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This dissertation explores the design and optimization of compliant systems through two case studies. In the first case study, a new six-axis positioner, called a hexblade positioner, that achieves high speeds over large ranges with high precision was introduced. The positioner achieves these capabilities due to its bent-blade-flexure topology, which decouples its 6 actuators. A matrix-based analytical approach is used to model the stiffness and inertia of the positioner’s topology and its performance capabilities are subsequently calculated and plotted for each version of the design over a comprehensive sweep of its geometric parameters. The approach is verified by comparing its modal analysis results with finite-element-analysis results performed on the same designs sampled from the parameter sweep. An optimal version of the design is fabricated and frequency-sweep data is provided to (i) demonstrate the design’s open-loop dynamic performance capabilities in all 6 degrees of freedom and (ii) experimentally validate the analytical approach. The second case study proposed a compliant-mechanism-based mattress designed to prevent the formation of bedsores by alternating the support pattern beneath patients' bodies to keep any region from being subjected to prolonged pressure exceeding threshold levels. A custom-designed actuator bed was fabricated and capable of changing patterns to identify the optimal configuration parameters for the mattress. Pressure data collected from an anatomically accurate dummy positioned on the actuator bed was analyzed to determine the optimal parameters, which were then subsequently used to design the geometric dimensions of the proposed mattress. The mattress achieves a stable 2D undulating pattern of alternating peaks and pits resembling a checkerboard layout under the user's weight. Results demonstrate that the mattress significantly reduces the areas under prolonged pressure exceeding threshold levels compared to when the dummy is on a flat surface, with the applied switching force considerably less than the weight of the dummy.

This dissertation lays the foundation for the FACT Design Add-in for SolidWorks. A software design tool that guides users to create compliant mechanisms with no prior knowledge of the theory. This tool implements the rules of the freedom and constraint topology (FACT) design approach and automates the steps that are rooted in screw theory so that only kinematically valid designs can be created. This automation, however, has required theoretical expansions to the FACT design theory. Namely, the autonomous identification of freedom spaces and visually based methods to analyze and synthesize interconnected hybrid mechanisms. The identification of freedom spaces from any set of twists is a core task of the add-in. This method is facilitated by the principal geometry, a proposed set of twists for each freedom space, that show all valid options of its origin and orientation. However, the main contribution of this work is the visual analysis and synthesis of interconnected hybrid mechanisms. These are the most generic type of mechanism where the joints are not purely parallel nor serial to one another. The analysis method is the visual implementation of prior numeric methods and introduces a comprehensive transmission and load path theory to the FACT design approach. The analysis method is then converted into a synthesis approach. This is the first general synthesis method for interconnected hybrid mechanisms and completes the field of visual mechanism synthesis. This dissertation also presents a one degree-of-freedom (DOF) transmission mechanism. This is a large-range-of-motion compliant mechanism that uses a central screw DOF of a joint to convert a rotational input to a collinear translational output and vice versa. This mechanism serves as a powerful example of what can be created with the FACT Design Add-in; facilitating such creations is the motivation behind this work.

Robots are traditionally composed of rigid components for their strength and predictability while performing precise, powerful, controllable movements. However, the lack of deformability limits a robot’s capacity to passively adapt to changing tasks and environments. Conversely, soft robots intentionally incorporate material and geometric compliance to passively adapt to challenges. Soft robot performance can be further advanced by leveraging anisotropy; physical properties that are different in different directions.In my work we use soft robotics with anisotropic properties to address a diverse array of robotic challenges. 1) We used gecko-inspired adhesives, an anisotropic compliant micro-structure which can apply high shear force with near-zero normal force, on a flexible belt in place of rigid gear teeth to create a low-cost, continuously variable transmission with high gear ratios. 2) We made a soft pneumatic gripper with fingers whose stiffnesses vary with direction and joint position to passively adopt a pinch or wrap grasp depending on the shape of the object it is to grasp. 3) We leveraged a woven fabric’s ability to stretch when pulled at 45° to its inelastic warp and weft directions to create a fabric pneumatic artificial muscle. 4) We advanced the design of a tip-extending vine robots, a device that is stiff radially but lengthens from its tip with little resistance when inflated, by creating a camera mount, retraction device, and steering method. 5) With a modified version of the isotropic vine robot concept, we used biologically inspired principles including tip extension and asymmetric, directional air fluidization to manipulate granular forces to enable robotic burrowing in sand. 6) And finally, we are exploring several planetary applications of self-anchoring by creating an anisotropic root-like anchor that requires more force to pull out of the ground than to grow deeper. I believe my work will have wide- ranging impacts on a variety of fields from medical devices and agricultural monitoring to industrial inspection and planetary exploration.

Differential mechanisms are remarkable mechanical elements that are widely utilized in various systems; nevertheless, conventional differential mechanisms are heavy and difficult to use in applications with limited design space. In this paper, a curved lightweight compliant type of differential mechanism is presented. This mechanism acquires its differential characteristic by having a high rotational stiffness when the mechanism is symmetrically actuated on two sides, while having a low rotational stiffness when actuated only on one side. The intrinsic elastic strain energy required for deformation of the compliant differential is compensated for by reintroduction of potential energy to make the mechanism neutrally stable. For the storage of potential energy, two preloaded linear springs were used. The rotational stiffness of the one-sided actuation around the neutral position of the compliant differential mechanism is hypothesized to be adjustable by changing the preload of the springs. The stiffness can be positive, zero, and negative, meaning that the mechanism can have neutral stability and bistability. The hypothesis is investigated using a simulated model in Ansys Parametric Design Language using optimized parameters to achieve the desired stiffness for the mechanism. The simulated model is validated using an experimental setup for both the one-sided and symmetrical actuation stages. The experimental results showed a high correlation with the simulations. The mechanism with optimized dimensions and preload showed neutral stability for a range of 16°. Bistability was found for preloads higher than the aforementioned optimized preload. A linear trend was found between the preload of the springs and the rotational stiffness of the mechanism at θ = 0. Furthermore, an output/input kinematic performance of 0.97 was found for the simulated results and 0.95 for the experimental results.

The purpose of this research is to investigate the design of an electrostatic discharge protection device made of single-layer graphene nanoribbons. The device is meant to trigger electrostatic discharge at a target voltage of 1.5V. Other design requirements include the minimization of parasitic capacitance, electrical response time and mechanical response time. The device is designed to discharge static electricity by being pulled to ground through electrostatic forces, then making contact with ground before returning to its original position. Previous designs experienced repeatability issues due to a lack of securing the ribbon and mechanical failure due to high stresses at the boundary conditions. New designs are presented and optimized to maintain a high effective spring constant for the device while reducing stress during electrostatic pull-in. A single-degree-of-freedom model is used in conjunction with the Bernoulli-Euler beam equations and Castigliano’s method to guide the design process. Multi-degree-of-freedom and finite element models are used to validate the predicted pull-in behavior of the new devices and to explore how stresses and reaction forces might affect the reliability. A residual PMMA layer that results from the fabrication process is also incorporated into the finite element model. Molecular dynamics simulations are performed to further explore the behavior of graphene nanoribbons under electrostatic pull-in and to check the accuracy of the finite element approach. The fabrication process is explained and experimental results for the new devices are reported.

This thesis introduces a general method for analyzing and synthesizing flexure systems of any configuration, including those that cannot be broken into parallel and serial subsystems. Such flexure systems are called interconnected hybrid flexure systems because they possess limbs with intermediate bodies that are connected by flexure systems or elements. Specifically, the method introduced utilizes screw algebra and graph theory to help designers determine the freedom spaces (i.e., the geometric shapes that represent all the ways a body is permitted to move) for all the bodies joined together by compliant flexure elements within interconnected hybrid flexure systems (i.e., perform mobility analysis of general flexure systems). This method also allows designers to determine (i) whether such systems are under-constrained or not and (ii) whether such systems are over-constrained or exactly-constrained (i.e., perform constraint analysis of general flexure systems). Although many flexure-based precision motion stages, compliant mechanisms, and microarchitectured materials possess topologies that are highly interconnected, the theory for performing the mobility and constraint analysis and synthesis of such interconnected flexure systems using traditional screw theory does not currently exist. The theory introduced here lays the foundation for an automated tool that can rapidly generate the freedom spaces of every rigid body within a general flexure system without having to perform traditional computationally expensive finite element analysis. Case studies are provided to demonstrate the utility of the proposed theory.

In this study, a flexure-based (compliant) linear guide with a motion range comparable to its footprint is presented. The design consists of two-folded leaf springs on which torsion reinforcement structures are added. Due to these structures, only two-folded leaf springs are needed instead of a minimum of five as in preexisting designs. The new design is compared to such a preexisting design, after optimizing both on a support stiffness metric. The new design scores over twice as high on the support stiffness metric, while occupying a smaller (−33%) and a less obstructive build volume. Stress, build volume, and manufacturing limitations are taken into account. In addition, a variation on the new design using three torsion reinforced folded leaf springs is presented and optimized. This design occupies a build volume similar to the preexisting design, but scores four times higher on the support stiffness metric. A prototype of the new design is built and its parasitic eigenfrequencies are measured, validating the theoretical models (normalized mean absolute error of 4.3%).

Continuum robots are able of in-situ inspection tasks in cluttered environments and narrow passages, where conventional robots and human operators cannot intervene. However, such intervention often requires the robot to interact with the environment, and the low stiffness and payload of continuum robots limits their intervention capabilities. In this paper, we propose a paradigm shift from individual to multiple continuum robots, which can reach the target environment from different paths and then physically connect, reconfiguring into a parallel architecture to enhance precision, stiffness, and payload. The main challenges in modelling and controlling cooperative continuum robots are outlined, and an experimental comparison between individual and cooperating continuum robots that connect through a novel shape-memory-alloy-based clutch highlights the advantages of the proposed technology.

Under-actuated robots are very interesting in terms of cost and weight since they can result in a state-controllable system with a number of actuators lower than the number of joints. In this paper, a comparison between an under-actuated planar three-degrees-of-freedom (DOF) robot and a comparable fully actuated two-degrees-of-freedom robot is presented, mainly focusing on the performances in terms of trajectories, actuator torques, and vibrations. The under-actuated system is composed of two active rotational joints followed by a passive rotational joint equipped with a torsional spring. The fully actuated robot is inertial equivalent to the under-actuated manipulator: the last link is equal to the sum of the last two links of the under-actuated system. Due to the conditions on the inertia distribution and spring placement, in a simple point-to-point movement the last passive joint starts and ends in a zero-value configuration, so the three DOF robot is equivalent, in terms of initial and final configuration, to the two DOF fully actuated robot, thus they can be compared. Results show how while the fully actuated robot is better in terms of reliable trajectory and actuator torques, the under-actuated robot wins in flexibility and in vibrations at a given configuration.

International audience; Compliant Mechanisms (CMs) present several desired properties for mechanical applications only depending on elastic deformation of the involved compliant beams/flexures. As reported in the current literature, most CM designs utilize straight beams and initially curved beams (ICBs) as the fundamental flexible members. In CM research community, many great contributions regarding modeling these elementary flexible members have been achieved. In this paper, a comprehensive modeling methodology, based on beam theory, has been established to characterize the static planar deflection of slender beam. Then such a methodology has been applied to solve 8 loading scenarios of large beam-deflection problems that exist in the design of CMs. Essentially speaking, all these beam-deflection problems are treated as a type of boundary value problems (BVPs) of an ordinary differential equation (ODE) and solved by a modified collocation method. After that, this methodology has been used to model some representative CMs with large-deflection strokes, such as compliant parallelograms.

Compliant mechanisms are widely used for instrumentation and measuring devices for their precision and high bandwidth. In this paper, the mechatronic model of a compliant 3PRS parallel manipulator is developed, integrating the inverse and direct kinematics, the inverse dynamic problem of the manipulator and the dynamics of the actuators and the control. The kinematic problem is solved, assuming a pseudo-rigid model for the deflection in the compliant revolute and spherical joints. The inverse dynamic problem is solved, using the Principle of Energy Equivalence. The mechatronic model allows the prediction of the bandwidth of the manipulator motion in the 3 degrees of freedom for a given control and set of actuators, helping in the design of the optimum solution. A prototype is built and validated, comparing experimental signals with the ones from the model. Authors would like to thank the Ministerio de Ciencia e Innovación of the Spanish government for funding the project PID2019-105262RB-I00.

Considering a modern approach to design, one of the viable options for developing innovative projects is the possibility of integrating the effectiveness of the solutions offered by nature and living beings with the latest design methods. With this in mind, the following research exploits the idea of reproducing the natural flexibility inherent in biological structures by combining the advantages of compliant mechanisms with the adaptability of additive manufacturing processes. In the specific, the authors intend to highlight the potential and critical aspects of a possible approach for the application of compliant mechanisms in the development of single-component structures suitable for the actuation of bio-inspired Flapping Wing Micro Air Vehicles (FWMAVs), which can be produced via low cost 3D printing. Some designs conceived by interpreting the movement of insects’ wings have been developed with the aim of reproducing the functionality and morphology of their thorax through single-component flexible mechanisms. The results of this research demonstrate the high potentiality of realizing bio-inspired single-component compliant mechanisms through 3D printing.

High-tech equipment critically relies on flexures for precise manipulation and measurement. Through elastic deformation, flexures offer extreme position repeatability within a limited range of motion in their degrees of freedom, while constraining motion in the degrees of constraint. Topology optimization proves a prospective tool for the design of short-stroke flexures, providing maximum design freedom and allowing for application-specific requirements. State-of-the-art topology optimization formulations for flexure synthesis are subject to challenges like ease of use, versatility, implementation complexity, and computational cost, leaving a generally accepted formulation absent. This study proposes a novel topology optimization formulation for the synthesis of short-stroke flexures uniquely based on strain energy measures under prescribed displacement scenarios. The resulting self-adjoint optimization problem resembles great similarity to classic compliance minimization and inherits similar implementation simplicity, computational efficiency, and convergence properties. Numerical examples demonstrate the versatility in flexure types and the extendability of additional design requirements. The provided source code encourages the formulation to be explored and applied in academia and industry., For associated video of prototypes see https://www.youtube.com/watch?v=jHqkL6dLo2M&t=24s&ab_channel=artofscience

This paper presents an approach for the topological design of multi-material compliant mechanisms with global stress constraints. The element stacking method and the separable stress interpolation scheme are applied to calculate the element stiffness and element stress of multi-material structures. The output displacement of multi-material compliant mechanisms is maximized under the constraints of the maximum stress and the structural volume of each material. The modified P-norm method is applied to aggregate the local von Mises stress constraints for all the finite elements to a global stress constraint. The sensitivities are calculated by the adjoint method, and the method of moving asymptotes is utilized to update the optimization problem. Several numerical examples are presented to demonstrate the effectiveness of the proposed method. The appearance of the de facto hinges in the optimal mechanisms can be suppressed effectively by using the topology optimization model with global stress constraints, and the stress constraints for each material can be met.

Lockable joints are widely used in robotic systems and adaptive structures for energy management and/or topology reconfiguration. However, it is still challenging to design a joint with desired properties, including high locking load, infinite locking positions, short switching time, energy-efficient control, and a compact and lightweight structure. This paper aims at this open problem by presenting a novel piezoelectric (PZT) actuated lockable prismatic joint. This joint is a compliant mechanism (CM) consisting of a compound bridge-type compliant mechanism (CBCM) and a pair of compound multibeam parallelogram mechanisms (CMPMs). It can produce the required input/output stiffness to transmit large forces for high-load locking. It can also provide a desired input/output motion range for PZT actuation-based unlocking and for facilitating preloading adjustment. An analytical model is presented based on a compliance matrix method and the nonlinear model of the CMPM to predict the joint's static characteristics under various input/output conditions. A two-step optimization framework is proposed for locking applications. The theoretical study and nonlinear FEA/experimental verification confirm the feasibility of the design and the accuracy of the proposed model.

Folding compliant mechanisms have the potential to be used for innovative designs tailored for specific applications such as energy absorption, shape morphing, or stress relief. This tailorability relies on multiple variables that define the geometric and material behavior. The combined effort of the geometric and material nonlinearity can emphasize certain features in the design that, individually, would not be possible. Folding as a concept is very important in origami engineering and requires careful choice in the design variables when it comes to dimensions and material properties. Finite element analyses for folding at the level of a unit cell, as well as the overall structural design, can be cumbersome and computationally expensive. Therefore, in this work, a segmented pseudo rigid body model that captures a high level of flexibility is developed for both a superelastic material, which is characterized using a shape memory alloy, and a hyperelastic, rubber-like material. By increasing the number of segments, the model allows the structure to undergo large deformations. The results from the segmented model are compared with FEA for the folding compliant mechanism. 3D-printing and experimental testing of the compliant mechanism is also explored.

In this paper, a novel alternative method of stiffness compensation in buckled mechanisms is investigated. This method involves the use of critical load matching, i.e., matching the first two buckling loads of a mechanism. An analytical simply supported five-bar linkage model consisting of three rigid links, a prismatic slider joint, and four torsion springs in the revolute joints is proposed for the analysis of this method. It is found that the first two buckling loads are exactly equal when the two grounded springs are three times stiffer than the two ungrounded springs. The force–deflection characteristic of this linkage architecture showed statically balanced behavior in both symmetric and asymmetric actuation. Using modal analysis, it was shown that the sum of the decomposed strain energy per buckling mode is constant throughout the motion range for this architecture. An equivalent lumped-compliant mechanism is designed; finite element and experimental analysis showed near-zero actuation forces, verifying that critical load matching may be used to achieve significant stiffness compensation in buckled mechanisms.

This article presents a nonlinear model of an inversion-based generalized cross-spring pivot (IG-CSP) using the beam constraint model (BCM), which can be employed for the geometric error analysis and the characteristic analysis of an inversion-based symmetric cross-spring pivot (IS-CSP). The load-dependent effects are classified into two ways, including the structure load-dependent effects and beam load-dependent effects, where the loading positions, geometric parameters of elastic flexures, and axial forces are the main contributing factors. The closed-form load–rotation relationships of an IS-CSP and a noninversion-based symmetric cross-spring pivot (NIS-CSP) are derived with consideration of the three contributing factors for analyzing the load-dependent effects. The load-dependent effects of IS-CSP and NIS-CSP are compared when the loading position is fixed. The rotational stiffness of the IS-CSP or NIS-CSP can be designed to increase, decrease, or remain constant with axial forces, by regulating the balance between the loading positions and the geometric parameters. The closed-form solution of the center shift of an IS-CSP is derived. The effects of axial forces on the IS-CSP center shift are analyzed and compared with those of a NIS-CSP. Finally, based on the nonlinear analysis results of IS-CSP and NIS-CSP, two new compound symmetric cross-spring pivots are presented and analyzed via analytical and finite element analysis models.

Compliant Mechanisms (CMs) present several desired properties for mechanical designs. Conventional rigid-body mechanisms composed of rigid links connected at kinematic joints, serve as devices to transfer motion, force and energy by the movements of rigid links whereas CMs are able to present the same function only through deflection of flexible members. Most designs of CMs in the current literature employ straight beams as the elementary flexible members whereas initially curved beams (ICBs) also provide potential advantages for CMs such as large range of motion and small strain range. This paper presents an efficient spatial compliance analysis method of general ICBs. The spatial compliance analysis of different types of ICBs (such as varying-curvature beams and varying-cross-section beams) was conducted, followed by Finite Element Analysis (FEA) verification. Next, the modeling and optimization of two types of CMs including ICB-based parallelogram mechanisms and ICB-based Ortho-planar springs were carried out by applying screw theory under the framework of position space concept and parameter normalization strategy where a class of anti-buckling translational parallelograms with high load-bearing capacity and a type of compact 2R1T (2 rotational DOF and 1 translational DOF) compliant kinematic joints were obtained. The corresponding FEA was conducted to verify the optimal results.

In the field of mechanism design, the behaviour of compliant shell mechanisms is commonly characterised via the eigenscrew decomposition of their spatial stiffness matrix. Recent developments have included the design of compliant shell mechanisms made with anisotropic materials. Conceptually, these compliant mechanisms are very similar to morphing composite structures that are typically designed using structural mechanics approaches. Eigenscrew decomposition could, therefore, provide additional insight to designers. To bridge the gap between the two communities, we present the equivalence of eigenscrews (eigenwrench and eigentwist) and familiar structural concepts such as shear centre and centre of twist for the special case of a cantilevered beam. It is hoped that this explicit link will help bridge these disparate fields, and encourage cross-fertilisation of ideas.

Current surgical devices are mostly rigid and are made of stiff materials, even though their predominant use is on soft and wet tissues. With the emergence of compliant mechanisms (CMs), surgical tools can be designed to be flexible and made using soft materials. CMs offer many advantages such as monolithic fabrication, high precision, no wear, no friction, and no need for lubrication. It is therefore beneficial to consolidate the developments in this field and point to challenges ahead. With this objective, in this article, we review the application of CMs to surgical interventions. The scope of the review covers five aspects that are important in the development of surgical devices: (i) conceptual design and synthesis, (ii) analysis, (iii) materials, (iv) manufacturing, and (v) actuation. Furthermore, the surgical applications of CMs are assessed by classification into five major groups, namely, (i) grasping and cutting, (ii) reachability and steerability, (iii) transmission, (iv) sensing, and (v) implants and deployable devices. The scope and prospects of surgical devices using CMs are also discussed.

Cylindrical developable mechanisms are devices that conform to and emerge from a cylindrical surface. These mechanisms can be formed or cut from the cylinder wall itself. This paper presents a study on adapting traditional hinge options to achieve revolute motion in these mechanisms. A brief overview of options is given, including classical pin hinges, small-length flexural pivots, initially curved beams, and an adaptation of the membrane thickness-accommodation technique. Curved Lamina Emergent Torsional (LET) joints are then evaluated in detail, and a thin-walled modeling assumption is checked analytically and empirically. A small-scale cylindrical developable mechanism is then evaluated with Nitinol curved LET joints.

Stiffness in compliant mechanisms can be dramatically altered and even eliminated entirely by using static balancing. This requires elastic energy to be inserted before operation, which is most often done with an additional device or preloading assembly. Adding such devices contrasts starkly with primary motivations for using compliant mechanisms, such as part count reduction, increased precision, and miniaturization. However, statically balanced compliant mechanisms with a fully monolithic architecture are scarce. In this article, we introduce two novel statically balanced compliant mechanisms with linear and rotary kinematics that do not require preloading assembly, enabling miniaturization. Static balance is achieved by the principle of opposing constant force and extended to a rotational device by using opposing constant torque mechanisms for the first time. A constant force mechanism based on existing work is used and inspired a novel constant torque mechanism. A single-piece device is obtained by monolithically integrating a bistable switch for preloading, which allows static balance to be turned on and off. The linear device reduces stiffness by 98.5% over 10 mm, has significantly reduced device complexity and has doubled relative range of motion from 3.3% to 6.6% compared to the state of the art. The rotary device reduces stiffness by 90.5% over 0.35 rad.

In robotics, the risk of collisions is present both in industrial applications and in remote handling. If a collision occurs, the impact may damage both the robot and external equipment, which may result in successive imprecise robot tasks or line stops, reducing robot efficiency. As a result, appropriate collision avoidance algorithms should be used or, if it is not possible, the robot must be able to react to impacts reducing the contact forces. For this purpose, this paper focuses on the development of a special end-effector that can withstand impacts. It is able to protect the robot from impulsive forces caused by collisions of the end-effector, but it has no effect on possible collisions between the links and obstacles. The novel end-effector is based on a bi-stable mechanism that decouples the dynamics of the end-effector from the dynamics of the robot. The intrinsically nonlinear behavior of the end-effector is investigated with the aid of numerical simulations. The effect of design parameters and operating conditions are analyzed and the interaction between the functioning of the bi-stable mechanism and the control system is studied. In particular, the effect of the mechanism in different scenarios characterized by different robot velocities is shown. Results of numerical simulations assess the validity of the proposed end-effector, which can lead to large reductions in impact forces. Numerical results are validated by means of specific laboratory tests.

Mechanisms that consist of many elements and are potentially small sized, benefit from kinematic elementary units like revolute joints that are compliant and monolithic, and therefore could be produced without need for assembly. We present a novel concept of a compliant revolute joint that features low axis drift, high support stiffness and a large range of motion. The concept is based on a helicoidal shell of which a portion reverses its twist direction upon application of a rotation. The reversed region increases gradually, resulting in a constant reaction moment. Analytical, numerical, and experimental analyses are presented to reveal and quantify the constant-moment behaviour. Prototypes of the concept are employed in exemplary linkages to demonstrate the ability to create a large variety of neutrally stable compliant linkages, which require extremely low actuation forces and exhibit large ranges of motion.

Compliant mechanisms gain motion through the elastic deformation of the monolithic flexible elements. The geometric design freedom of metallic additive manufacturing enables the fabrication of complex and three dimensional (3D) compliant elements within mechanisms previously too complicated to produce. However, the design of metallic additive manufactured mechanisms faces various challenges of manufacturing restrictions, such as avoiding critical overhanging geometries and minimizing the amount of support structure, which has been reported in a few cases. This paper presents a synthesis approach for translational compliant elements, involving building blocks based on leaf-type springs and covering building orientations between 0° and 90°. In particular, this range is approached by the synthesis of self-supported 3D building blocks with orientations of 0°, 45°, and 90°. The compliant elements are built based on linear and circular plane curves and compared numerically according to their mechanical performance to create preferable building blocks. The applicability of the presented procedure and the manufacturability of the compliant mechanisms are proven by printing individual 3D building blocks and their serial aggregation with laser based powder bed fusion. Consequently, several prototypes are demonstrated, including a bistable switch mechanism and a large displaceable rotational spring joint. In addition, a small-scale highly maneuverable segment of a surgical instrument with a grasping mechanism at the distal end is proposed., Journal of Mechanical Design, 143 (5), ISSN:1050-0472, ISSN:1528-9001

This paper presents the development of a new microgripper actuated by means of rotary-comb drives equipped with two cooperating fingers arrays. The microsystem presents eight CSFH flexures (Conjugate Surface Flexure Hinge) that allow the designer to assign a prescribed motion to the gripping tips. In fact, the adoption of multiple CSFHs gives rise to the possibility of embedding quite a complex mechanical structure and, therefore, increasing the number of design parameters. For the case under study, a double four-bar linkage in a mirroring configuration was adopted. The presented microgripper has been fabricated by using a hard metal mask on a Silicon-on-Insulator (SOI) wafer, subject to DRIE (Deep Reactive Ion Etching) process, with a vapor releasing final stage. Some prototypes have been obtained and then tested in a lab. Finally, the experimental results have been used in order to assess simulation tools that can be used to minimize the amount of expensive equipment in operational environments.

The Cross-Axis Flexural Pivot (CAFP) is a well-established compliant rotational joint characterized by a highly configurable behavior. Its classic form, consisting of two uniform beams that cross at an arbitrary angle, has been thoroughly examined via either theoretical approaches or Finite Element Analysis (FEA). Conversely, the effects of utilizing variable section beams have had minor consideration, possibly due to the more complex modeling phase. The present paper addresses the analysis of CAFPs incorporating beams whose width and thickness are assumed to vary along the axis with either linear or parabolic functions. The CAFP planar behavior is studied resorting to the Beam-Constraint Model (BCM) for different load cases, namely with an ideal rotation applied to one rigid link or a more practicable cable-driven actuation. To extend the use of BCM to large deflections, each CAFP’s beam is modeled as a chain of two BCM elements, named Bi-BCM. A preliminary study has been carried out to establish empirical equations that provide the BCM characteristic coefficients for every considered beam shape. Next, these have been used to perform the pivot behavioral analysis and to generate, as an output of the sensitivity studies, the performance maps of stiffness, maximum stress and center shift. These results have been verified with FEA, which confirmed the Bi-BCM accuracy for any tested configuration. Finally, direct comparisons between predicted behaviors of the CAFP actuated via the flexible cable and experimental data obtained with 3D printed specimens further validated the proposed Bi-BCM model.

Continuum robots have the potential to form an effective interface between the patient and surgeon in minimally invasive procedures. Magnetic actuation has the potential for accurate catheter steering, reducing tissue trauma and decreasing radiation exposure. In this paper, a new design of a monolithic metallic compliant continuum manipulator is presented, with flexures for precise motion. Contactless actuation is achieved using time-varying magnetic fields generated by an array of electromagnetic coils. The motion of the manipulator under magnetic actuation for planar deflection is studied. The mean errors of the theoretical model compared to experiments over three designs are found to be 1.9 mm and 5.1 deg in estimating the in-plane position and orientation of the tip of the manipulator, respectively, and 1.2 mm for the whole shape of the manipulator. Maneuverability of the manipulator is demonstrated by steering it along a path of known curvature and also through a gelatin phantom, which is visualized in real time using ultrasound imaging, substantiating its application as a steerable surgical manipulator.

In soft robotics, there is still a great need for a universal but simple gripper that realizes a high level of adaptability as well as a gentle touch to a wide variety of unknown objects of different size, shape, stiffness, and weight without the use of sensors or vision. Various, mostly complex grippers already exist based on certain actuation concepts. However, each solution has specific limitations, especially regarding gripping different soft and delicate objects. Therefore, this paper introduces a new approach to design a simple, adaptive, and versatile soft robotic two-finger gripper that is based on compliant mechanisms. More specifically, an inherently gentle touch is realized by utilizing an optimally synthesized mechanism with distributed compliance in combination with a conventional linear actuator. It is shown by finite elements method (FEM) simulations that the gripper realizes a high force and motion transmission at the same time. Furthermore, it is demonstrated by tests with a gripper prototype that reliable, safe, and fast grasping as well as manipulation are possible for a wide variety of objects. It is shown that beside regular and stiff objects also very challenging objects can be easily gripped, e.g., small, irregular, soft, and squeezable objects like fruits, berries, and vegetables. Moreover, it is confirmed that the developed compliant two-finger gripper can be used beneficially without sensors and control for differently sized and shaped objects with a comparable weight.

Lamina emergent torsion (LET) joints for use in origami-based applications enables folding of panels. Placing LET joints in series and parallel (formulating LET arrays) opens the design space to provide for tunable stiffness characteristics in other directions while maintaining the ability to fold. Analytical equations characterizing the elastic load–displacement for general serial–parallel formulations of LET arrays for three degrees-of-freedom are presented: rotation about the desired axis, in-plane rotation, and extension/compression. These equations enable the design of LET arrays for a variety of applications, including origami-based mechanisms. These general equations are verified using finite element analysis, and to show variability of the LET array design space, several verification plots over a range of parameters are provided.

Binary logic gates are building blocks of computing machines, in particular, electronic computers. One variant is the programable logic gate, also known as the reconfigurable logic gate, in which the logical function implemented can be modified. In this paper, we construct a mechanism to implement a reconfigurable logic gate. This mechanism is based on the concept of programable multistable mechanisms which we introduced in previous work. The application of a programable multistable mechanism is superior to the different bistable mechanisms previously used to implement logic gates since a single mechanism can be used to implement several logic functions. Our reconfigurable logic gates use a novel geometric construction where the geometric data depend on the stability behavior of the mechanism. There are 16 binary logic gates and our construction can theoretically produce nine of these and our physical model produces six logical gates. Input and output of the mechanism are displacement and the mechanisms can be combined serially, i.e., output of a mechanism is an input for another. We show that we can implement nor and nand gates, so combinations of our mechanism can express any logical function. The mechanism is therefore theoretically universal, i.e., implement any computation. We give an analytic model of the mechanism based on Euler–Bernoulli beam theory to find the geometric data, then validate it using finite element analysis and experimental demonstration.

The purpose of this thesis is to prove that the use of compliant mechanisms in gearbox applications is viable. Compliant mechanisms are developed for their implementation in Scania’s hybrid asynchronous gearboxes. These mechanisms are presented as a replacement for the latch assembly currently in use to hold the position of the gear-shifting elements. The objective is to implement a compliant mechanism in order to avoid wear and increase the life cycle within the given constraints, as well as to have a better understanding of this kind of mechanisms. The presented literature study shows that bistable and tristable compliant mechanisms are the most suitable ones for this application. Titanium alloys, tool steels, and bulk metallic glasses are discussed as the best material options for compliant mechanism manufacturing. A mechanism idea generation and selection process is conducted. Finite Element Analysis (FEA) is developed with the chosen bistable and tristable compliant mechanism ideas. The tristable concept results on being inappropriate for this application, as it does not fulfil the volume and positioning constraints. The bistable device is proven to be suitable, and further analysis is carried out to study its fatigue resistance and show that it fulfils all the requirements, solving the weaknesses of the latch and absorbing the impact in the shaft. Additive manufacturing methods and injection moulding are found to be incompatible with the designed mechanisms. That is why the chosen bistable mechanism is designed to be made out of different parts. Future work is presented to strengthen the weaker points of this project.

This paper proposes and investigates two formulations to topology optimization of compliant mechanisms considering stress constraints, manufacturing uncertainty and geometric nonlinearity. The first formulation extends the maximum output displacement robust approach with stress constraints to incorporate the effects of geometric nonlinear behavior during the optimization process. The second formulation relies on the concept of path-generating mechanisms, where not only the final configuration is important, but also the load–displacement equilibrium path. A novel path-generating formulation is thus proposed, not only to achieve the prescribed equilibrium path, but also to take stress constraints and manufacturing uncertainty into account during the optimization process. Although both formulations have different goals, the same main techniques are employed: density approach to topology optimization, augmented Lagrangian method to handle the large number of stress constraints, three-field robust approach to handle the manufacturing uncertainty, and the energy interpolation scheme to handle convergence issues due to large deformation in void regions. Several numerical examples are addressed to demonstrate applicability of the proposed approaches. The optimized results are post-processed with body-fitted finite element meshes. Obtained results demonstrate that: (1) the proposed nonlinear analysis based maximum output displacement approach is able to provide solutions with good performance in situations of large displacements, with stress and manufacturing requirements satisfied; (2) the linear analysis based maximum output displacement approach provides optimized topologies that show large stress constraint violations and rapidly varying stress behavior under uniform boundary variation, when these are post-processed with full nonlinear analysis; (3) the proposed path-generating formulation is able to provide solutions that follow the prescribed control points, including stress robustness.

During the last decades, the modeling of flexures undergoing large deflections has been the subject of many investigations. Various rigid body models have been proposed in an effort to reproduce with high accuracy the path followed by the free-end section of the flexible element. Systems with multiple degrees of freedom have been also presented considering the possible occurrence of an inflection point. However, as the number of DoFs increases, optimization techniques must be implemented to define the characteristic parameters. In this investigation, a one-DoF rigid body model is developed focusing on the pole of the displacements associated to the poses of the free-end section. Two different cases are analyzed, depending on whether the pole is a proper point or an improper point. Strain energy is evaluated to calculate the stiffness coefficients of the rigid body model. Considering end moments and combined loads, two different formulations are elaborated to achieve analytical and numerical solutions, respectively. The proposed model is load dependent and provides an exact solution of the modeling problem, both in the case of rotation and in the case of translation of the free-end section. Occurrence of an inflection point is also considered and various examples are presented.

Compliant shape-preserving mechanisms fill a small niche within the established research field of compliant mechanisms. To date no report exists on a compliant shape-preserving ring, even though these mechanisms can give rise to a multitude of practical applications. They can essentially act as novel sealing mechanisms, compliant grippers or find use in medical applications. This paper presents three compliant shape-preserving rings that maintain their circular shape up to 99% for their full range-of-motion. The best design can expand in diameter by ≈ 45%. A prototype of a compliant shape-preserving ring was constructed from PETG (Polyethylene Terephtalate Glycol-modified) using fused-filament-fabrication. The experimental evaluation of this prototype showed a good agreement with the numerical model describing the design. A novel compliant scissor mechanism was obtained in the design process and this mechanism can prove useful in the design of other compliant shape-preserving mechanisms.

Hydrostatic bearings are superior in terms of their friction and load carrying characteristics when compared to contact based bearings, but non-usable in applications with non-constant curvature counter surfaces. A possible solution to this limitation is the introduction of deformable hydrostatic bearings components that cope with these required deformations. To reduce the required deformation of a single bearing pad, multiple pads can be connected through a so-called whiffletree support system. In this work, a symmetric whiffletree based hydrostatic bearing embodiment is introduced. A 2D quasi-static model is introduced that allows for determining the kinetostatic and path following properties of such a type of bearing. Design considerations are given regarding the joint rotational-, normal-, and shear stiffness of each individual joint, as well as basic bearing layout. The potential of a whiffletree suspended bearing is presented through the use of a case study.

In this paper a method is demonstrated for tuning the stiffness of building blocks for statically balanced compliant ortho-planar mechanisms. Three post-buckled mechanisms are proposed where the flexural rigidity can be manipulated over a part of their length in order to tune the ratio between the first two critical loads. A sensitivity analysis using finite element simulation showed that the best balancing performance is obtained in these mechanisms when this ratio was maximized. The results were validated experimentally by capturing the force-deflection relations.

Curved-line folding, the act of folding paper along a pattern of curved lines to obtain a 3D shape, is an interesting starting-point for the design of innovative pliable structures. There exists a kinematic connection between two surfaces linked through a curved crease that can be used to generate a folding motion. However, due to the interdependency of geometry, forces and material properties the design of pliable structures based on curved-line folding is very complex. To facilitate the design process, adequate computational modelling methods are essential. This paper presents two ways of modelling: a geometric modelling method based on discretisation of the crease pattern and a method based on Finite Element Analysis (FEA). The proposed methods are validated by means of a case study in which a physical model is compared to digital ones. It can be concluded that the method based on FEA corresponds very well with the physical model, proving its potential. The accuracy of the geometric modelling is improved by the introduction of a set of guidelines based on the direction of the principal bending moments in the pliable structure. Furthermore, the case study exposes how the material-dependent behaviour of pliable structures increases the complexity of the design and should certainly be part of future research.

Compliant Mechanisms (CMs) are employed in several applications requiring high precision and reduced number of parts. For a given topology, CM analysis and synthesis may be developed resorting to the Pseudo-Rigid Body (PRB) approximation, where flexible members are modelled via a series of spring-loaded revolute joints, thus reducing computational costs during CM simulation. Owing to these considerations, this paper reports about a practical method to determine accurate PRB models of CMs comprising out-of-plane displacements and distributed compliance. The method leverages on the optimization capabilities of modern CAE tools, which provide built-in functions for modelling the motion of flexible members. After the validation of the method on an elementary case study, an industrial CM consisting of a crank mechanism connected to a fully-compliant four-bar linkage is considered. The resulting PRB model, which comprises four spherical joints with generalized springs mounted in parallel, shows performance comparable with the deformable system.

The most important property for accurate mechanical time bases is isochronism: the independence of period from oscillation amplitude. This paper develops a new concept in isochronism adjustment for flexure-based watch oscillators. Flexure pivot oscillators, which would advantageously replace the traditional balance wheel-spiral spring oscillator used in mechanical watches due to their significantly lower friction, exhibit nonlinear elastic properties that introduce an isochronism defect. Rather than minimizing this defect, we are interested in controlling it to compensate for external defects such as the one introduced by escapements. We show that this can be done by deriving a formula that expresses the change of frequency of the oscillator with amplitude, i.e., isochronism defect, caused by elastic nonlinearity. To adjust the isochronism, we present a new method that takes advantage of the second-order parasitic motion of flexures and embody it in a new architecture we call the co-RCC flexure pivot oscillator. In this realization, the isochronism defect of the oscillator is controlled by adjusting the stiffness of parallel flexures before fabrication through their length Lp, which has no effect on any other crucial property, including nominal frequency. We show that this method is also compatible with post-fabrication tuning by laser ablation. The advantage of our design is that isochronism tuning is an intrinsic part of the oscillator, whereas previous isochronism correctors were mechanisms added to the oscillator. The results of our previous research are also implemented in this mechanism to achieve gravity insensitivity, which is an essential property for mechanical watch time bases. We derive analytical models for the isochronism and gravity sensitivity of the oscillator and validate them by finite element simulation. We give an example of dimensioning this oscillator to reach typical practical watch specifications and show that we can tune the isochronism defect with a resolution of 1 s/day within an operating range of 10% of amplitude. We present a mock-up of the oscillator serving as a preliminary proof-of-concept.