Rotation Control, Interlocking and Self-positioning of Active Cogwheels

Gears and cogwheels restrain degrees of freedom and channel power into a specified motion. They are fundamental components of macroscopic machines. Interlocking microrotors similarly constitute key elements toward feasible micromachinery. Their assembly, positioning and control is a challenge at microscale, where noise is ubiquituous. Here, we show the assembly and control of a family of self-spinning cogwheels with varying teeth numbers and study interlocking mechanisms in systems of multiple cogwheels. The cogwheels are autonomous and active, with teeth formed by colloidal microswimmers that power the structure, and control its rotation rate. Leveraging the angular momentum of light with optical vortices, we control the direction of rotation of the cogwheels. We study pairs of interlocking cogwheels, that roll over each other in a random walk and curvature-dependent mobility. We leverage this feature to achieve self-positioning of cogwheels on structures with variable curvature and program microbots, notably demonstrating the ability to pick up, displace and release a load. This work highlights untapped opportunities of manufacturing at microscale using self-positioning components and constitutes an important step towards autonomous and programmable microbots.


Introduction
Biological nanomachines thrust life and dynamic processes across scales [1]: Molecular motors organize chromosomes [2], play a key role in cell division and are responsible for muscular contraction [3]. In contrast, our ability to realize microstructures that rival their biological counterparts is still in its infancy. Challenges are manifold, requiring: (i) suitable fabrication and assembly strategies at small scale, (ii) development of tools of control and communication in noisy environment and (iii) power generation at micro and nanoscale. It calls for novel strategies marrying tools of basic science with the recent progress in robotics [4,5]. The emerging field of active colloids -microscale particles that transduce energy at small scale-is uniquely suited to unlock those challenges and envision autonomous microbots of increasing complexity and versatility [6,7]. Progress in synthesis allows for bespoken design of microscale building blocks with programmable interactions [8,9,10,11,12], while energy injection enables motility and emergent properties of communications and control. For example, colloidal microswimmers direct autonomously in flows [13,14], leverage machine-learning strategies to navigate through noisy and unexplored environments [15] or communicate via clouds of chemical [16]. Remarkably, proofs of concepts of applications have also already been achieved, highlighting the relevance of the pathway for biomedical applications: swarms micropropellers penetrate the vitreous body of the eye [17], multifunctional rollers deliver cargos in physiological blood flow [18] and enzymatic nanomotors can travel in vivo within the bladder [19]. Further examples can be found in recent reviews of the impact of robotics for biomedical applications [20] or therapeutic treatments [21,22]. Those breakthroughs remain however limited to behavior at the single particle level and lack elementary mechanisms between elements, such as the interlocking of cogwheels. Previous works on cogwheels considered the realization of microfabricated devices powered by active colloids or bacteria [23,24,25], momentum transfer from light [26] or lightdriven dielectrophoretic forces [27,28]. They constituted large (> 30µm), monolithic structures, whose direction of rotation was encoded by a rigid template. We previously demonstrated the self-assembly of self-spinning microgears notably limited to a single number of teeth and lacking control on the direction of the rotation [29].
In contrast, we recently proposed a novel approach that uses templates of optical traps as algorithm to program metamachines, or machines made of machines [30]. In the present work, we leverage this versatile tool to assemble a family of autonomous cogwheels with varying number of teeth and control their chirality using optical vortices of light. We study this family of cogwheel and the behavior of interlocking pairs in contact. They exhibit a diffusive behavior when in contact, the two cogwheels rolling over each other with a mobility, which depends on the curvature. It makes possible for cogwheels to self-position, when interlocked with a structure of variable curvature, which we demonstrate. The ability of the cogwheels to self-position position highlights untapped opportunities for structures and microbots made from active components.

Assembly of a Family of Active Cogwheels
A family of self-spinning cogwheels is assembled using templates of optical traps as algorithms to program machines made of self-propelled colloids [30]. In brief, a colloidal bead is optically trapped and decorated with N peripheral optical traps, N being the number of teeth for the cogwheel [Fig.1A]. Active heterodimers travel along the substrate and are captured when crossing the optical traps. The trapping itself is a result of the interplay between alignment by repulsive scattering forces and propulsion, we previously discussed in [30]. As a result, we can assemble cogwheels made of a central sphere surrounded by N peripheral heterodimers: the teeth of the cogwheel [ Fig.1B, movie S1]. The optical traps are subsequently removed and the cogwheel spins autonomously. The procedure is repeated with different N to form a collection of cogwheels with varying teeth numbers. Practically, we use identical active heterodimers of radii d and vary the radius of the central particle to control the number of teeth N of the cogwheel. Repeating the procedure for central beads of increasing radii, we find that stable cogwheels correspond to active heterodimers packed on the periphery of the central sphere, i.e. 2πR = 2N d. Slight deviations from compact packing yields to unstable structures that disassemble [ Fig.1C]. We obtain from timelapse videos, the average rotation rateΩ N for self-spinning cogwheels from N=6 to 13 [ Fig.1D] and orientation θ N of the heterodimers forming the teeth of the cogwheel [ Fig.1E]. Remarkably, we observe that the mean orientation θ N follows cos θ N ∝ 1/R (Eq.1) [ Fig.1F], high-lighting a coupling between orientation of the heterodimers of the cogwheel and curvature. A quantitative understanding of this scaling will require the detailed modeling of hydrodynamics and phoretic interactions in this multi-body systems and is beyond the scope of this paper. We however use this empirical relationship to relate rotation rate of the cogwheels with their curvature. As the rotation of the cogwheel results from the translational velocity V 0 of the active heterodimers, we expect RΩ N ∝ V 0 cos θ N , which gives Ω N ∝ 1/R 2 [Eq.2], in reasonable agreement with experimental data [ Fig.1D], notwithstanding that the simple geometric argument neglects interactions between active heterodimers.

Rotation Control by Optical Vortices
At this point, we demonstrated the assembly of a family of spinning cogwheels, with tunable gears number. After release of the template, the active heterodimers, that form the teeth, momentarily fluctuate, before a cogwheel starts spinning. The direction of rotation is random, resulting from a spontaneous symmetry-breaking.

Dynamics of Interlocked Cogwheels
When two microgears are distant, they interact via phoresis, leading to synchronization mediated by clouds of chemicals. The description of the synchronization can be found in [29,33], with the notable predictions that the radial component of the interaction decays rapidly with distance, as 1/r N +2 , where r is the center to center distance between two cogwheels and N is the teeth number. Distant synchronization furthermore requires to prevent the cogwheels to drift apart by phoretic repulsion [29,33]. We instead turn to the study of the interlocking behavior of pairs of cogwheels in contact and show that it forms a robust and autonomous mechanism.
We consider a cogwheel with fixed number of teeth, N 1 = 8, in contact with a second cogwheel, for which N 2 varies between N 2 = 6 and N 2 = ∞, the flat in-

Discussion
It results, that a cogwheel interlocked with a structure with variable curvature constitutes will remain in contact and form a stable pair with a dynamical structure.
In order to test this prediction, we study the dynamics of a cogwheel, with N=8, put in contact with a structure with variable curvature [Fig.3E] This work demonstrates the potential of active colloids to form autonomous structures, and mechanisms. It shows autonomous machinery with external control: direction of rotation set by optical vortices or migration along optical tracks formed by a light gradient. Using self-positioning components, it unveils an untapped approach to manufacture complex microbots. It highlights how modern robotics can benefit from fundamental advances in colloidal science and active matter. The ability to direct the mechanism using external stimuli, such as light patterns, or concentrations gradients to achieve cyclic transformations or pro-grammable morphing of structures remains to be explored. Similarly the communications between structures and coordinated movement between parts is a challenge that will need to be addressed towards advanced machineries. The potential of active cogwheels to power passive microstructures is a possible avenue of progress towards active microfluidics and robotics at small scale that will similarly benefit from this work.

Synthesis of hematite cubes
Synthesis of hematite cubes follows the method described by Sugimoto [36].
Briefly, we mix 100 mL of 2M FeCl 3 · 6H 2 O, 90 ml 6 NaOH and 10 ml water, in a 250 mL pyrex bottle and shake thoroughly. The bottle is then placed in an oven at 100 • C for 3 to 4 days, until the hematite particles reach desired size. The resulting hematite cubes in the gel network are isolated by successive sedimentation and resuspended in DI water.

Synthesis of heterodimers
Synthesis of heterodimer particles is performed by heterogeneous nucleation of trialkoxysilanes (oil precursor) on hematite particles as seeds. The synthesis procedure is adapted from ref. [37], with chemical modification to reinforce the stability of the heterodimer under light illumination. In particular, we make use of a hydrophobic copolymer Hexadecyltrimethoxysilane (HTS) to chemically protect the bond between the hematite and polymer core against highly reactive hydroxil radicals generated during H 2 O 2 consumption. A beaker with 100 mL of DI water is prepared, and mixed with 120 µL of a 50% NH 3 solution, giving a pH ∼ 10.

Data availability
The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon request. (C) Experimental procedure leading to the control of chirality of the cogwheels using Optical Vortices and measurement of the rotation velocity of a cogwheel, with N=9 (green trace). The cogwheel is initially spinning counter-clockwise rotation. It is shortly immobilized (∼ 1s) by a template of optical traps (grey area). The traps are removed and an optical vortex is applied briefly (∼ 100ms, red area and arrow), applying a torque, that reorient the teeth and set the chirality of the cogwheel. The cogwheel spins clockwise. In inset, bright field images of the cogwheel corresponding to the black dot on the timeline. Scale bar is 5µm. (D) The procedure is repeated to control the chirality over 15 cycles of reversal, exhibiting remarkable reproducibility of the rotation velocity. The shaded area corresponds to the timeline shown in (C).