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Table of contents
- Granular Media
- Universal robotic gripper based on the jamming of granular material | PNAS
- Granular material
- Original Research ARTICLE
For other target shapes, the seal thickness d will likely depend on the local curvature of the surface it is pressed against, with flatter surfaces allowing for larger values of d. In fact, simply releasing the vacuum Fig. Evaluating the compressive stress in Fig. A gripper with an elastic membrane might conform to protruding parts of objects as in Fig.
To investigate the mechanism for interlocking quantitatively and in a simple geometry, we therefore manually molded the jammed gripper around the porous sphere.
Then, to break the interlocking effect, the jammed material must both bend out of the way and stretch azimuthally to open enough to let the sphere through. Thus, we expect the holding force in this regime to depend on the resistance to a combination of bending and stretching. Stress-strain curves measured from a 3-point bending test and a triaxial test for extension stretching of the granular material are shown in Fig. To understand the interlocking effect we first consider these two limits.
Universal robotic gripper based on the jamming of granular material | PNAS
Where there is minimal interlocking, i. The minimum contribution from interlocking, F i , to the holding force is the amount required to bend the ring wrapped around the sphere to vertical so the sphere can slip out. Because the location of the bend is not predetermined and the thickness is typically nonuniform, these predictions for the scaling can only provide a rough estimate for the magnitude. This simplification gives the same scaling for both bending and stretching.
The stress-strain curve for bending in Fig. Integrating the stress over the bending area gives. The resulting cross-over is shown as the solid blue line in Fig. During operation a grip may experience off-axis forces and torques, in addition to lifting forces discussed so far. We show in the SI Text holding forces measured for off-axis forces and torques. We find that the friction mechanism is operative at about the same magnitude for resisting forces in all directions and torques applied at the surface. Suction may be operative in some cases but this is dependent on the target geometry and force direction.
Because its rigidity is determined by how deep the material is driven into the jammed state by the vacuum-induced volume contraction, the key control parameter for the gripping strength is the confining pressure P jam. In particular, the confining pressure sets the overall scale for the stresses 30 obtained from triaxial compression, 3-point bending, and stretching tests of the granular material as seen in Fig. Furthermore, the holding forces are approximately proportional to P jam Fig. This scaling can be used to estimate the sizes of objects that can be lifted. For such big grippers, the weight of the granular material itself might become an issue but can be reduced by using hollow particles.
Indeed, meter-size panels of vacuum-packed hollow spheres show remarkable stiffness and have been proposed as structural elements in architectural projects 31 — While suction is not operative for all objects, interlocking is expected to be prevalent in a multibag, jaw-type gripper 17 — Thus, friction provides more than enough force to pick up any of the objects shown in Fig.
The above analysis was applied to spheres as test objects, but it allows us to draw some general conclusions. We can then rewrite Eq. With this model we can now explain the variation in holding forces measured in Fig. The three-dimensional-printed plastic material in this test is not smooth enough for the gripper to achieve an airtight seal. Thus, the sphere is gripped by friction only and F h is in the range of what we see in Fig. Despite its sharp edges, the cube is held with a large force in the range of what is observed for suction with smooth spheres. The flat vertical faces allow for a large contact area from pinching comparable to the area that could be covered by suction, so the frictional effect is about as large as suction.
Compared to the cube, the vertical contact area of the cuboid is reduced, just as it is in the comparison between sphere and cylinder. The flat disk cannot be lifted since the gripper cannot get around the sides; thus the contact angle effectively is zero. The helical spring is similar to the cylinder in shape, and a similar lifting force is found.
The jack displays a larger force than can be expected from friction alone, indicating some amount of interlocking, as seen in Fig. Another aspect concerns the hardness of the object being gripped. So far, we assumed the target was relatively hard so the stress response was solely determined by the gripper hardness. However, for softer targets, the combination of the target and gripper must be considered in series.
A soft target will be strained as the gripper contracts, and the pinching pressure at the interface cannot exceed the strain of the gripper under vacuum times the target modulus. Thus, soft targets will experience less holding force. Indeed, foam earplugs were gripped readily by the setup shown in Fig.
In this regard, small grain size will be advantageous. However, very fine powders do not flow well and tend to stick. Furthermore, the gas permeability of a powder scales with the square of the grain diameter 34 , 35 ; thus, decreasing that diameter will increase the pumping time required to reach a strongly jammed state. The gripping capabilities are therefore expected to be quite robust. Without the need for active feedback, this gripper achieves its versatility and remarkable holding strength through a combination of friction, suction, and geometrical interlocking mechanisms.
Applied to spheres as test objects the simple model we introduced captures quantitatively the holding force for all three mechanisms. Specifically, the model relates the gripping performance to the jamming pressure P jam and the stress-strain relationship of the granular material, and it predicts how the holding force scales with object size, surface roughness to the extent that an airtight seal can form , and surface normal angle at the gripper-object interface.
A universal gripper based on jamming may have a variety of applications where some of the high adaptability of a human hand is needed but not available, or where feedback is difficult to obtain or expensive. Examples include situations where very different objects need to be gripped reliably and in rapid succession. A granular system can move with ease from gripping steel springs to raw eggs, and it can pick up and place multiple objects without changing their relative orientation. Its airtight construction also provides the potential for use in wet or volatile environments.
Another situation where such a gripper has a significant advantage over traditional designs is when minimal initial information is available, for example when the detailed shape or material properties of the target object are not known a priori, or when precise positioning is not feasible. Because the gripper material adapts and conforms autonomously to the surface of the target object, a jamming-based system can be expected to perform particularly well for complex target shapes. For pick-and-place performance evaluation we used a CRS A robotic arm, which includes high-pressure air lines, controlled by an imbedded solenoid valve.
Original Research ARTICLE
Ground coffee was chosen as the grain material for these tests because of its performance in jamming hardness tests. The relatively low density of ground coffee is also advantageous, as it can be used to fill relatively large grippers without weighing them down and straining the membrane. The items shown in Fig. For the compressive stress-strain curves and the volumetric strain measurements Fig.
For bending tests a cylindrical sample 0. The fact that this value is slightly larger than unity is likely caused by the indentation of the spheres into the soft membrane. We thank Sid Nagel for insightful discussions and Helen Parks for performing initial tests of the gripping strength. Author contributions: E. Conflict of interest statement: E. This article contains supporting information online at www. NOTE: We only request your email address so that the person you are recommending the page to knows that you wanted them to see it, and that it is not junk mail.
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Zakin , Hod Lipson , and Heinrich M. Eric Brown. Abstract Gripping and holding of objects are key tasks for robotic manipulators. Results and Discussion To evaluate gripping performance we performed pick-and-place operations in which objects were gripped, lifted, and moved Fig. Materials and Methods For pick-and-place performance evaluation we used a CRS A robotic arm, which includes high-pressure air lines, controlled by an imbedded solenoid valve.
Acknowledgments We thank Sid Nagel for insightful discussions and Helen Parks for performing initial tests of the gripping strength. Footnotes 1 To whom correspondence should be addressed. Int J Production Res 29 : — OpenUrl CrossRef. KGaA , Weinheim. Bicchi A Hands for dexterous manipulation and robust grasping: A difficult road toward simplicity. Int J Robotics Res 5 : 20 — Yoshikawa T , Nagai K Manipulating and grasping forces in manipulation by multifingered robot hands.
Int J Robotics Res 11 : — Smart Mater Struct 5 : — Ponce J , Faverjon B On computing three-finger force-closure grasps of polygonal objects. Choi H , Koc M Design and feasibility tests of a flexible gripper based on inflatable rubber pockets. Int J Mach Tool Manu 46 : — Hirose S , Umetani Y Development of soft gripper for the versatile robot hand. Mechanism and Machine Theory 13 : — Schmidt I Flexible molding jaws for grippers.