Abstract:
The present invention relates to a gripping device that consists of four artificial muscle rings arranged in parallel. A grasper is placed in the middle of the rings. Sequential activation of the rings produces a peristaltic motion that moves the grasper back and forth within the rings. By activating the grasper appropriately, it can grab, ingest, and move soft and irregular material from one side of the lumen formed by the rings to the other side.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application is a continuation of U.S. patent application Ser. No. 11/172,526, filed on 30 Jun. 2005, which claims the benefit of U.S. Provisional Patent Application No. 60/584,281, filed on 30 Jun. 2004, both of which are incorporated herein by reference. 
     
    
     FEDERALLY SPONSORED RESEARCH 
       [0002]    The contents of this application were developed under a Presidential Research Initiative Grant, NSF Grant IBN99-74394 and NSF grant IBN-0218386. The United States Government has certain rights in the invention. 
     
    
     FIELD OF THE INVENTION 
       [0003]    The present invention relates to control devices, and specifically to control of devices that are capable of gripping and manipulating materials. 
       BACKGROUND OF THE INVENTION 
       [0004]    A major focus of robotic applications is the development and control of devices that are capable of gripping and manipulating materials. Basic grippers consist of two surfaces that can be brought together; more dexterous grippers use fingers, some of which can be individually controlled as disclosed in Causey, G.,  Guidelines for the design of robotic gripping systems . Assembly Automation, 2003, 23: p. 18-28; Marcincin, J. N. and J. Smrcek,  Biomechanical grippers: important elements of biomechanical robots . Industrial Robot, 1997, 24: p. 234-238; and Arimoto, S., K. Tahara, M. Yamaguchi, P. Nguyen, and H.-Y. Han,  Principles of superposition for controlling pinch motions by means of robot fingers with soft tips . Robotica, 2001, 19: p. 21-28. For rigid objects, grippers usually fall into two broad classes: friction grippers or encompassing grippers, as disclosed in the Causey article. If the gripper uses the friction between its surfaces and the object to grip it, the gripper requires about four times the force of an encompassing gripper, whose surfaces partially conform to those of the held object, as disclosed in Zajac, T. J.,  Robotic Gripper Sizing: The Science, Technology and Lore . http://www.grippers.com/size.htm, 2002. 
         [0005]    Holding and manipulating soft or delicate materials is an area of intense research. A recent survey of devices that could grip materials such as fabrics, leathers, or food products found three major categories: pinching using friction (similar to the principles described above), intrusive grippers that insert pins into the material to lock it in place, and surface attraction grippers that make use of adhesives or vacuum, as disclosed in Taylor, P.,  Presentation and gripping of flexible materials , Assembly Automation, 1995. 15: p. 33-35. A difficulty with such prior art devices is that they may crush, deform, or in other ways change the properties of the object that has been gripped. Thus, it would be of great value and interest to develop grippers that could handle soft, pliable, fragile, slippery and irregular materials without inducing significant material deformation. 
         [0006]    Biological organisms are frequently confronted with highly complex materials that they must manipulate to achieve their goals. For example, animals that feed on seaweed must be capable of harvesting large amounts of slippery, irregularly shaped material that is usually connected to a substrate by a holdfast. Many organisms have successfully solved these problems using a variety of different feeding-mechanisms. One very successful group is the mollusks, which are capable of feeding on highly irregular materials using a feeding apparatus known as the radula (rasper) controlled by underlying musculature (the odontophore) and moved forward and backward by other muscles in order to contact food, and then convey food into the animal&#39;s body, as disclosed in Brusca, R. and G. Brusca,  Invertebrates.  1990, Sunderland, Mass.: Sinauer Associates, Inc, p. 728-738. 
         [0007]    The sea slug,  Aplysia californica , uses a muscular structure called the buccal mass to grasp and ingest food. As shown in  FIG. 1 , the central grasper within the buccal mass consists of a thin, flexible surface covered with fine teeth (the radula), that is opened or closed by a set of muscles known as the odontophore. The structure is moved towards the jaws (protracted) using a thin, sheet like muscle (I2), and can be moved towards the esophagus using thick bands of muscle that form the jaws (I1/I3 jaw muscles), as disclosed in Kandel, E.,  Behavioral Biology of Aplysia,  1979, San Francisco: W. H. Freeman and Co., p. 88-96; Kupfermann, I.,  Feeding behavior in Aplysia: A simple system for the study of motivation ; Behav. Biol., 1974, 10: p. 1-26; and Neustadter, D., R. Drushel, P. Crago, B. Adams, and H. Chiel,  A kinematic model of swallowing in Aplysia californica based on radula/odontophore kinematics and in vivo magnetic resonance images . J exp Biol, 2002. 205: p. 3177-3206. 
         [0008]    U.S. Pat. No. 6,764,441 and Mangan, E. V., D. A. Kingsley, R. D. Quinn, and H. J. Chiel,  Development of a peristaltic endoscope . International Congress on Robotics and Automation 2002, 2002: p. 347-352, disclose a self-propelled device capable of peristaltic locomotion caused by a plurality of braided pneumatic actuators that surround a central flexible tube. This device demonstrates the use of braided pneumatic actuators for locomotion, whereas the device disclosed in this application demonstrates the use of these actuators for gripping and manipulating flexible and irregular materials. Moreover, the braided pneumatic actuators in that application are arranged in series, and thus are not used in the same form as disclosed in this application. 
       ASPECTS AND SUMMARY OF THE INVENTION 
       [0009]    It is an aspect of the present invention to provide a device capable of gripping and manipulating materials. 
         [0010]    It is a further aspect of the present invention to provide a biologically-inspired gripper device that can transfer pliable materials through a lumen. 
         [0011]    It is a still further aspect of the present invention to provide a biologically-inspired gripper device that can surgically remove plaque from blood vessels and clean plumbing. 
         [0012]    The present invention relates to a gripping device that is based on the feeding apparatus of a mollusk, known as the buccal mass. The device consists of four artificial muscle rings arranged in parallel. A grasper is placed in the middle of the rings. Sequential activation of the rings produces a peristaltic motion that moves the grasper back and forth within the rings. By activating the grasper appropriately, it can grab, ingest, and move soft and irregular material from one side of the lumen formed by the rings to the other side. Such a device would be useful in medical and plumbing applications, where the material to be removed is very compliant. 
         [0013]    According to the present invention, a flexible gripping device comprises a plurality of pneumatic actuator sections each in the form of a pneumatic actuator ring; and a grasper element disposed within the plurality of pneumatic actuator rings and adapted to move back and forth within the actuator rings. The gripping device includes means for sequentially activating the plurality of actuator rings to produce a peristaltic motion that moves the grasper element back and forth within the actuator rings. The plurality of actuator rings can be disposed in parallel relation to each other and secured to each other to form a tubular device with a central interior or lumen through which the grasper element moves back and forth. The gripping device includes a means of connecting each of the actuator rings to an adjacent ring so that each of the actuator rings remain in contact with adjacent rings as any ring expands or contracts whereby each ring may expand in volume and occupy part of the central interior or lumen so as to exert force on the grasper element. 
         [0014]    Also according to the present invention, structural means are provided to actuate the actuator rings to move the grasper element forwards or backwards relative to the central interior of the tubular device. 
         [0015]    Further, according to the present invention, structural means are provided for returning the grasper element to an initial resting position in the central interior of the tubular device if the actuator rings are not actuated. The structural means for returning the grasper element can be an elastic band attached to the grasper element and to a substrate that constrain the grasper element to rotate and for pulling the grasper element back to the initial resting position. 
         [0016]    Still further, according to an embodiment of the present invention, the grasper element comprises: a generally spherically shaped, elastomeric element; a first cleft shaped opening extending from a peripheral surface towards the interior of the elastomeric element; a second cleft shaped opening extending from an opposite side of the peripheral surface towards the interior of the elastomeric element; structural means, such as a spring, within the second cleft shaped opening to provide a passive closing force; and at least one pneumatic actuator disposed across the second cleft shaped opening and attached at opposite ends of the actuator to the peripheral surface for opening the second cleft shaped opening and simultaneously closing the first cleft shaped opening so as to enable them to grasp a material to be moved. 
         [0017]    Also according to another embodiment of the present invention, the grasper element comprises: a generally ellipsoid shaped element with a groove having a flat bottom surface formed around the circumference of the ellipsoid shaped element; a pair of inflatable tubular actuators disposed in the groove and spaced from each other; structural means to inflate the tubular actuators so that they expand radially and press against each other to enable a material to be grasped and moved. The grasper element can include structural means for securing the pair of inflatable tubular actuators disposed in the groove. The groove in the grasper element can be disposed parallel to the minor axis of the generally ellipsoid shaped element. 
         [0018]    According to the present invention, sensing means are provided for sensing physical properties encountered by the grasper element and control means to control the gripping device in response to the physical properties encountered by the grasper element. The control means of controlling the gripping device further includes means for responding to changes in physical properties encountered by the grasper element by altering the duration or intensity of protraction or retraction of the grasper element or opening or closing of the grasper element. 
         [0019]    According to the present invention, a method of moving a material with a flexible gripping device comprises the steps of: providing a plurality of pneumatic actuator rings secured to each other to form a tubular device with a central interior; disposing a grasper element within the plurality of pneumatic actuator rings at an initial resting position; and sequentially activating the plurality of actuator rings to produce a peristaltic motion that moves the grasper element back and forth within the interior of the actuator rings. 
         [0020]    Still further, according to the present invention, the method includes the step of returning the grasper element to the initial resting position in the central interior of the tubular device if the actuator rings are not actuated. 
         [0021]    Also according to the present invention, the method includes the steps of: providing the grasper element with a pair of inflatable tubular actuators; and inflating the tubular actuators so that they expand radially and press against each other to enable a material to be grasped and moved. 
         [0022]    Further, according to the present invention, the method includes the steps of sensing physical properties encountered by the grasper element; and controlling the gripping device in response to the physical properties encountered by the grasper element. 
         [0023]    Still further, according to the present invention, the method includes the steps of changing the timing of opening and closing the grasper element relative to protraction and retraction of the plurality of actuator rings so that material can be transported from outside the central interior into the central interior, or from within the central interior outside of the central interior. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0024]    The structure, operation, and advantages of the present invention will become further apparent upon consideration of the following description taken in conjunction with the accompanying figures. The figures are intended to be illustrative, not limiting. 
           [0025]    Certain elements in some of the figures may be omitted, or illustrated not-to-scale, for illustrative clarity. The cross-sectional views may be in the form of “slices”, or “near-sighted” cross-sectional views, omitting certain background lines which would otherwise be visible in a “true” cross-sectional view, for illustrative clarity. 
           [0026]    In the drawings accompanying the description that follows, often both reference numerals and legends (labels, text descriptions) may be used to identify elements. If legends are provided, they are intended merely as an aid to the reader, and should not in any way be interpreted as limiting. 
           [0027]    Often, similar elements may be referred to by similar numbers in various figures of the drawing, in which case typically the last two significant digits may be the same, the most significant digit being the number of the drawing figure. 
           [0028]      FIG. 1  shows a schematic view of the anatomy of the buccal mass of  Aplysia californica;    
           [0029]      FIG. 2  shows the side view, in cross section, of a flexible gripping device, in accordance with the present invention; 
           [0030]      FIGS. 3A-3B  are respective side views of an unexpanded and expanded existing art pneumatic actuator; 
           [0031]      FIGS. 4A-4B  shows the schematic of an inflated and deflated assembly of four pneumatic actuators to form a ring, in accordance with the present invention; 
           [0032]      FIGS. 5A and 5B  shows the schematic of a first embodiment of a grasper element, in accordance with the present invention; 
           [0033]      FIGS. 6A and 6B  shows the schematic of a second embodiment of a grasper element, in accordance with the present invention. 
           [0034]      FIGS. 7A and 7B  show the operation cycle of the flexible gripping device, in accordance with the present invention; 
           [0035]      FIG. 8  shows the force normal to the rings, In accordance with the present invention; 
           [0036]      FIG. 9  shows a schematic of the mechanical analysis, in accordance with the present invention; 
           [0037]      FIG. 10  shows the free body diagrams for the mechanical analysis of the action of the rings on the central grasper, in accordance with the present invention. 
           [0038]      FIG. 11  shows the mechanical analog, in accordance with the present invention; 
           [0039]      FIG. 12  shows the schematic of inflatable “lips” type grasper device, in accordance with the present invention; 
           [0040]      FIG. 13  shows the schematic of a hinged grasper device, in accordance with the present invention; 
           [0041]      FIG. 14  shows predicted and actual positions and a region in which the rings cannot act on the grasper, in accordance with the present invention; and 
           [0042]      FIG. 15  shows a schematic of a control system, in accordance with the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0043]    The present invention relates to a flexible gripping device  10 , as shown in  FIG. 2 , that uses a plurality of braided pneumatic actuators  12   a ,  12   b ,  12   c ,  12   d  ( 12   a - 12   d ) arranged in rings to form a tube like structure in combination with a grasper element  14 . As discussed in more detail below, the flexible gripping device  10  operates to move the grasper element  14  through the lumen or central interior of the tube like structure formed of the plurality of pneumatic actuators ( 12   a - 12   d ). While four rings are shown creating the lumen, it is within the scope of the present invention to use three or more rings depending on the particular application. 
         [0044]    The pneumatic actuators ( 12   a - 12   d ), can be modified McKibben artificial muscles that approximate or mimic the function of the I1/I3 jaw muscles of a sea slug as previously described and shown in  FIG. 1 . A McKibben artificial muscle ring, as shown in  FIG. 3A , consists of an expandable bladder  20 , such as for example of a latex material, located inside of a tubular mesh  22  made of relatively inextensible fibers, such as for example braided nylon. The mesh  22  is clamped or otherwise affixed to the bladder  20  at its ends  24 . As fluid, i.e., gas, air or liquid, is supplied into the bladder  20  through an inlet line  26 , the diameter of the bladder  20  expands radially, as shown in  FIG. 3B . Because of the inextensible fiber mesh  22 , the surface area of the expanding bladder  20  remains relatively constant. Thus, at the time the bladder&#39;s diameter increases, its length decreases, i.e., tending from a cylindrical to a more spherical shape, as shown in  FIG. 3B . This is understood because the tubular mesh  22  imposes an isovolumetric constraint on the bladder  20 , so expansion in the radial direction causes a contraction in the axial direction, as disclosed in Colbrunn, R. W. DESIGN AND CONTROL OF A ROBOTIC LEG WITH BRAIDED PNEUMATIC ACTUATOR, Department of Mechanical and Aerospace Engineering, Case Western Reserve University, 2000. M.S. thesis, p. 1-37. 
         [0045]    Referring to  FIGS. 4A and 4B , there is illustrated a side view of an actuator ring  30  (corresponding to the ring actuators  12   a - 12   c ) in accordance with the present invention. A plurality of pneumatic actuator sections  32   a - 32   d  are connected end to end and attached to each other by a cylindrical connector  34  or a t-shaped connector  36 . While the actuator ring  30  is shown constructed of four braided, pneumatic actuator sections  32   a - 32   d , it is within the scope of the present invention to use three or more actuator sections depending on the particular application. To actuate the pneumatic actuator sections  32   a - 32   d , pressurized air, gas or liquid of between 2.5 psi and 100 psi and preferably between 10 psi and 60 psi and most preferably between 15 psi and 30 psi is delivered to the interior of the actuator ring  30 , of the type shown in  FIG. 3A , through an opening such as through the inlet  36   a  of the t-shaped connector  36 . As the outer circumference of the actuator ring  30  is inflated and gets larger, the inner circumference of the actuator ring gets smaller (see  FIG. 4B ). That is, there is an overall decrease in the diameter d 1  of the actuator ring  30  in the uninflated ring in  FIG. 4A  as compared to the diameter d 2  of the inflated actuator ring in  FIG. 4B . 
         [0046]    The flexible gripping device  10 , as generally shown in  FIG. 2 , includes a grasper element  14  that is initially disposed in the center of the central interior of the tube formed of pneumatic actuator rings  12   a - 12   d , which are disposed in parallel relation to each other. A device  32 , such as for example, an elastic band, is provided for returning the grasper element  14  to an initial resting position in the central interior of the tubular device if the actuator rings  12   a - 12   d  are not actuated. The elastic band  32  is secured at one end to the grasper element  14 . The elastic band  32  extends between rings  12   b  and  12   c  and is secured at its opposite end to a substrate  34 . The elastic band  32  operates to both constrain the grasper element so that the grasper element rotates and for pulling the grasper element back to the initial resting position. When the device  10  is not anchored, e.g. if it operates autonomously at the end of a moving manipulator, the substrate  34  will move with the end of the manipulator. 
         [0047]    Referring to  FIGS. 5A and 5B , there is illustrated a first embodiment of the grasper element  40  (corresponding to element  14 ). The grasper element  40  incorporates a pair of inflatable, lip-like tubular actuators  42  and  44  constructed similar to the braided pneumatic actuators shown in  FIG. 3A . The inflatable, lip-like tubular actuators  42  and  44  are disposed around a relatively rigid ellipsoid shaped element  46 , such as one formed from rubber. At the approximate center of the ellipsoid  46 , there is a groove  47  with a flat bottom surface formed around the circumference of the ellipsoid. The groove  47  is disposed parallel to the minor axis of the generally ellipsoid shaped element. Disposed within the groove  47  are a pair of tubular actuators  42  and  44  that are placed against the edge walls  47   a  and  47   b  of groove  47  and held in place by any desired means such as a rubber band  48  secured to opposite ends of the actuators or artificial muscles  42  and  44 . The actuators  42  and  44  extend around the circumference of the groove  47  for about 5° to about 345° and preferably about 60° to about 180° and most preferably about 90° to about 180°. Each of the actuators  42  and  44  has an air, gas or liquid line  49  for inflating the inflatable lip-like tubular actuators  42  and  44 . When the actuators  42  and  44  are inflated by air or any other inflation fluid, they expand radially press against each other, as shown in  FIG. 5B  so as to be able to squeeze on a material to be moved. At the same time, the length of the actuators  42  and  44  decreases as shown in  FIG. 5B  and as previously described. 
         [0048]    A second embodiment of a hinged grasper element  50  (corresponding to element  14 ) is shown in  FIGS. 6A and 6B . The hinged grasper element  50  is constructed of a generally spherically shaped, flexible element  51 , such as an elastomeric or rubber ball. The spherically shaped element  51  has a cleft opening  52  formed therein. The cleft opening  52  typically has a generally wedge like shape that extends from the peripheral surface  54  of the spherically shaped element  51  to a location near a centerline  55  extending through the spherically shaped element. The angle “a” of the wedge shaped opening  52  is preferably between about 5° to about 45° and preferably about 15° to about 40° and most preferably about 25° to about 35°. On the opposite side of the spherically shaped element  51  from the wedge shaped opening  52  is formed a second cleft opening  56 , generally of a wedge like shaped which can be substantially identical to the cleft opening  52 . There is a small section of flexible material separating the cleft openings  52  and  56  and providing a hinge-like action between the two openings. It is within the terms of the invention to form the second opening  56  with a different shape than first opening  52 , depending on the particular design and application for which the grasper element will be used. Within the cleft opening  56  is a means  58  to provide a passive closing force. The means can be a torsional spring hinge secured to the wedge walls  56   a  and  56   b . One or more pneumatic actuators or artificial muscles  60  (operating by the principles described before see  FIG. 3A ) are attached at opposite ends to the peripheral surface  54  of the spherically shaped element  51  and extend across the opening  56 . Each of the actuators or artificial muscles  60  can be disposed in a groove  54   a  as shown in  FIG. 6B . When activated (see  FIG. 6A ), the artificial muscle(s)  60  contract and shorten (according to the principles previously described) to close the cleft opening  56  against the bias force of spring  58 . Simultaneously, the cleft opening  52  is opened as shown in  FIG. 6A . Then, when the artificial muscle(s)  60  are expanded by relieving the pressure in the artificial muscle(s)  60 , the bias force of spring  58  opens cleft opening  56  (see  FIG. 6B ) and simultaneously causes the cleft opening  52  to close. When cleft opening  52  closes, it is capable of grasping some object in accordance with the present invention. 
         [0049]    A peristaltic cycle is used to control the gripper device  10  as generally shown in  FIGS. 7A and 7B . Using compressed air at a desired pressure, e.g., 60-75 psi, each of the rings  12   a - 12   d  can be alternately contracted and then expanded. The elastic band  32  kinematically induces the grasper element  14  to rotate as it is protracted (see  FIG. 7A ), and pulls the grasper element  14  back to its initial resting position once the rings  12   a - 12   d  are deflated. 
         [0050]    With the grasper element  40 , of the type shown in  FIGS. 5A and 5B , at the start of a protraction, i.e., the rest position as shown in  FIG. 7A , the inflatable, lip like actuators  42  and  44  are open as shown in  FIG. 5A . In  FIG. 7A , the central interior is an elongate space having longitudinally separated peak protraction (the rightmost position in  FIG. 7A ) and peak retraction (the leftmost position in  FIG. 7A ) locations with the rest position located therebetween. The grasper element  40  is shown initially in the rest position in the topmost image of  FIG. 7A ; the images of  FIGS. 7A and 7B  each are shown in a sequence running from the top to the bottom of the page, in the orientation of these FIGURES. Then ring  12   c  is activated to start the grasper element&#39;s movement to the peak protraction location, or toward the right in the orientation of  FIG. 7A . Next, ring  12   b  and finally ring  12   c  are activated so that the grasper element moves to the peak protraction location and is substantially absent from the peak retraction location (i.e., the left side of the central interior in  FIG. 7A ). Once peak protraction is reached, the inflatable lip like actuators close (see  FIG. 5B ) on a material to be grasped. Then rings  12   a - 12   c  are relaxed, by lowering the pressure on the actuating gas or fluid and the grasper element  40  is passively pulled back from the peak protraction location to its rest position by the elastic band  32 . As shown in  FIG. 7A , ring  12   c  can be relaxed prior to relaxing rings  12   a  and  12   b.    
         [0051]    Next, as shown in  FIG. 7B , the grasper element  40  is actively retracted by the rings, while the lip like actuators remain in the closed position (see.  FIG. 5B ), until peak retraction is reached. First ring  12   b  is activated to start the grasper element&#39;s movement from the rest position leftward (in the orientation of  FIG. 7B ) to the peak retraction location. Next ring  12   c  and finally ring  12   d  are activated so that the grasper element moves to the (leftmost) peak retraction location and is substantially absent from the (rightmost) peak protraction location. The inflatable lip like actuators  42  and  44  then open again (see  FIG. 5A ) and can deposit the grasped material on the outward side of ring  12   d  and opposite from the side of the gripper device  10  from where it was initially grasped. Next, by lowering the pressure on the actuating gas or fluid on the rings  12   b ,  12   c  and  12   d , the grasper element  14  is passively pulled back from the peak retraction location to the rest position by the elastic band  32  while the inflatable lip like actuators  42  and  44  remain in the open position so that the cycle can repeat. As shown in  FIG. 7B , ring  12   b  can be relaxed prior to relaxing rings  12   c  and  12   d.    
         [0052]    In another embodiment, the gripper device  10  can operate the same way as just described but the hinged grasper element  50  can be substituted for the grasper element  40 . When the grasper element  50 , as shown in  FIGS. 6A and 6B , is in the rest position at the start of a protraction as shown in  FIG. 7A , the cleft opening  52  is open as shown in  FIG. 6A . Once peak protraction is reached, the cleft opening  52  is closed (see  FIG. 6B ) on the material to be grasped. Then rings  12   a - 12   c  relax and the grasper element  50  is passively pulled back to its rest position by the elastic band. Next, as shown in  FIG. 7B , the grasper element  50  is actively retracted while remaining in the closed position (see  FIG. 5B ) by the rings until peak retraction is reached. The cleft opening  52  is then opened again (see  FIG. 6A ) and the grasped material is deposited on the other side of the rings from which it was initially grasped. Next, the grasper element  50  while in the open position is passively pulled back to the rest position, as previously described, and the cycle can repeat. 
         [0053]    The sequence of operations described here can be reversed, so that the grasper (embodied either as  40  or  50  or in a functionally equivalent form) can close upon material within the lumen while the grasper is retracted, and then the grasper can be protracted, and the material can be released outside of the lumen. Thus, the device could be used for transport of material in either direction through the lumen. 
         [0054]    It is possible to compute the force that a ring will exert on a grasper element. If the ring contacts the grasper at four points, the force produced by the axial contraction of the artificial muscles can be translated to a force normal to the rings (See  FIG. 8 ). 
         [0055]    The force at each contact point i is 2 T cos λ. Since the ring actually contacts the grasper at m points, the total force F over m contact points is 2 T cos λ. 2 Tm cos λ. The angle λ is π/2-π/m, and so the force, F, becomes 2 T m cos(π/2-π/μ), which is equal to 2 Tm sin π/m. As m increases to infinity, as it does for a circular ring, the value of sin π/m approaches π/m and so the total inward force around the ring becomes 
         [0000]    
       
         
           
             
               
                 
                   F 
                   = 
                   
                     
                       2 
                        
                       Tm 
                        
                       
                         π 
                         m 
                       
                     
                     = 
                     
                       2 
                        
                       
                           
                       
                        
                       π 
                        
                       
                           
                       
                        
                       T 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0056]    To compute the force on the gripper in the horizontal direction, we analyze the device as shown in  FIG. 9 . We assume that the rings can only move vertically (constraint force F), and the grasper can only move horizontally (constraint force Fx). This is mechanically equivalent to the diagram shown in  FIG. 11 . 
         [0057]    The relationship between the input force, F, and the net horizontal force, Fx, can now be determined from a free body diagram (see  FIG. 10 ). Using the free body diagram for the ring, which includes the normal force, N, on the grasper (see  FIG. 10A ), the frictional force, μN, and the force, F, generated by the actuators, the sum of the forces in the y direction is F-N Cos (θ)-μN sin(θ). Thus the normal force N is equal to 
         [0000]    
       
         
           
             
               
                 
                   N 
                   = 
                   
                     F 
                     
                       
                         cos 
                          
                         
                             
                         
                          
                         θ 
                       
                       + 
                       
                         μsin 
                          
                         
                             
                         
                          
                         θ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0058]    From the free body diagram of the grasper, the horizontal components of the normal and frictional forces sum to N sin(θ)-μN cos(θ)-Fx. Substituting (2) into this equation yields 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           F 
                            
                           
                               
                           
                            
                           sin 
                            
                           
                               
                           
                            
                           θ 
                         
                         
                           cos 
                           + 
                           
                             μsin 
                              
                             
                                 
                             
                              
                             θ 
                           
                         
                       
                        
                       
                         
                           μ 
                            
                           
                               
                           
                            
                           F 
                            
                           
                               
                           
                            
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                            
                           
                               
                           
                            
                           θ 
                         
                         
                           
                             cos 
                              
                             
                                 
                             
                              
                             θ 
                           
                           + 
                           
                             μsin 
                              
                             
                                 
                             
                              
                             θ 
                           
                         
                       
                     
                     - 
                     
                       F 
                       x 
                     
                   
                   = 
                   0 
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
       
         
           
             which simplifies to 
           
         
       
     
         [0000]    
       
         
           
             
               
                 
                   
                     Fx 
                     F 
                   
                   = 
                   
                     
                       
                         sin 
                          
                         
                             
                         
                          
                         θ 
                       
                       - 
                       
                         μcos 
                          
                         
                             
                         
                          
                         θ 
                       
                     
                     
                       
                         cos 
                          
                         
                             
                         
                          
                         θ 
                       
                       + 
                       
                         μsin 
                          
                         
                             
                         
                          
                         θ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0060]    Plotting equation (4) shows that at low angles of contact, friction creates a dead zone in which no application of force will cause the grasper to move forward (see  FIG. 14 , left side). Since F=2πT, the overall force of the ring on the grasper becomes 
         [0000]    
       
         
           
             
               
                 
                   Fx 
                   = 
                   
                     2 
                      
                     
                         
                     
                      
                     π 
                      
                     
                         
                     
                      
                     T 
                      
                     
                       
                         
                           
                             sin 
                              
                             
                                 
                             
                              
                             θ 
                           
                           - 
                           
                             μcos 
                              
                             
                                 
                             
                              
                             θ 
                           
                         
                         
                           
                             cos 
                              
                             
                                 
                             
                              
                             θ 
                           
                           + 
                           
                             μsin 
                              
                             
                                 
                             
                              
                             θ 
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0061]    Finally, to convert the pressure in the McKibben actuator into tension T, we use a model of the forces within the actuator [Colbrunn, 2000]: 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                     = 
                     
                       ( 
                       
                         
                           b 
                           2 
                         
                          
                         
                           P 
                            
                           
                             ( 
                             
                               
                                 3 
                                  
                                 
                                   
                                     L 
                                     2 
                                   
                                   / 
                                   
                                     b 
                                     2 
                                   
                                 
                               
                               - 
                               1 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     4 
                      
                     π 
                      
                     
                         
                     
                      
                     
                       n 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0062]    where L is the current length of the actuator, n is the number of helices in the actuator, b is the length of a strand of braid which is estimated from the braid angle α[the greek letter alpha] using the equation b=L/cos α[the greek letter alpha], and P is the input pressure of the actuator. 
         [0063]    In an actual test, the inflatable lip like actuator  40  was able to protract, grab a piece of silicon tubing, then retract and deposit the tubing on the other side of the rings (see  FIG. 12 ). During operation, the grasper  40  could do this repeatedly with a cycle time of 16 seconds. 
         [0064]    In another actual test, the hinged grasper  50  was able to protract, grasp a piece of silicon tubing, retract, and then deposit the tubing on the other side of the rings (See  FIG. 13 ). 
         [0065]    At this stage of development, the maximum amount of force that the rings imposed on the inflatable “lips” gripper is estimated by measuring the restoring force in the elastic hinge, which is equal and opposite to the force exerted by the gripper when the hinged grasper  50  was fully protracted or fully retracted. In one test, the force was approximately 5 newtons (N). 
         [0066]    Based on the theoretical analysis done above, and measurements from the grasper devices, it is possible to calculate the force that the rings should optimally exert on the grasper. The number of helices (n) in an actuator segment was 1, the length of a strand of a braid (b) was 7.4 cm, the input pressure (P) was 60 psi, equal to 410 kPa, and the length (L) of the actuator was 7 cm. Using equations (5) and (6), and the measured spring force, the final extended position of the grasper when the most anterior ring was fully actuated could be estimated. The predicted position matched the actual position very well (see  FIG. 14 ). 
         [0067]    By adding physical property sensors, such as pressure sensors  60 ,  61 , or other sensors (e.g., temperature, chemical) to the inner surfaces  47  of the grasper device  40  or inner surface of cleft opening  52  of the grasper device  50 , respectively, (see  FIGS. 5B and 6A ) or to an inner surface of a functionally equivalent embodiment of a grasper device), the flexible gripping device  10  could sense the physical properties or local conditions encountered by the grasper element as it grasped material, and could flexibly and rapidly respond to these changes in conditions. Pressure sensors  60 ,  61  can be connected by lines  63  and  64  to a control system  66  such as a computer or a neural network that controls the braided pneumatic actuators  12   a - 12   d  by one or more lines  67  and actuators  42  and  44  of grasper  40  and/or the actuators or artificial muscles  60  of grasper  50  by one or more control lines  68 . That is, the control system  66  could respond to changes in physical properties encountered by the grasper element by altering the duration or intensity of protraction or retraction of the grasper element through the flexible gripping device  10  or opening or closing of the grasper element. In addition, the control system could change the timing of opening and closing the grasper element relative to protraction and retraction of the plurality of actuator rings so that material can be transported from outside the central interior (lumen) into the central interior, or from within the central interior outside of the central interior of the tubular shaped flexible gripping device  10 . For example, if the grasper failed to encounter material, it could protract further, rather than performing a full protraction/retraction cycle. If the material resisted attempts to pull it into the lumen of the flexible gripping device, the flexible gripping device could sense this and increase the force (intensity) it exerted. 
         [0068]    The present application describes a biologically-inspired gripping device  10  that can transfer pliable materials through a lumen. The gripping device  10  has many potential applications including surgically removing plaque from blood vessels and cleaning plumbing to name a few. 
         [0069]    Although the invention has been shown and described with respect to a certain preferred embodiment or embodiments, certain equivalent alterations and modifications will occur to others skilled in the art upon the reading and understanding of this specification and the annexed drawings. In particular regard to the various functions performed by the above described inventive components the terms are intended to correspond, unless otherwise indicated (sensing, controlling, exerting force, etc.) the terms (including a reference to a “means”) used to describe such components are intended to correspond, unless otherwise indicated, to any component that performs the specified function of the described component (i.e., that is functionally equivalent), even though not structurally equivalent to the disclosed structure which performs the function in the herein illustrated exemplary embodiments of the invention. In addition, while a particular feature of the invention may have been disclosed with respect to only one of several embodiments, such feature may be combined with one or more features of the other embodiments as may be desired and advantageous for any given or particular application.