is then the drivingforce. As with a pneumatic cylinder, this force should be interpreted either as tensile or com-pressive force.Positionanalysisof the mechanismneeds a numericalprocedurewithpredictionand correctionof the co-ordinate values. Starting at a given position (all co-ordinate values given), the input canbe incremented (given a nite deformation), which can iteratively be reduced to zero to nd theneighbouring position. The Newton/Rapson method is suited because the required partial de-rivatives are available.Aspringelement,intheformofacoilspring,canbemodelledusingthecontinuityequationforthe length of a truss element. Now the internal normal force rkis to be given as a function of thelength, which means a spring characteristic must be known. Length of this spring element shouldnot be prescribed, but can be calculated in the known mechanism position. This spring force canbe converted to applied forces at the connection points, using (3)fkokoxkC20C21C1 rk6The theory given above is available in a computer program 11, which has been used for theinvestigations.5.Forceamplicationon thedriving cylinderThedrivingconceptassumesaxedstrokeofthepneumaticcylinder.Iftheendpositioncanbemechanism were chosen. The spring force at the jaws and the driving force of the1516 A.J.G. Nuttall, A.J. Klein Breteler / Mechanism and Machine Theory 38(2003) 15091522Fig. 4. Mechanism model for motion and force analysis.cylinder have been depicted in Fig. 5 for the largest and the smallest width of the twistlock. Thegraphs have been marked with DRIVE_57(driving force for collar width d 57mm) andGRASP_57(contact force for collar width d 57mm) etc. Apparently a d