Kinematic amplification strategies in plants and engineering Victor Charpentier, Philippe Hannequart, Sigrid Adriaenssens, Olivier Baverel, Emmanuel Viglino, Sasha Eisenman To cite this version: Victor Charpentier, Philippe Hannequart, Sigrid Adriaenssens, Olivier Baverel, Emmanuel Viglino, et al.. Kinematic amplification strategies in plants and engineering. Smart Materials and Structures, IOP Publishing, 2017, 26 (6), pp.63002 - 63002. 10.1088/1361-665X/aa640f. hal-01618277 HAL Id: hal-01618277 https://hal-enpc.archives-ouvertes.fr/hal-01618277 Submitted on 17 Oct 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. 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Page 1 of 30 AUTHOR SUBMITTED MANUSCRIPT - SMS-104018.R2 1 2 3 Kinematic amplification strategies in plants and engineering 4 5 6 1 2,3 1 2 7 Victor Charpentier* , Philippe Hannequart* , Sigrid Adriaenssens , Olivier Baverel , 3 4 8 Emmanuel Viglino , Sasha Eisenman 9 10 1Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ, USA 11 12 2 Laboratoire Navier, UMR 8205, École des Ponts, IFSTTAR, CNRS, UPE, Champs-sur-Marne, France 13 14 3 Arcora, Ingérop Group, Rueil-Malmaison, France 15 16 4 Department of Landscape Architecture and Horticulture, Temple University, Ambler, PA, USA 17 18 19 *The authors designated have contributed equally to the research and writing of the manuscript 20 21 22 23 Abstract: 24 While plants are primarily sessile at the organismal level, they do exhibit a vast array of 25 movements at the organ or sub-organ level. These movements can occur for reasons as diverse 26 as seed dispersal, nutrition, protection or pollination. Their advanced mechanisms generate a 27 28 myriad of movement typologies, many of which are not fully understood. In recent years, there 29 has been a renewal of interest in understanding the mechanical behavior of plants from an 30 engineering perspective, with an interest in developing novel applications by up-sizing these 31 mechanisms from the micro- to the macro-scale. This literature review identifies the main 32 strategies used by plants to create and amplify movements and anatomize the most recent 33 34 mechanical understanding of compliant engineering mechanics. The paper ultimately 35 demonstrates that plant movements, rooted in compliance and multi-functionality, can 36 effectively inspire better kinematic/adaptive structures and materials. In plants, the actuators 37 and the deployment structures are fused into a single system. The understanding of those natural 38 movements therefore starts with an exploration of mechanisms at the origins of movements. 39 40 Plant movements, whether slow or fast, active or passive, reversible or irreversible, are 41 presented and detailed for their mechanical significance. With a focus on displacement 42 amplification, the most recent promising strategies for actuation and adaptive systems are 43 examined with respect to the mechanical principles of shape morphing plant tissues. 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 AUTHOR SUBMITTED MANUSCRIPT - SMS-104018.R2 Page 2 of 30 1 2 3 4 5 Introduction 6 Biology serves as inspiration for engineering kinematics and has been doing so for a long time. 7 Designers tend to search nature for solutions to particular engineering problems. This direct approach 8 9 has provided many successful engineering products but has constrained us, engineers, to the role of 10 observers. As exposed by Vincent [1], the solutions provided by biology to problems challenge our 11 rational, rigorous problem solving approaches. Taking note of the variety of mechanisms involved in 12 plant movements, there has been a renewal of the interest in understanding the mechanical behavior of 13 plants for structural morphings. Structural morphings modify the structures with continuous shape 14 changes only, no movements of discrete parts are involved [2]. As such they are a subcategory of 15 adaptive structures, a structure is called adaptive as soon as it presents an alteration of its geometry 16 and/or material properties [3]. Plants are morphing structures in the purest sense of the term. The 17 continuity of the material is key to the existence of a living entity and to the coherent movement of 18 autonomous structures. The diversity of environments and situations where plants successfully adapted 19 provides a breadth of problem solving examples. There is however a need to break down the mechanical 20 strategies developed in plants to insure that identified kinematic mechanisms are made available to the 21 22 designer. 23 Engineered adaptive structures and actuators increasingly implement compliance in their design. As 24 such, the observation of plant-generated movements can lead to novel morphing schemes in engineered 25 structures. The origins of active plant movements and plant mechanics have been presented in detail in 26 [4-12]. In light of material advances, downscaling of manufacturing and computer aided design, many 27 new interdisciplinary applications appear that make use of a nature-inspired palette of solutions for 28 engineering problems. In engineering the interest for morphing is growing in many fields such as 29 aerospace industry [2, 13], building engineering [14], micro-scale actuation [15], wind turbines [16, 17], 30 automotive industry [18] or medicine [19]. 31 Kinematic amplification in plants and in engineering is reviewed in this paper. The kinematic 32 amplification, also called distance advantage, is defined as the ratio of output displacement to input 33 displacements in a kinematic system. The amplification ratio measures the efficiency of structures at 34 35 transforming the input actuation into large displacements. The input displacement considered in this 36 paper encompasses both the rigid bar displacements of classical mechanisms and the displacement 37 resulting from material strain over the whole length of the active material. Assessing the kinematic 38 amplification in mechanisms is essential to understanding and emulating their strategies in adaptive 39 structures. Parallel to kinematic amplification but not treated here is force amplification, also referred 40 to as mechanical advantage. It is the ratio of the output force over the input force of the mechanism. 41 Force amplification is not considered in this review but it is not completely unrelated to kinematic 42 amplification. In the simpler case of lever mechanisms or gears, the force amplification ratio (FAR) is 43 the inverse of the kinematic amplification ratio (KAR)1. 44 The hypothesis guiding the biology study is that even the most basic generations of plant movement 45 involve some degree of kinematic amplification. In hydraulics powered movements (active or passive), 46 the input displacement considered for the kinematic amplification is the total expansion of the active 47 48 layer of tissue (intermediate-scale assemblage of cells to create a rigid building material). Such 49 mechanism can be so effective that the kinematic amplification ratio can reach ∼200 in Aldrovanda 50 Vesiculosa [20] and ∼160 in pine cones [21]. Similarly high KAR values have been measured in bimetal 51 actuators (∼140 in [22]), which gives ground for a comparison of plant and engineering mechanisms. 52 In animals this value is often lower due to the lever mechanisms in musculoskeletal systems. For 53 instance, the KAR reaches values of ∼2 in the mantis shrimp raptorial appendage [23] or ∼6 in the 54 human biceps-elbow joint [24]. 55 This review presents an organized comparison of natural and state-of-the-art engineered movements and 56 draws parallels to nature from recent engineering studies to categorize strategies that have successfully 57 replicated or synthesized plants. Plant mechanics have often been described on a case-by-case basis. By 58 59 60 1 Considering a lever of short arm length a and long arm length b, the FAR given by the equation of equilibrium at the fulcrum is a/b while the KAR given by the ratio of arc length of the end points of the lever is b/a. Considering a set of two gears A (input) and B (output) of respectively radii rA & rB and angular speeds ωA & ωB, the FAR given by the gear reduction is rB / rA. while the KAR given by the equation of equal speed at the point of contact is rA / rB Page 3 of 30 AUTHOR SUBMITTED MANUSCRIPT - SMS-104018.R2 1 2 3 grouping the kinematic amplification types in plants, the objective is to provide the designer a toolbox 4 to explore new possibilities in compliant mechanisms. By placing those amplification mechanisms in 5 their context, another objective is to help the engineer understand the origin of the solutions found in 6 biology and to create the basis for new innovative combinations of actuations and amplifications. The 7 8 engineered structures are not necessarily directly inspired by plant mechanics but similarities organically 9 appeared between the two. Therefore the review also includes a large exploration of engineering 10 kinematic amplification mechanisms. 11 In section 2 the origins of plant movements and five identified kinematic