Patent Application: US-201615200110-A

Abstract:
two - phase gripper . the gripper reorients and grasps an object while being picked up , the gripper includes a parallel jaw gripper including a pair of opposed , two - phase fingers , each finger including a cavity covered by an elastic strip wherein the elastic strip includes a point contact . closure of the jaws of the gripper on as object at a first relatively lower force results in contact with lower friction between the point contact on the elastic strip on the fingers and the object allowing the object to rotate under gravity as the gripper is raised . thereafter , closure of the jaws of the gripper on the object at a second relatively higher force causes the elastic strip to receded into the cavity resulting in multi - point contact with higher friction between the fingers and the object to securely grasp the object . in a preferred embodiment , the cavity is a y - shaped groove and the object is cylindrical or prismatic .

Description:
we present a novel design of two - phase fingers which eliminate the need for part feeders by grasping and passively reorienting a set of parts . two - phase refers to a discrete change in the contact geometry between fingers and part as the gripping force increases , where the gripper function - switches from passive reorientation of the part to a secure grasp . in particular , this patent application focuses on grasping and reorienting cylindrical or prismatic parts , very frequent geometries in industrial assembly settings [ 2 ]. we demonstrate how the two - phase gripper reorients cylindrical parts to an upright pose and grasps them securely in an uninterrupted and continuous motion . fig1 illustrates the two - phase finger in action . the design is composed of a small contact point 3 on an elastic strip 2 mounted over a v - groove cavity 1 . when an object is grasped with low gripping force , it pivots about the contact points on the strips until it aligns with gravity . as the gripping force increases , the elastic strips recede into the cavities , and the object sits into the v - grooves securing the grasp . we demonstrate the design by instrumenting two commercially available grippers ( 2 - finger 85 from robotiq , and wsg32 from weiss robotics ) and testing them with three different object types . the experiments validate the effectiveness of the design in reorienting and securing the parts . fig1 shows that the design of the two - phase finger can be retrofitted to any common parallel - jaw gripper . in this application we focus on a particular case commonly encountered in assembly operations — reorienting cylindrical parts from a horizontal pose on a table or a conveyor belt to an upright pose required for assembly . we focus on cylindrical parts which are one of the most common geometries within industrial assembly , with the goal of providing a reliable and fest method for picking , reorienting and securing . 1 ) passive reorientation of a cylindrical object from a horizontal pose to an upright pose . the motion of a grasped object is governed by the kinematic and motional properties of all contacts it makes . to let an object pivot under gravitational three , contacts must offer minimal motional torque , characteristic of contacts with small area . on the other hand , to localize and to hold the object securely after it pivots , specific kinematic constraints and significant frictional resistance needs to be provided . the proposed design aims to fit both needs . we rely on a built - in mechanism in the fingertips to change the finger - object contact geometry from point contact with low - friction to multi - point contact with high friction . the change on the contact geometry is triggered by the magnitude of the gripping force . the functionality is depicted in fig2 . in the figure , an object 10 is first gripped with point contact to allow pivoting . thereafter , as the jaws close on the object 10 the elastic strip 2 deforms and the cylindrical object 10 is securely grasped by the gripper . the cavity 1 is meant to provide kinematic constraints that force the object to align to an upright pose , and later maintain that pose even when the robot or hand is freely moved . this application focuses on cylindrical objects , and consequently a canonical v - groove gives an appropriate geometry for the cavity . given the radius r of the cylinder to pick , we chose the values for the depth of the cavity h and its angle 2θ so that the fingers will not touch each other when holding the object . otherwise the object would be able to move even with the gripper fully closed . we impose then : as illustrated in fig3 , the expectation is that the kinematic constraints offered by the v - grooves will push the cylindrical object to the center of the cavity and make it vertical from anywhere within the groove . after the alignment , and when combined with friction from contacts within the v - groove , we get a force - closure grasp on the object [ 26 ]. the role of the elastic strip 2 is to facilitate the transition from a point contact to patch contact as the gripping force increases . at low gripping force , we would like the elastic strip 2 to provide high stiffness to maintain a point contact between fingers and object , and low stiffness as fee gripping force increases above certain threshold so that the snip recedes into the cavity and allows surface contact between the finger and the object however , practically achieving such “ softening spring ” behavior can be involved . for the purpose of prototyping , we used a rubber band with a preload as the elastic strip . the required stillness value for the elastic strip is bounded by two constraints based on the desired application . let δ pivot be a maximum allowable deflection in the strip for the gripping force suitable for pivoting the object f pivot . this gives a low bound on the stiffness of the strip ( k ). similarly , let δ grasp be the minimum deflection needed in the strip when the object is held in the v - groove cavities giving an upper bound on the stiffness of the strip . where δ grasp = 2h ( 1 − sinθ )/ cosθ is the minimum extension needed in the strip so that it can recede and sit in the cavity and f grasp is the high gripping force applied for grasping the object . f grasp is limited by the maximum grasping force the gripper can apply . we will proceed under the assumption that as long as the stiffness of the strip satisfies ( 2 ) and ( 3 ), the variation in the stiffness does not affect the functionality of the gripper , and that the stiffness of the strip remains constant throughout the operation . the role of the point contact 3 on the elastic strip 2 is to act as a hinge to support and allow minimal frictional resistance to the rotation of the object in the fingers under gravity . though ideally we want point contacts between the object and the lingers for pivoting , in reality they are patch contacts with small area . we now explain a typical operation for the two - phase gripper . the complete manipulation task can be broken down into the following steps : 1 ) the two - phase gripper reaches over a cylindrical object lying on a flat surface with its longitudinal axis horizontal . 2 ) the fingers hold the object offset from the center of mass with a low gripping force , just sufficient to prevent the object from slipping . 3 ) the object is raised , while it pivots about the axis between the finger contacts , until it is completely lifted from the surface and aligned upright in the gripper . 4 ) the grip on the object is tightened , which passively shifts the cylinder to the center of the cavity and secures the grasp . we analyze now the mechanics of the pivoting manipulation and the criterion to select an appropriate value for the gripping force . fig4 shows the schematic of a cylinder 10 being grasped and lifted . the gripping force plays a key role in determining the success of the pivoting operation . it must suffice to prevent slipping of object , but needs to be small enough to allow pivoting under gravity . in order to lift the object without slipping , the linear frictional force at the finger contacts must balance the gravitational force . this determines lower bound on the gripping force during the pivoting phase : where m is the mass of the object , g is the gravitational acceleration and μ is the linear coefficient of friction at the finger contacts . the upper bound on f pivot is determined by the limit on the motional resistance to allow pivoting , which to a large extent is determined by the size of the contact area between the part and fingers . following , we compare two different approaches to estimate the upper bound , first with idealized point contacts and second with more realistic small patch contacts . an idealized point contact with friction can transmit forces along three linear dimensions , one along the contact normal and mo along the contact plane , in the ideal case , it does not offer any torsional resistance at contact [ 26 ]. this means that , as long as there is an offset between the center of gravity ( cg ) of the object and the finger contact locations , for any positive value of the gripping force , the object is tree to pivot about the fingertips under the effect of gravity . effectively , there is no upper bound on f pivot . in practice , it is hardly possible to get point contacts . there is always a finite surface area at contacts that can provide some degree of torsional resistance . we assume those contacts to be planar patches . a planar contact with friction can transmit a torque about the contact normal in addition to the forces along three directions as in the previous case . that torque , specially when an object is picked close to the center of gravity with high force , can counterbalance the gravitational torque and prevent the part from pivoting , which can cause problems . the simplest approximation to capture torsional friction is to model a patch contact as a point contact that transmits a torque about that point with a certain torsional coefficient of friction ( μ tors ), producing the frictional torque μ tors f pivot . this model is often known as soft contact model [ 26 ]. however , estimation of μ tors is not trivial and in general depends on the contact geometry , so needs to the updated when the contact geometry changes . there are more involved ways to model patch contacts . a model commonly used in manipulation planning is the limit surface model [ 27 ]. there are other models that are based on finite element approximations [ 28 ] which do not assume explicit knowledge of the torsional friction coefficient . the focus of this invention is the mechanical , design of the two - phase fingers , and for the sake of simplicity , we will assume contacts to be circular , and finitely approximate them as a rigid set of point contacts forming a polygon concentric with the circular patch . the total frictional torque on the object can then be approximated as : where f grip is the gripping force and r is the radius of the circular patch contact . for an object to rotate in the fingers , the frictional torque created at the finger contacts must be smaller than the moment created by the gravitational force on the object , τ fric ≦ mglcosφ , which sets an upper bound on the gripping force : where l is a moment arm , the offset between the cg of the object and the fingertip location , and φ is the angle between the axis of the cylinder and the horizontal plane . φ changes from 0 ° to 90 ° as the object pivots from the horizontal pose to the upright pose . though the moment arm reduces as the object slowly pivots , the inertia gained by the object can help it to pivot as the the moment approaches zero . so , we only check if the following constraint holds true when the part is in the horizontal configuration : in summary , constraints ( 1 )-( 7 ) collectively define the geometry of the v - groove cavity , stillness of the elastic strip over it and foe limits on the gripping force to pivot the object about the finger contacts . we now discuss the experimental validation of the effectiveness of the two - phase fingers . in particular we focus on the validation of the small patch models for the linger contacts and the effect of changes in the grasping location on the required gripping force for pivoting . for prototyping , we used 3d printed fingers with a v - groove cavity , and a rubber band with preload for the elastic strip . the point contact on the strip is - made by placing a drop of liquid rubber on the strip and then curing it the elastic strip is held in place using a cap screw . we attached these lingers to two different grippers : weiss robotics wsg - 32 , with force feedback and force control , and the robotiq 2 - finger 85 without force control . see fig5 a . both the grippers were mounted on an abb irb 140 industrial manipulator . we chose three different cylinders with different diameters and materials and one with a square flange , as our test objects . fig5 b shows a typical experimental setup with two of the test objects , the two - phase gripper and the manipulator . for every experimental trial , we lifted the object from the ground with a low gripping force in a range suitable for pivoting the object and then grasped it tightly after it is fully lifted from , the ground . the attempt is counted as a success if the part is reoriented to an upright pose without slipping and securely held in the v - groove at the end of the procedure . we conducted this experiment for multiple gripping forces , and at multiple gripping locations along the length of the cylinder , for all the tested objects . fig6 shows the results of those experiments for one of the objects , and for comparison , fig7 shows our expectation from the discussed pivoting models . as discussed above , we approximate the contacts between an object and the fingertips by small patch contacts which offer small but non - negligible frictional torque about the contact normal to let the object pivot between contacts , the gripping force must satisfy constraint ( 7 ). as we pick an object farther away from its center of gravity , the moment arm l increases making the range of compatible gripping forces for pivoting bigger . we conducted a series of experiments of picking up a cylindrical object at varying offset distances from the center with different gripping forces . fig6 shows the outcome of the experimental trials . the run is counted as a success if the object pivoted under gravity without slipping , and a failure otherwise . due to the limitations of the gripper used , we limited the range for the gripping forces to the region 5 n - 3 n the fig . shows the increase in the valid gripping force region as the object is grasped farther away from the center . fig7 shows the estimation of the limits on the gripping force found analytically for successful execution of pivoting . the analytical model used here assumes circular patch contacts of 3 mm diameter at the fingertips , which give a good match for the fingers used . to evaluate the coefficient of friction between the object and the fingers , we made rigid fingers with the same rubber material at the tips . we picked the desired object and attempted to push it linearly in the grasp . based on the gripping force and pushing force data generated from multiple experiments the linear coefficient of friction for the finger - object pair is estimated to be 0 . 6 . following the ‘ no slip ’ criterion governing the minimum force at the fingers ( 4 ) and ‘ minimal torsional resistance ’ criterion governing the maximum force ( 7 ), we calculated the bounds on the gripping force which are shown in fig7 . they are overlapped with the regions of success and failure trials observed during the experiments . close resemblance of analytical and experimental results show that , given the mass of the object and the coefficient of friction between the fingers and the object , we can model the process well enough to predict the gripping force required to successfully operate the two - phase gripper . this patent application has disclosed the design of a two - phase gripper , composed of a standard parallel - jaw gripper instrumented with special fingers capable of passively reorienting and securely holding a set of objects . the contact geometry between the fingers and the object changes from a point contact , which allows reorientation through pivoting , to a multi - point contact , which secures the grasp in the new orientation , as the gripping force increases . we focus on the application of the two - phase gripper to reorientation of cylindrical objects from a horizontal to as upright pose and then securely grasping them . the two - phase fingers disclosed herein can be retrofitted to any parallel - jaw gripper of an appropriate size . the idea of two - phase fingers can be easily extended to different shapes of objects by reconfiguring the cavity in the fingers . the numbers in square brackets refer to the references listed herein . the contents of all of these references are incorporated herein by reference in their entirety . it is recognized that modifications and variations of the present invention will be apparent to those of ordinary skill in the art and it is intended that all such modifications and variations be included within the scope of the appended claims . g . monkman , s . hesse , r . steinmann , and h . schunk , robot grippers . john wiley and sons , 2006 . p . gorce and j . fontaine , “ design methodology approach for flexible grippers ,” journal of intelligent and robotic systems , vol . 15 , no . 3 , pp . 307 - 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