Compliance effects in a parallel jaw gripper.pdf

Compliance eff ects in a parallel jaw gripper A J G Nuttall A J Klein Breteler Faculty of Design Construction and Production Department of Transportation Technology University of Technology Delft Mekelweg 2 2628 CD Delft The Netherlands Received 17 April 2002 received in revised form 24 April 2003 accepted 30 June 2003 Abstract This paper discusses mechanical compliance eff ects in a gripper with parallel jaws In it a case study of a dedicated gripper design is presented to analyse two diff erent design elements infl uencing the compliant behaviour the fl exibility introduced by preloaded springs and the resistance caused by friction The gripper manipulates semi automatic twistlocks used for securing seagoing cargo containers The compliance eff ects are eff ective to reduce misalignment and overload of the gripper 2003 Elsevier Ltd All rights reserved Keywords Mechanical compliance Twistlock manipulator Preloaded springs Friction force 1 Introduction Robots grasp and manipulate objects with the aid of a gripper Usually the object is presented at a predefi ned pickup location where the robot can grasp and move it to another predefi ned location Diffi culties arise when the pickup location and destination are part of a heavy rigid body that can move due to external disturbances If the robot cannot adapt to this movement during pickup or release the full force of the movement will be transferred into the robot s components which can result in damage Therefore the robot should be fl exible or compliant where the environment is stiff 3 Compliance can be introduced to the robot by using a compliant end eff ector or gripper This can be done in diff erent ways In literature a variety of subjects on gripper compliance can be found 1 3 4 these are mainly focussed on control theories for universal grippers and fi ne Corresponding author Tel 31 15 278 3130 fax 31 15 278 1397 E mail address a j kleinbreteler wbmt tudelft nl A J Klein Breteler 0094 114X see front matter 2003 Elsevier Ltd All rights reserved doi 10 1016 S0094 114X 03 00100 9 Mechanism and Machine Theory 38 2003 1509 1522 manipulation In 5 6 such a compliance is investigated using stiff ness models and in 7 a remote compliance 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 control possible With this form of electronic control the universal gripper can manage many diff erent tasks and objects This is in contrast to the special purpose end eff ector that is to be designed for a specifi c task and object By making use of simple sensors and actuators combined with a mechanical form of compliance an eff ective reliable and robust gripper can result which will also be able to adapt all be it in a limited manner to a moving pickup point The adaptation of this form of compliance for gripper confi gurations has proven hard to fi nd in literature This paper gives an insight into the eff ects of mechanical compliance in a gripper A case study of a gripper design will aid as example to discuss two diff erent modes of mechanical compliance This example case consists of a parallel jaw gripper confi guration intended for the manipulation of semi automatic twistlocks 2 Background to the twistlock manipulator A manipulator was required to automatically connect and remove semi automatic twistlocks to and from a container s bottom corner castings In Fig 1 a semi automatic twistlock is shown on the left This type of twistlock is a lashing device that is used to secure sea going cargo containers to the deck of a ship It consists of a body an upper and lower rotating cone and a handle for manual operation of the cone positions The upper cone can be inserted into the bottom corner casting depicted on the right side of Fig 1 by unlocking it through rotating the lower cone The top collar fi xes into the hole of the corner casting because it matches the shape of the hole When the cones are rotated back to their original position the twistlock is secured to the bottom corner casting The handle is intended for manual operation If it is pulled the shaft rotates that connects the cones together Fig 1 A semi automatic twistlock and a corner casting of a container 1510A J G Nuttall A J Klein Breteler Mechanism and Machine Theory 38 2003 1509 1522 For automation of this securing procedure and the reverse operation a gripper had to be de signed that can hold diff erent types of twistlocks by their collars with suffi cient grasping force 10 The jaws also have to open far enough to prevent collisions with the cones while the manipulator is 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 pneumatic tyres The wind is an example of a disturbance that can generate fl uctuating forces on the side of the container which can result in an oscillating movement Due to the possible movement of the large container mass 30 ton and the robust construction of the twistlock the gripper will have to be compliant to prevent damage to itself or other components of the robot Mechanical com pliance will also help tackle the problem of the moving pickup point on the container and keep the required control system simple The collar was chosen as contact surface for the gripper because it is the common element in diff erent twistlock designs It has to fi t into the standardised hole of the corner casting so the shape and size will be roughly the same Although the width of the hole is only allowed a tolerance of 1 5 mm the collar widths found in practice can vary between 57 and 62 mm This 5 mm range in collar sizes had to be taken into account for a reliable operation of the gripper In Fig 2a the forces applied by the jaws during a grasp are presented The frictional forces generated on the collar sides will have to be suffi ciently large to compensate the static and dy namic 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 dynamic forces caused by movement of the manipulator and the static gravitational force With a fric tional coeffi cient l of 0 125 the grasping force exerted by each jaw Fjaw can be calculated as follows Ftot 2 lFjaw Fjaw Ftot 2l 800 N This is the minimal force that has to be guaranteed during the manipulation of a twistlock for all collar sizes Fig 2b shows the open and closed position of the jaws It shows how far the jaws have to open during the positioning of the open gripper There has to be enough clearance between the cone Fig 2 Grasping forces on twistlock and the required jaw travel A J G Nuttall A J Klein Breteler Mechanism and Machine Theory 38 2003 1509 15221511 and jaw to prevent a collision because the cone diameter is larger then the collar width To get a clearance of 15 mm the displacement of a jaw has to be 40 mm 3 Finding a suitable gripper confi guration An 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 acting pneumatic cylinder Attached to the cylinder s piston rod is a dual rack gear which drives two partial sectors of pinion gears Two pairs of the symmetrical arranged parallel closing linkages are mounted 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 contact with the object before they are fully closed Therefore the piston will not travel to its end position during this closing operation This makes it possible to grasp diff erent sized objects It will however be more diffi cult to sense the closed position of the jaws A special sensing method like force detection will be required to measure the closed position The gripper confi guration 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 horizontal direction Preloading the springs gives two advantages First of all the stroke required to build up suffi cient 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 the minimal required grasping force can be guaranteed with the aid of a proximity sensor that can detect the end position of the pneumatic cylinder If the cylinder reaches the end of the closing stroke with an object between the jaws the springs will have been pressed in and the grasping force would at least have to be equal to the set preload Fig 3 Parallel gripper confi gurations with compliance 1512A J G Nuttall A J Klein Breteler Mechanism and Machine Theory 38 2003 1509 1522 This gripper design with springs in the jaws was not used for the twistlock manipulator because the springs take up too much space Special measures would have to be taken to keep the jaw construction suffi ciently compact An alternative confi guration with spring elements can be seen in Fig 3c The preloaded springs are not directly connected to the jaws but they have been placed between the actuator and the lever of the jaw parallelograms The mechanism amplifi es the force of the cylinder when the jaws are closing if the springs would have been ordinary bars The generated grasping force is largest when the jaws are nearly closed The more they are opened the smaller the possible force but the larger their displacement versus the cylinder displacement In this confi guration another eff ect is introduced with respect to compliant behaviour If a horizontal force is applied a resistance is generated by friction in the contact surfaces The horizontal force has to be large enough to overcome this resistance and to move the jaws with the object in between The cause of this eff ect is illustrated in Fig 3d When the grasped object moves to the right the left jaw swings up and the right jaw swings to a lower position while they both remain parallel to each other This causes the jaws to slide over the surface and generate frictional forces if the grasped object does not change orientation In the example case the object or twistlock will not change orientation because it is fi xed to the container during the grasping manoeuvre It can only move with the container in the horizontal direction The design in Fig 3c will be considered further for the twistlock manipulator and will be analysed using the theory given below 4 Modeling the gripper FEM approach When the frictional compliancy is in eff ect the jaws will slip relatively to the twistlock surface The friction forces under slip will be considered proportional to the contact force This is a reasonable 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 gripper mechanism are considered as internal forces Their virtual work must be equal to the virtual work of the compliant force which is considered as the driving force To perform the actual calculations a general computer program for kinematic and dynamic analysis can be used in which this theory has been embedded The portion of the theory used to perform the analysis calculations is described below briefl y The theory is also known as fi nite element approach 8 9 From FEM the two maps displacements on deformations and applied forces on internal forces are 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 same matrix as used for kinematic motion analysis A J G Nuttall A J Klein Breteler Mechanism and Machine Theory 38 2003 1509 15221513 A model of the gripper mechanism can be built with truss elements each having constant length In the FEM concept a constant length is considered to have deformation zero For kinematics it concerns just a mathematical variation of the length for force analysis a normal force exists as an internal force The length itself is a continuous function of global co ordinates position vector x of the el ement For a truss element defi ned by the end points P and Q and numbered k the continuity equation can be written as xk jxPyPxQyQjT k xk ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffiffi yQ yP 2 xQ xP 2 q 1 Moving with deformation zero can be expressed in kinematics with a continuity equation of the fi rst order like here for constant length o k oxk T oxk o k 1 2 Written out with the help of 1 cosbk sinbk cosbk sinbk oxk o k 1 3 where b is the angle of the element that can be obtained from the given xkvector Comparable continuity equations can be constructed to prescribe a fi xed angle of the truss element or a fi xed angle w between two truss elements Those partial derivatives concerning fi xed nodes are known zero those concerning moving nodes are the unknowns in a linear system of fi rst order continuity equations In a correct mechanism model there are as many equations prescribed deformations vector ep as unknown partial derivatives the total amount of co ordinates of moving nodes vector xc Following the FEM approach the mechanism input is also to be modelled as a prescribed deformation In the gripper mechanism this concerns the elongation of the pneumatic cylinder To calculate all unknown partial derivatives co ordinates with respect to deformations the matrix called Dc the known coeffi cients of the fi rst order continuity equations can be inverted oxc oep Dc 1 4 and this determines implicitly the kinematic transfer function of fi rst order as one column or more columns in case of a multiple DOF mechanism of the inverse of matrix Dc Applied forces vector f c can be exerted at the co ordinates Their amount of virtual work will be consumed by the internal forces vector rp which should be regarded as multipliers for the prescribed deformations This equilibrium condition yields rp DcT 1 f c 5 known in the FEM for stress analysis of statically determined structures Eqs 4 and 5 show clearly the dual use of the maps the matrix Dccan be used both for position analysis and for force 1514A J G Nuttall A J Klein Breteler Mechanism and Machine Theory 38 2003 1509 1522 analysis The deformation modelled for input has a corresponding r which is then the driving force As with a pneumatic cylinder this force should be interpreted either as tensile or com pressive force Position analysis of the mechanism needs a numerical procedure with prediction and correction of the co ordinate values Starting at a given position all co ordinate values given the input can be incremented given a fi nite deformation which can iteratively be reduced to zero to fi nd the neighbouring position The Newton Rapson method is suited because the required partial de rivatives are available A spring element in the form of a coil spring can be modelled using the continuity equation for the length of a truss element Now the internal normal force rkis to be given as a function of the length which means a spring characteristic must be known Length of this spring element should not be prescribed but can be calculated in the known mechanism position This spring force can be converted to applied forces at the connection points using 3 f k o k oxk rk 6 The theory given above is available in a computer program 11 which has been used for the investigations 5 Force amplifi cation on the driving cylinder The driving concept assumes a fi xed stroke of the pneumatic cylinder If the end position can be detected with a simple on off switch the required contact forces between jaws and twistlock can be guaranteed by preloaded springs The jaws need a relatively wide opening see Fig 2b and a high force at the end of the stroke to hold the twistlock This combination tends to both a large cylinder diameter and a large stroke Force amplifi cation such that the high forces apply only when needed can reduce the cylinder diameter This is advantageous for space occupation of the moving end eff ector Not just the diameter but also the overall length decreases because the piston length bearing and end cap are shorter A second advantage is the decreased volume of the air supply To investigate the force amplifi cation mainly intended to help to choose the driving cylinder a numerical experiment has been performed Having in mind the mechanism of Fig 3c and springs at the jaws like in Fig 3b the whole subsystem of the two springs and the twistlock can be replaced by one spring see Fig 4 With d as the width of the twistlock the spring characteristic could 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 performed using the mechanism model in Fig 4 Some trials have been made before the fi nal dimensions of the gripper mechanism were chosen The spring force at the jaws and the driving force of the A J G Nuttall A J Klein Breteler Mechanism and Machine Theory 38 2003 1509 15221515 cylinder have been depicted in Fig 5 for the largest and the smallest width of the twistlock The graphs have been marked with DRIVE 57 driving force for collar width d 57 mm and GRASP 57 contact for