The design of grippers for the agro-industry is challenging. To be cost-effective, the picked object should be moved around fast requiring a firm grip on the fruit of different hardnesses, shapes, and sizes without causing damage. This article presents a self-adaptive flexure-based gripper design optimized for high acceleration loads. A main novelty is that it is actuated through a push-pull flexure that is loaded in tension when the gripper closes, allowing it to handle high actuation forces without the risk of buckling. To create a robust gripper that can handle relatively high loads, flexures are used that are reinforced and have a thickness variation over the length. The optimal thickness distribution of these flexures is derived analytically to facilitate the design process. The derived principles are generally applicable to flexure hinges. The resulting advanced cartwheel flexure joint, as used in this gripper, has a 2.5 times higher support stiffness and a 1.5 times higher buckling load when compared to a conventional cartwheel joint of the same size and actuation stiffness. The PP-gripper is numerically optimized for a high pull-out force, using analytical design insights as a starting point. The gripper can grip circular objects with radii between 30 and 40 mm. The pull-out force is 21.4 N, with a maximum actuation force of 100 N. Good correspondence is found between the geometric design approach, the numerically optimized design, and the results of the experimental validation.

Compliant mechanisms often have the advantage of high precision at the cost of a limited range of motion. In this research, a single Degree of Freedom hollow compliant hinge is developed for use in an Atmospheric Dispersion Corrector (ADC) found in the Extremely Large Telescope (ELT). The ADC contains two sets of optical prisms to correct for the unwanted dispersion effect that occurs when light meets the atmosphere at an angle. These prisms must perform a near-pure rotation around the optical axis, which must not be obstructed by the geometry of the ADC. This study strives to achieve the required deflection range while having sufficiently high unwanted eigenfrequencies, support stiffness, and low stress levels while bearing a relatively large load. The eigenfrequencies should be sufficiently high because of the vibrations originating from underlying systems in the ELT. This paper presents a comparison of various concepts, optimized with 3D nonlinear numerical finite element and multibody analysis software. Both high kinematic and dynamic performance is achieved through the addition of a kinematic coupler, or synchronizer. The existing concept adapted to the requirements of this work is called the Large Angle Flexure Pivot (LAFP), which is analyzed and expanded upon with a newly developed synchronizer to align with the requirements of the ADC.

Compliant mechanisms offer a number of benefits over sliding joint based mechanisms; however, their design is more complicated. As a result multiple design methods have been developed to assist with the design of compliant mechanisms. The kinematic FACT method assists in the manual design of mechanisms but has seen limited use in computational optimization. This research presents an alternative kinematics based computational optimization approach towards the automatic placement of a chosen set of flexures in 3D space such that a desired constraint space is obtained while minimizing the redundancy of constraints within a parallel spatial mechanism. A continuous measure for vector space misalignment is developed and utilized in a cost function optimization to manipulate the coordinate frame transformation of screws associated with flexural building blocks. This continuous measure is also used to formulate constraints for the cost function optimization. The approach is tested in three design cases within a limited design volume: a spherical hinge composed of wire flexures, a single rotation degree of freedom (DOF) hinge composed of leaf flexures and a parallel mechanism with three non-intersecting rotational DOFs consisting of wire flexures. The flexures are introduced and optimized sequentially and kinematically valid designs are obtained. This research is a stepping stone towards the development of a more general automatic 3D building block based synthesis approach for compliant mechanisms.

Flexure-based grippers offer an attractive alternative to conventional grippers used in robotics and automation. However, most existing designs appear to suffer from insufficient range of motion, loadability, and support stiffness. This article presents an approach to obtain well-performing flexure hinges for compact anthropomorphic grippers made via metal additive manufacturing. We propose a flexure hinge architecture that achieves a high range of motion despite the challenging combination of a small design space, high Young's modulus, and limited minimum feature size. Furthermore, we present an optimization procedure to generate suitable tendon-driven designs with high loadability. Using this framework, a flexure hinge with an outer diameter of 21.5 mm and range of motion of +/- 30 deg is synthesized. For the range of 0-30 deg, simulations show a lateral loadability of 52.5-18.6 N and lateral support stiffness of 12,309-11,130 N/m, determined at a gripper interface located 41.2 mm from the hinge pivot axis. Experiments confirm a loadability of at least 15.4 N and determined a stiffness of 8982 to 9727 N/m for same conditions. The results show that the flexure hinge architecture has large potential for a wide range of applications, while in combination with the optimization procedure, superior designs for tendon-driven grippers can be obtained.

Robotic manipulation in the agri-food industry faces several issues, including object variation, fragility and food safety. Underactuated flexure-based gripper allow passive adaptation to object variation, whilst monolithic flexure joints drive down cost, part-count, hygiene requirements, contamination and wear. However, designing flexure-based grippers presents challenges in achieving sufficient support stiffness, load-bearing capacity and joint deflection. Additionally, modeling the non-linear flexure behavior may become computationally expensive, especially under wide a variety of load cases, limiting the optimization approaches to simple structures and joints. In this work we present an interleaved computational optimization algorithm for underactuated flexure-based grippers, aimed at maximizing the range of graspable circular objects under a given load. This method achieves a superior design faster than state-of-the-art methods that optimize all design parameters simultaneously. A prototype constructed using rapid-prototyping validates the usage of the design method, and experimentally illustrates gripper performance.

Design optimizations of flexure-based mechanisms take a lot of computation time, in particular when large deformations are involved. In an optimization procedure, statically deformed configurations of many designs have to be obtained, while finding the statically deformed configuration itself requires tens to hundreds of load step iterations. The kinematically started deformation method (KSD-method) (Dwarshuis, K. S., Aarts, R. G. K. M., Ellenbroek, M. H. M., and Brouwer, D. M., 2020, “Kinematically Started Efficient Position Analysis of Deformed Compliant Mechanisms Utilizing Data of Standard Joints,” Mech. Mach. Theory, 152, p. 103911) computes deformed configurations fast by starting the computation from an approximation. This approximation is obtained by allowing the mechanism only to move in the compliant motion-direction, based on kinematic equations, using data of the flexure joints in the mechanism. This is possible as flexure-based mechanisms are typically designed to be kinematically determined in the motion directions. In this paper, the KSD-method is extended such that it can also be applied without joint-data, such that it is not necessary to maintain a database with joint-data. This paper also shows that the method can be used for mechanisms containing joints that allow full spatial motion. Several variants of the KSD-method are presented and evaluated for accuracy and required computation time. One variant, which uses joint-data, is 21 times faster and shows errors in stress and stiffness below 1% compared to a conventional multibody analysis on the same model. Another variant, which does not use joint-data, reduces the computation time by a factor of 14, keeping errors below 1%. The KSD-method is shown to be helpful in design optimizations of complex flexure mechanisms for large range of motion.

Design and optimization, as well as real time control, of flexure mechanisms require efficient but accurate models. The flexures can be modelled using beam elements and the frame parts can be modelled using superelements. Such a superelement efficiently models arbitrarily shaped bodies by few coordinates, using models obtained by model order reduction. The interfaces between the frame parts and the flexures often experience considerable deformation which affects the stiffness. To define the interface deformation in a reduced order model, this paper derives a multipoint constraint formulation, which relates the nodes on the deformable interface surface of a finite element model to a few coordinates. The multipoint constraints are imposed using a combination of the Lagrange multiplier method and master–slave elimination for efficient model order reduction. The resulting reduced order models are used in the generalized-strain multi-node superelement (GMS) that was defined in (Dwarshuis et al. in Multibody Syst. Dyn. 56(4):367–399, 2022 ). The interface deformations can be coupled to the cross-sectional deformation of higher order beam elements (i.e. beam elements of which the deformation of the cross-sections is explicitly taken into account). This paper applies this technique to model flexure joints, where the flexures are modelled with beam elements, and the frame components and critical connections using the GMS. This approach gives generally over 94% accurate stiffness, compared to nonlinear finite element models. The errors were often more than 50% lower than errors of models which only contain beam elements.

Flexure joints are rapidly gaining ground in precision engineering because of their predictable behavior. However, their range of motion is limited due to a stress limitation and a loss of support stiffness in deformed configurations. The support stiffness can be significantly increased by using leafsprings of which the width and thickness vary over the length of the leafspring. This paper presents formulations for two beam elements with a varying cross section that can be used for the efficient modeling of these types of leafsprings. One of these beam-formulations includes the modeling of the warping due to torsion, which is shown to be essential for accurate modeling. The 90% accuracy in stiffness results and 80% accuracy in stress results, in comparison with results of finite element analyses, are sufficient for the evaluation of concept-designs. Optimizations show that the support stiffness of two typical flexure joints can be increased by a factor of up to 4.0 keeping the same range of motion, by allowing the cross section to vary over the length of the leafspring. In these two flexure joints, 98% of this improvement can already be obtained by only varying the thickness, and keeping a constant width.

Passive shoulder supports show large potential for a wide range of applications, such as assisting activities of daily living and supporting work-related tasks. The rigid architectures of currently available devices, however, may pose an obstacle to finding designs that offer low protrusion and close-to-the-body alignment. This study explores the use of mechanisms that employ a flexible element which connects the supported arm to an attachment at the back and acts as energy storage, transmission and part of the load bearing structure. Based on the synthesis method explained in this paper, we conducted a large scope investigation into possible flexure-based mechanism topologies. Many potential designs were discovered and are presented, categorized and compared. Two promising designs were developed into prototypes that were built and tested on a dedicated test bench. These mechanisms reduce the necessary moment to lift the arm by more than 80 % throughout 85 % of the range of motion, while staying within 18 cm and 10 cm distance from the body, respectively. Our study indicates that, due to its lower protrusion and interface loads, a design with a tapered flexure connecting the upper arm via a hinge to a spring loaded slider at the back offers the most promising solution.

Design and optimization of flexure mechanisms and real time high bandwidth control of flexure based mechanisms require efficient but accurate models. The flexures can be modeled using sophisticated beam elements that are implemented in the generalized strain formulation. However, complex shaped frame parts of the flexure mechanisms could not be modeled in this formulation. The generalized strain formulation for flexible multibody analysis defines the configuration of elements using a combination of absolute nodal coordinates and deformation modes. This paper defines a multinode superelement in this formulation, i.e., an element having its properties derived from a reduced linear finite element model. This is accomplished by defining a local element frame with the coordinates depending on the absolute nodal coordinates. The linear elastic deformation is defined with respect to this frame, where rotational displacements are defined using the off-diagonal terms of local rotation matrices. The element frame can be defined in multiple ways; the most accurate results are obtained if the resulting elastic rotations are as small as possible. The inertia is defined in two different ways: the so-called "full approach" gives more accurate results than the so-called "corotational approach" but requires a special term that is not available from standard finite element models. Simulations show that (flexure based) mechanisms can be modeled accurately using smart combinations of superelements and beam elements.

In this work, 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 pre-existing designs. The new design is compared to such a pre-existing 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. Additionally, 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 pre-existing 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%).

The computation of stress in beam elements requires the internal stress resultants like axial force and bending moments.For displacement-based beam elements, these resultants can be obtained 1) based on equilibrium, 2) consistent to the constitutive law or 3) based on load interpolation functions.Although the methods give similar results in case of small deformation, the discrepancies in case of large deformation are significant.This paper shows that the method based on equilibrium gives the most accurate results.Torsion of beam elements causes warping of the cross section.This warping is constrained at clamped ends of beam elements, causing extra stress.This paper shows a method to accurately obtain the corresponding internal stress resultants, i.e. the Saint-Venant torsion moment and bimoment.

Six degree of freedom manipulation provides full control over position and orientation, essential for many ap-plications. However, six degree of freedom parallel kinematic manipulators (e.g. hexapods) either have a limited range of motion combined with a good repeatability when comprising flexure joints, or they have limited repeatability with a large workspace when using traditional rolling-or sliding-element bearings. In this paper, the design and optimization of a fully flexure-based large range of motion precision hexapod robot is presented. The flexure joints have been specifically developed for the purpose of large range of motion and high support stiffness for this manipulator. The obtained system allows for +/- 100 mm of translational and more than +/- 10 degrees of rotational range of motion in each direction combined with a footprint of 0.6 m(2) and a height of 0.4 m. Furthermore, a dedicated flexure-based design for the actuated joints combines high actuation forces with the absence of play and friction, allowing for accelerations exceeding 10 g. Experiments on a prototype validate the sub-micron repeatability, which is merely limited by the selected electronics.

Topology optimization of a flexure-based mechanism requires the properties of the mechanism in several deformed configurations. This paper presents a fast and accurate method to compute these configurations. It is generally applicable on mechanisms with complex standard flexure joints. First kinematic equations of the mechanism are derived by allowing the mechanism to move only in the directions for which it is designed. Secondly the configurations of the joints are approximated based on the rotations of the elements by which the joints are modeled. These orientations are obtained by a parameterization based on a priori knowledge of standard flexure joints. Finally, the resulting approximation is used as initial guess to obtain the configuration accurately, after which relevant properties like stiffness can be derived. For a manipulator with three complex joints the computation time was reduced up to a factor of 65 compared to a conventional method. When for optimization purposes an approximation is acceptable, the computation time can be reduced by a factor of 600, using a linear description of the deformation that remains in the first part of the method. (C) 2020 The Author(s). Published by Elsevier Ltd.

The exact-constraint design principle is commonly applied to flexure mechanisms to ensure deterministic behavior, but at the cost of reduced robustness, support stiffness, load capacity and usually an increased complexity of design. To explore the potential benefit of overconstrained design in flexure mechanisms, this paper investigates an elementary two-flexure cross-hinge with a single overconstraint as a case study. The stiffness effects of inadvertent stress due to misalignment are investigated experimentally, numerically and analytically. A measurement set-up with controllable misalignment has been designed. Measurements show that the first natural frequency of the cross-hinge decreases strongly with misalignment, suggesting that the actuation stiffness decreases due to the misalignment stress, and ultimately vanishes due to bifurcation buckling at a critical misalignment of the order of 0.1 mm for the mechanism at hand. Simulations with a detailed numerical model support the measurements and expose some additional factors, such as warping and shuttle compliance, which influence the system behavior. Importantly, they also show that the compliance in the support directions of the mechanism increases strongly at the critical misalignment, demonstrating that the mechanism no longer functions at the critical misalignment. An extensive analytical buckling analysis shows how the stress due to misalignment poses a functional operation limit on the overconstrained mechanism in terms of bifurcation buckling. The analysis serves to corroborate the numerical predictions. An expression is derived for the critical misalignment force and displacement as a function of the geometry and material of general cross-hinge mechanism designs.

The sheet flexure is commonly used to provide support stiffness in flexure mechanisms for precision applications. While the sheet flexure is often analyzed in a simplified form, e.g. by assuming planar deformation or linearized stiffness, the deformation in practice is spatial and sufficiently large that nonlinear effects due to the geometric stiffness are significant. This paper presents a compact analytical model for the nonlinear stiffness characteristics of spatially deforming sheet flexures under general 3-D load conditions at moderate deformations. This model provides closed-form expressions in a mixed stiffness and compliance matrix format that is tailored to flexure mechanism analysis. The effects of bending, shear, elongation, torsion and warping deformation are taken into account, so that the stiffness in all directions, including the in-plane lateral support direction, is modeled accurately. The model is verified numerically against beam and shell-based finite elements. The approach for deriving closed-form solutions in a nonlinear context is detailed in this paper. The Hellinger-Reissner variational principle with a specific physically motivated set of low-order interpolation functions is shown to be well-suited to the geometrically nonlinear analysis of flexures. An extension of the derivation approach to the nonlinear closed-form analysis of general flexure mechanisms consisting of multiple sheet flexures connected in parallel is presented. This is demonstrated with the case of a spatially deforming parallelogram flexure mechanism and a cross-hinge flexure mechanism.

Flexure mechanisms are commonly designed to be exactly constrained to favor determinism, though at the expense of limitations on the maximum parasitic natural frequencies and support stiffness. This paper presents the use of viscoelastic material for providing additional support stiffness in a certain frequency range without the indeterminism commonly associated with overconstraining. This design principle of dynamically stiffened exact-constraint design is exemplified by a parallelogram flexure mechanism. Experiments demonstrate that a custom synthesized elastomer compound can compensate for unintended misalignments without significant internal stress buildup, while improving the dynamic performance in terms of a higher first parasitic natural frequency. An analytical investigation clarifies the relationship between misalignment, internal load, stiffness and natural frequency. Using the buckling modes of the system, the nonlinear geometric stiffness is modeled accurately up to the bifurcation. The measurements and analytical model are corroborated by a nonlinear flexible multibody analysis.

In this letter we demonstrate a pneumatic bending actuator for upper-limb assistive wearable robots which uses thin McKibben muscles in combination with a flexure strip. The actuator features both active soft actuation and passive gravity support, and in terms of force transmission bridges the gap between the classic rigid type actuators and the emerging soft actuator technologies. Its flexure strip leverages the high-force low-displacement properties of McKibben muscles towards a large rotational range of motion and reduces localized forces at the attachments. We explain the synthesis method by which these actuators can be obtained and optimized for high specific moment output. Physical specimens of three optimized actuator designs are built and tested on a dedicated experimental setup, verifying the computational models. Furthermore, a proof-of-concept upper-limb assistive wearable robot is presented to illustrate a practical application of this actuator and its potential for close-to-body alignment. We found that based on our currently available components actuators can be built which, given a width of 80 mm, are able to produce a moment exceeding 4 Nm at an arm elevation of 90 deg.