Liquid crystal elastomer strips as soft crawlers

Abstract

In this paper, we speculate on a possible application of Liquid Crystal Elastomers to the eld of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a at solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal,`breathing-like' deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a dierential inclusion for the displacement eld. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a nite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.

Rate-independent soft crawlers

“…Example 3.2. The case of a homogeneous discrete crawler with two contact points, Ω = {ξ 1 , ξ 2 } has been considered in [23]; such model is similar to the prototype presented in [51], and should be compared with two-anchor crawlers, for which shape change and friction manipulation occur at separate time phases (cf. Section 5).…”

“…The term ε(t, ξ), which represents our input on the system, is the active distortion, corresponds to the spontaneous strain of the point ξ of the body at time t. Such model applies well to active materials such as nematic elastomers [23]. The internal energy E(t, x) can be written in the form (2.3) by taking…”

“…Example 3.5. In [23], the motility of a homogeneous continuous crawler with anisotropic dry friction has been explicitly solved for a cyclic input consisting on a homogeneous contraction-extension, namely ε(t, ξ) = ε 0 (t), with ε 0 (t) a triangular wave oscillating between 0 and ∆ε > 0. Indicating with l = ξ b − ξ a the rest length of the crawler for ε 0 = 0, and assuming without loss of generality that µ − > µ + , it is shown that on average the crawler moves only if ∆ε > µ + l/k and the displacement produced in a cycle, in the direction of lower friction, is equal to…”

Coupled swelling and nematic reordering in liquid crystal gels

“…In fact, LCE crawlers can exploit the available maximal elongation in a cycle more effectively than LCG swimmers, reaching displacement per cycle of the order of the maximal available deformation (see equations (4.19) and (5.40) in Ref. 6), which is in turn a sizable fraction of the body length if deformations are sufficiently large.…”

Textures and shapes in nematic elastomers under the action of dopant concentration gradients

“…Reversible transitions of this kind were used for the construction of artificial walkers [23,24]. Further theoretical models envisage the use of repeated reshaping for propelling nematoelastic walkers [25,26] and swimmers [27]. Other reshaping effects were explored to produce the various bent forms that may serve as actuators [28][29][30][31][32] and "4D-printing" of structures variable in time [33].…”