On zero stiffness

Zero-stiffness structures have the remarkable ability to undergo large elastic deformations without requiring external work. Several equivalent descriptions exist, such as (i) continuous equilibrium, (ii) constant potential energy, (iii) neutral stability and (iv) zero stiffness. Each perspective on zero stiffness provides different methods of analysis and design. This paper reviews the concept of zero stiffness and categorises examples from the literature by the interpretation that best describes their working principle. Lastly, a basic spring-to-spring balancer is analysed to demonstrate the equivalence of the four different interpretations, and illustrate the different insights that each approach brings. This is the accepted version of an article first published in Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. The final version is available online at http://pic.sagepub.com/content/early/2013/11/14/0954406213511903.abstract

Study on the large-displacement behaviour of a spiral spring with variations of cross-section, orthotropy and prestress

This work is dedicated to the study of the large-displacement behaviour of a spiral spring. Parameters that influence the local torsion stiffness of the beam that constitutes the spiral are varied and their effect is studied. Cross-sectional shape, orthotropic material orientation and prestress are the three classes of parameters that are varied. The effect that the local change in torsional stiffness has on the overall behaviour is illustrated in a linearised way by comparing in-plane and out-of-plane stiffnesses, and nonlinearly, by inspecting a graphical representation of the potential energy field of the system. Several embodiments composed of multiple spirals are showed to illustrate how the understanding of the nonlinear behaviour could be exploited in conceptual design of compliant mechanisms.</p

Kinky structures

Rotational springs are not widely used in structural engineering other than within undergraduate texts to aid with the understanding of strut buckling or other similar theoretical exercises.The inclusion of rotational springs can significantly alter the behaviour of a structure, bringing several potential benefits if inserted strategically. For instance, allowing a frame to be delivered to site as a single deployable piece, where the rotational springs introduce an element of temporary stability during erection; by ensuring hinges form in specific locations during extreme loading events, creating reliable load paths whilst retaining structural integrity; or by limiting the axial force in specific elements, forcing an element to buckle at specific loads. Currently, there is a significant gap in the existing research with regards the analysis and behaviour of structures that have springs distributed through the frame. The inclusion of springs within structural frames will typically encourage gross, yet controlled and predictable displacements that are challenging to analyse. Equally, deployable structures require an element of instability to deploy. With most research focusing on the packed and deployed states of these structures, there is still considerable research to be done on the structural performance of the intermediate stages of deployment. Several forms of deployable structure, such as cable-chain arches for example, are vulnerable and unstable during their intermediate deployment phase and it is proposed that the integration of rotational springs in these types of structure could help control the deployment and maintain stability from a packed shape into the final in-service form as well as preventing phenomenon such as snap-through buckling under large loads. Original work within this thesis creates several repeatable and reliable methods for undertaking buckling analysis of sprung chains to determine an initial balanced equilibrium form to which in-service loadings can then be applied as well as determining the post-buckled behaviour for sprung structures. The application of numerical analysis methods is demonstrated as giving reliable results for single and multiple degrees of freedom systems, but due to the potential for incompatibilities between the stiffnesses of the rotational springs and beam elements there are issues associated with ill-conditioning and methods have been established to identify and mitigate these effects.Alternative structural forms, beyond simple arches, have also been developed through seeking inspiration from the higher buckling modes. Shapes resembling these higher modes have been generated through the careful manipulation of spring stiffnesses (mobilising linear and non-linear springs) combined with the introduction of initial geometrical imperfections allowing the structures to adopt alternative stable states in direct response to specific loading conditions.The analysis methods contained within this thesis are currently more advanced than the manufacturing techniques required to realise these designs in the real world. Although, flexible springs are already being cut into stiff plywood panels using living hinges and multi-material 3D printing is commonplace within the maker community, but these techniques have not yet progressed through to the scale and consistency needed to fabricate a large structural element.However, as these manufacturing techniques mature, the work presented within this thesis will provide a solid base from which the effective analysis of multi-stiffness structures will be possible

Developing Design and Analysis Framework for Hybrid Mechanical-Digital Control of Soft Robots: from Mechanics-Based Motion Sequencing to Physical Reservoir Computing

The recent advances in the field of soft robotics have made autonomous soft robots working in unstructured dynamic environments a close reality. These soft robots can potentially collaborate with humans without causing any harm, they can handle fragile objects safely, perform delicate surgeries inside body, etc. In our research we focus on origami based compliant mechanisms, that can be used as soft robotic skeleton. Origami mechanisms are inherently compliant, lightweight, compact, and possess unique mechanical properties such as– multi-stability, nonlinear dynamics, etc. Researchers have shown that multi-stable mechanisms have applications in motion-sequencing applications. Additionally, the nonlinear dynamic properties of origami and other soft, compliant mechanisms are shown to be useful for ‘morphological computation’ in which the body of the robot itself takes part in performing complex computations required for its control. In our research we demonstrate the motion-sequencing capability of multi-stable mechanisms through the example of bistable Kresling origami robot that is capable of peristaltic locomotion. Through careful theoretical analysis and thorough experiments, we show that we can harness multistability embedded in the origami robotic skeleton for generating actuation cycle of a peristaltic-like locomotion gait. The salient feature of this compliant robot is that we need only a single linear actuator to control the total length of the robot, and the snap-through actions generated during this motion autonomously change the individual segment lengths that lead to earthworm-like peristaltic locomotion gait. In effect, the motion-sequencing is hard-coded or embedded in the origami robot skeleton. This approach is expected to reduce the control requirement drastically as the robotic skeleton itself takes part in performing low-level control tasks. The soft robots that work in dynamic environments should be able to sense their surrounding and adapt their behavior autonomously to perform given tasks successfully. Thus, hard-coding a certain behavior as in motion-sequencing is not a viable option anymore. This led us to explore Physical Reservoir Computing (PRC), a computational framework that uses a physical body with nonlinear properties as a ‘dynamic reservoir’ for performing complex computations. The compliant robot ‘trained’ using this framework should be able to sense its surroundings and respond to them autonomously via an extensive network of sensor-actuator network embedded in robotic skeleton. We show for the first time through extensive numerical analysis that origami mechanisms can work as physical reservoirs. We also successfully demonstrate the emulation task using a Miura-ori based reservoir. The results of this work will pave the way for intelligently designed origami-based robots with embodied intelligence. These next generation of soft robots will be able to coordinate and modulate their activities autonomously such as switching locomotion gait and resisting external disturbances while navigating through unstructured environments

A Programmably Compliant Origami Mechanism for Dynamically Dexterous Robots

We present an approach to overcoming challenges in dynamical dexterity for robots through programmably compliant origami mechanisms. Our work leverages a one-parameter family of flat sheet crease patterns that folds into origami bellows, whose axial compliance can be tuned to select desired stiffness. Concentrically arranged cylinder pairs reliably manifest additive stiffness, extending the programmable range by nearly an order of magnitude and achieving bulk axial stiffness spanning 200–1500 N/m using 8 mil thick polyester-coated paper. Accordingly, we design origami energy-storing springs with a stiffness of 1035 N/m each and incorporate them into a three degree-of-freedom (DOF) tendon-driven spatial pointing mechanism that exhibits trajectory tracking accuracy less than 15% rms error within a (2 cm)^3 volume. The origami springs can sustain high power throughput, enabling the robot to achieve asymptotically stable juggling for both highly elastic (1 kg resilient shotput ball) and highly damped (“medicine ball”) collisions in the vertical direction with apex heights approaching 10 cm. The results demonstrate that “soft” robotic mechanisms are able to perform a controlled, dynamically actuated task