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Research Papers

Development of n-DoF Preloaded Structures for Impact Mitigation in Cobots

[+] Author and Article Information
S. Seriani

Department of Architecture and Engineering,
University of Trieste,
via A. Valerio 10,
Trieste 34127, Italy
e-mail: sseriani@units.it

P. Gallina

Department of Architecture and Engineering,
University of Trieste,
via A. Valerio 10,
Trieste 34127, Italy
e-mail: pgallina@units.it

L. Scalera

Polytechnic Department of Engineering
and Architecture,
University of Udine,
via delle Scienze 206,
Udine 33100, Italy
e-mail: scalera.lorenzo@spes.uniud.it

V. Lughi

Department of Architecture and Engineering,
University of Trieste,
via A. Valerio 10,
Trieste 34127, Italy
e-mail: vlughi@units.it

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received November 24, 2017; final manuscript received May 31, 2018; published online July 18, 2018. Assoc. Editor: Raffaele Di Gregorio.

J. Mechanisms Robotics 10(5), 051009 (Jul 18, 2018) (10 pages) Paper No: JMR-17-1395; doi: 10.1115/1.4040632 History: Received November 24, 2017; Revised May 31, 2018

A core issue in collaborative robotics is that of impact mitigation, especially when collisions happen with operators. Passively compliant structures can be used as the frame of the cobot, although, usually, they are implemented by means of a single-degree-of-freedom (DoF). However, n-DoF preloaded structures offer a number of advantages in terms of flexibility in designing their behavior. In this work, we propose a comprehensive framework for classifying n-DoF preloaded structures, including one-, two-, and three-dimensional arrays. Furthermore, we investigate the implications of the peculiar behavior of these structures—which present sharp stiff-to-compliant transitions at design-determined load thresholds—on impact mitigation. To this regard, an analytical n-DoF dynamic model was developed and numerically implemented. A prototype of a 10DoF structure was tested under static and impact loads, showing a very good agreement with the model. Future developments will see the application of n-DoF preloaded structures to impact-mitigation on cobots and in the field of mobile robots, as well as to the field of novel architected materials.

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Figures

Grahic Jump Location
Fig. 1

Behavior of cobots during a collision: in (a), a rigid-link cobot is shown in its initial position with respect to an obstacle; in (b), the collision between the two is shown;in (c), a cobot with compliant links is shown; and in (d), the collision is shown to cause an elastic deformation of the first link

Grahic Jump Location
Fig. 2

Difference between linear and preloaded elastic structures: in (a), a simple linearly elastic structure is shown, while in (b) a preloaded elastic mechanism is visible in series to the structure; preload is defined by the pair of outward-looking triangles, indicating a compressed spring. Respectively, in (c) and (d), the force–displacement relations between linear and preloaded structures are illustrated, whereas in (e) and (f) the stored elastic energies E1,2 are represented for the two cases.

Grahic Jump Location
Fig. 3

Definitions of the fundamental preloaded elements and their elementary combinations, along with an illustration of the nominal elastic behavior: in (a), a translational traction element is shown. The mechanical limit is shown in blue, where the spring preload direction is indicated by the inward facing triangles, meaning that a traction preload is present; in (b), the compression counterpart is shown, in this case the preload is compressive; in (c), the combination of (a) and (b) is visible; in (d)–(f), the same is illustrated for the rotational case. The plots in (g)–(i) show the elastic law for the solutions above each one.

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Fig. 4

Some examples of preloaded structures, from one-dimensional (1D) element to 3D arrays. The first row shows the fundamental preloaded elements: translational and rotational. Combinations of monodimensional preloaded structures are visible in the second row: a translational compression-traction solution, a 2DoF rotational one, and a combined translational-rotational structure. The third row shows planar 2D arrays of translational preloaded elements and of combined translation-rotation elements. The last row shows a 3D translation-rotation array.

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Fig. 5

Multiple-DoF model for a serial preloaded structure: in (a), the kinematics is shown; in (b), the boundary constraints and loading conditions are shown: the elastic “ground” implementation and the impactor of mass md; and in (c), the shape of the nonlinear preloaded stiffness curve is shown for the general joint i; note that the relation is symmetric with respect to zero

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Fig. 6

Diagram of the fundamental unit of the s-structure: in (a), a general “at rest” view is shown, along with labels to the main components; in (b), the upward configuration is shown; and in (c), the downward one

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Fig. 7

Prototype segment: in (a), the structure can be seen from the outside and in (b), a section view is shown, with the main internal components

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Fig. 8

Experimental prototype and capture system. The complete system is shown in (a), along with the impactor and the impact spring. The reader can appreciate the different visible portion of the screws on the joints' springs, signaling different preload values. In subfigures (b)–(e), some snapshots of the beam are visible during the impact experiment. In this case, time is referred to the instant when impact happens (t=0s).

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Fig. 9

Error analysis: in the first plot from the top, the cable length error due to the asymmetric effect of the pulley on the cable can be seen; in the second plot, the y-coordinate of point Qn is shown against time in both the nominal and small-angles approximation, whereas in the last plot the relative error εn,rel can be seen

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Fig. 10

Static stiffness plot of the beam. The displacement Δy is measured at point P6 in the model and at the corresponding point in the prototype. On the left, the numerical and experimental curves are shown, while on the right the displacement error is reported.

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Fig. 11

Coordinate y of the barycenter Qi of the links over time following impact at t=0.225s of the impactor. A comparison between results of the numerical (solid line, Δt=10−5) and experimental (dashed line, Δt=10−3) runs is shown.

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Fig. 12

Relative error between experimental and numerical results for the five links; the values are relative to the maximum absolute Qy,i of each link's experimental result. Error values are bound to the 0–1 interval.

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