Torsional Spring Research Articles

Platform Design and Preliminary Test Result of an Insect-like Flapping MAV with Direct Motor-Driven Resonant Wings Utilizing Extension Springs

In this paper, we propose a platform for an insect-like flapping winged micro aerial vehicle with a resonant wing-driving system using extension springs (FMAVRES). The resonant wing-driving system is constructed using an extension spring instead of the conventional helical or torsion spring. The extension spring can be mounted more easily, compared with a torsion spring. Furthermore, the proposed resonant driving system has better endurance compared with systems with torsion springs. Using a prototype FMAVRES, it was found that torques generated for roll, pitch, and yaw control are linear to control input signals. Considering transient responses, each torque response as an actuator is modelled as a simple first-order system. Roll, pitch, and yaw control commands affect each other. They should be compensated in a closed loop controller design. Total weight of the prototype FMAVRES is 17.92 g while the lift force of it is 21.3 gf with 80% throttle input. Thus, it is expected that the new platform of FMAVRES could be used effectively to develop simple and robust flapping MAVs.

Optimization of spring parameters by using the Bees algorithm for the foldable wing mechanism

In this study, the design of the torsion and compression springs of the foldable wing mechanism used in the missile is considered an optimization problem. After the missile leaves the tube, the wings waiting in a closed state must be opened and fixed within a specific time. The study it is aimed to maximize the energy stored by the springs so that the wing can be opened in a minimum time. In this context, the energy equation in both publications is defined as the objective function in the optimization process. Wire diameter, coiling diameter, coiling number, and deflection parameters required for spring design were determined as optimization variables. There are geometrical constraints for the variables due to the dimensions of the mechanism and there are also safety factor constraints due to the loads to which the springs are exposed. The Bees Algorithm (BA) was used to solve this optimization problem and perform the spring design. The energy values obtained with BA were better than the values obtained with the Design of Experiment (DOE) study before. The springs and mechanism designed with the parameters obtained from the optimization were first analyzed in the ADAMS program. Afterward, experimental tests carried out by integrating the produced springs into the actual mechanism. As a result of the tests, it was observed that the wing opened at approximately 90 ms. This value is well below the project target of 200 ms. In addition, there is only a 16 ms difference between the analysis and the experimental results.

Dynamic stability, and absorbed energy measurements in a sandwich structure resting on the novel frictional viscoelastic torsional substrate and horizontal friction force

Like metallic materials, fiber metal laminate (FML) lets the material has a simple metal structure behavior but with such advantages as specialized strength properties, impact, fire resistance, weight savings, corrosion resistance, and metal fatigue. The main focus of this article is to indicate the dynamic response of circular size-dependent circular plates made of FML material via 3D-elasticity theories. The size-dependent structure is simulated by coupling the modified nonlocal couple stress and 3D-elasticity theories (MNCS-3DET). For accurate modeling of the elastic substrate, torsional and linear spring and Pasternak foundation are modeled using the equations of horizontal friction force and torsional interaction. Harmonic differential quadrature method and Chebyshev–Gauss–Lobatto grid distribution points are coupled for solving the partial differential equations of the current micro/nano-structure. Novelties of this work consider the effects of MCS-3DET, torsional interaction, horizontal friction force, and FML material in the construction of the circular micro/nanoplate. In the results section, the outputs are verified with other published articles, and the outcomes show that the MCS-3DET parameter, elastic foundation coefficient, horizontal friction force coefficient, and geometry have an essential role in the dynamic stability of the FML micro/nano-structure.

Localized Damage Identification in the Last Stage Low-Pressure Steam Turbine Blade Using Dynamic Parameter Measurements

Abstract Steam turbine blades are the important components in power system shaft lines subjected to severe temperatures, leading to low/high cycle fatigue failures. The transient conditions occurring during startup and shutdown events generate alternative stresses causing the fracture at the blade roots. The present work deals with the effect of localized damage on the vibration characteristics and damage identification study in the last stage low-pressure (LP) steam turbine blade. Initially, free vibration studies and transient analysis of the last row LP blade section are conducted using the finite element model. A crack near the root region is modeled by a torsional spring, whose stiffness is expressed in terms of crack depth ratio. Effects of crack depth ratio and location near the roots on the natural frequencies and transient response amplitudes are studied in detail. The relationship between the damage parameters and blade frequencies is established through the backpropagation neural network model.

A Torque-Controlled Actuator With High Rigidity and Low Aspect Ratio

To ensure safe and accurate environment-robot interaction, a torque sensor is usually mounted at the output of an actuator to detect and control the output torque. Deformation-based sensors at the actuator output would significantly increase the actuator size and complexity while decreasing the output rigidity in off-axis directions. To reduce the extra complexity, space, and output compliance required for torque sensing, this article proposes a torque-controlled actuator that does not rely on deformation-based sensing at the actuator output. Instead, a torsion spring is mounted at the input of the harmonic drive. Encoders are used to sense the spring deformation to control the output torque with low sensing noise. Hence, the size of the actuator can be minimized while the output rigidity can be maintained. Using the torsion spring can also significantly reduce the reflected output inertia of the actuator. Experiments are provided to demonstrate torque control accuracy and bandwidth. Position control results also show a comparable response to actuators that do not have torque sensors. This new torque-controlled actuator can provide a more competitive solution for collaborative robots to interact with humans or the environment.

Multistability, symmetry and geometric conservation in eightfold waterbomb origami

The nonlinearities inherent in the mechanics of origami make it a rich design space for multistable structures and mechanical metamaterials. Here, we investigate the multistability of a classic origami base: the symmetric eightfold waterbomb. We prove that the waterbomb is bistable for certain crease properties, and derive bounds on, and closed-form approximations of, its stable states. We introduce a simplified form of the waterbomb kinematics and present a design procedure for tuning the depth and the symmetry/asymmetry of its energy wells. By incorporating the concept of pretensioned torsional springs, we also demonstrate the existence of tristable cases for the waterbomb fold pattern. We then apply the analysis of a single waterbomb to study quasi-one-dimensional arrays of waterbombs, where we discover a conserved geometric-kinematic quantity in which the number of popped-up and popped-down vertices is determined uniquely through analysis of the origami structure’s boundaries. This culminates with a discussion of how the quasi-one-dimensional array may be designed to achieve stable states with various degeneracies, kinematics and gaps between energy levels. Collectively, this work presents an alternative approach for characterizing origami multistability properties and reveals an origami design motif that has potential applications in physically reconfigurable structures, mechanical energy absorption and metamaterials.

A mechanical adhesive gripper inspired by beetle claw for a rock climbing robot

Rock climbing robots have wide application prospects in field operations and planetary exploration. Herein, a spiny gripper inspired by the beetle (Coleoptera) claw is developed, which can accomplish easy attachment, detachment and good compliance on irregular rough surfaces without complex controls. The attachment probabilities of various microspine layouts are simulated to determine the optimal design parameters for the spine tile. By referencing the structure and attachment process of the beetle claw, a spiny gripper with four bioinspired branches is designed to enable adaptive attachment and smooth detachment. The gripper employs a novel drivetrain hybridized with passive torsion springs and active tendons driven by an ingenious winch to achieve light weight, load-sharing, self-adaptation, and strong adhesion on irregular rough surfaces. The grasp sequence, grasp wrench and gripper maximum adhesion are all investigated. Tests on various surfaces verify its excellent performance. With a weight of 0.352 kg, its normal adhesion and tangential adhesion are 39.7 N and 47.5 N, respectively. In addition, the gripper is integrated into the climbing robot RockClimbo to allow it to move on extreme terrain.

Conformer Ring Flip Enhances Mechanochromic Performance of ansa-Donor-Acceptor-Donor Mechanochromic Torsional Springs.

Mechanochromophores based on conformational changes of donor-acceptor-donor (DAD) springs allow sensing of forces acting on polymer chains by monotonic changes of absorbance or photoluminescence (PL) wavelength. Here, we identify a series of thiophene (D)-flanked quinoxalines (A) as molecular torsional springs for force sensing in bulk polymers at room temperature. The mode of DAD linkage to the polymer matrix and linker rigidity are key parameters that influence the efficacy of force transduction to the DAD spring and thus mechanochromic response, as probed by in situ PL spectroscopy of bulk films during stress-strain experiments. The largest shift of the PL maximum, and thus the highest sensitivity, is obtained from an ansa-DAD spring exhibiting bridged D units and a stiff A linker. Using detailed spectroscopy and density functional theory calculations, we reveal conformer redistribution in the form of a thiophene ring flip as the major part of the overall mechanochromic response. At forces as low as 27 pN at early stages of deformation, the ring flip precedes mechanically induced planarization of the ansa-DAD spring, the latter process producing a PL shift of 21 nm nN-1. Within the stress-strain diagram, the thiophene ring flip and DAD planarization are thus two separated processes that also cause irreversible and reversible mechanochromic responses, respectively, upon sample failure. As the thiophene ring flip requires much smaller forces than planarization of the DAD spring, such micromechanical motion gives access to sensing of tiny forces and expands both sensitivity and the force range of conformational mechanochromophores.

An dynamical evaluation of size-dependent weakened nano-beam based on the nonlocal strain gradient theory

This paper examines the free lateral vibration of a cracked nano-beam based on Euler-Bernoulli beam theory and nonlocal strain gradient theory (NSGT). Due to the importance and application of nanostructures, their mechanical and mechanical properties are essential. The governing equations and boundary conditions related to using the Hamilton principle have been extracted. The beam separation with the nano-beams division into two parts attached to the Torsion spring is modeled. The model calls the excess strain energy due to crack and increases the discontinuity in the deflection slope. This study investigated the effects of crack propagation, crack intensity, material length scale parameter, and various nonlocal parameters. A comparison of previous studies has been published, where a good agreement is observed. The results show that the parameters mentioned above play an important role in dynamical behavior.

Efficient self-propelled locomotion by an elastically supported rigid foil actuated by a torque

A new theoretical model is presented for an aquatic vehicle self-propelled by a rigid foil undergoing pitching oscillations generated by a torque of small amplitude applied at an arbitrary pivot axis at which the foil is elastically supported to allow for passive heaving motion. The model is based on 2D linear potential-flow theory coupled with the self-propelled dynamics of the semi-passive flapping foil elastically mounted on the vehicle hull through translational and torsional springs and dampers. It is governed by just three ordinary differential equations, whose numerical solutions are assessed with full viscous numerical simulations of the self-propelled foil. Analytical approximate solutions for the combined effect of all the relevant non-dimensional parameters on the swimming velocity and efficiency are also obtained by taking advantage of the small-amplitude of the applied torque. Thus, simple power laws for the velocity and efficiency dependencies on Lighthill number and torque intensity are obtained. It is found that the swimming velocity and transport efficiency can be greatly enhanced by selecting appropriately the non-dimensional constants of the translational and torsional springs, which are mapped for typical values of the remaining parameters in aquatic locomotion. These resonant values serve to select optimal frequencies of the forcing torque for given structural and geometric parameters. Thus, the present model and analysis provide a useful guide for the design of an efficient flapping-foil underwater vehicle.

Design and fabrication of non-resonant PZT MEMS micromirror with buried piezoresistors for closed loop position control

This paper reports on a 1D PZT micromirror integrated with buried piezoresistors for quasi-static feedback position control. The piezoresistors located along or below the PZT actuators could achieve the sensitivity as high as 3.1 mV/°, which was two orders of magnitude higher than the traditional ones located at the torsion springs (8.2 μV/°). This increased the signal-to-noise ratio by 2 orders of magnitude, which could enable the accurate position control. The response of the longitudinal sensors along the beams had a fast settling time less than 1 ms. The average position error was 0.975%, which was much better than that from the conventional shear stress sensor on the torsion bar of 3.1%.

Co-optimization of robotic design and skill inspired by human hand evolution

During evolution of the human hand, evolutionary morphology has been closely related to behavior in complicated environments. Numerous researchers have revealed that learned skills have affected hand evolution. Inspired by this phenomenon, a co-optimization approach for underactuated hands is proposed that takes grasping skills and structural parameters into consideration. In our proposal, hand design, especially the underactuated mechanism, can be parameterized and shared with all the local agents. These mechanical parameters can be updated globally by the independent agents. In addition, we also train human-like ‘feeling’ of grasping: grasping stability is estimated in advance before the object drops, which can speed up grasping training. In this paper, our method is instantiated to address the optimization problem for the torsion spring mechanical parameters of an underactuated robotic hand with multi-actuators, and then the optimized results are transferred to the actual physical robotic hand to test the improvement of grasping. This collaborative evolution process leverages the dexterity of the multi-actuators and the adaptivity of the underactuated mechanism.

Design of Hybrid Fully Actuated and Self-Adaptive Mechanism for Anthropomorphic Robotic Finger

Abstract Prior research on robotic hands predominantly focused on high degrees-of-freedom of fully actuated fingers to replicate a natural human hand or on creative designs of underactuated fingers to make a self-adaptive motion. However, in most cases, fully actuated fingers encounter difficulty in grasping unstructured objects, while underactuated fingers experience problems in performing precise grasping motions. To deal with any possible scenarios, this study presents a novel design of an anthropomorphic robotic finger that combines both advantages—fully actuated and self-adaptive (FASA) modes—at once. Actuated by tendons, the FASA finger can grasp objects adaptively and achieve accurate angle positioning with the same mechanical design. Based on the kinetostatic analysis, the guideline for selecting a torsion spring is proposed to fulfill the functions of the FASA finger and attain the optimal design of torsional stiffness, which manifests itself in a series of tests on different configurations of torsion spring. Likewise, the kinematic analysis for the fully actuated mode is given proof that two joints can move independently by controlling two motors. Ultimately, experimental results reflected the capability of the FASA finger to perform not only independent precision angle motion but also self-adaptive grasping motion without any change in mechanical structure.

Three-dimensional correction of scoliosis by a double spring reduction system as a dynamic internal brace: a pre-clinical study in Göttingen minipigs

BACKGROUND CONTEXTAdolescent idiopathic scoliosis (AIS) is a major skeletal deformity that is characterized by a combination of apical rotation, lateral bending and apical lordosis. To provide full 3D correction, all these deformations should be addressed. We developed the Double Spring Reduction (DSR) system, a (growth-friendly) concept that continuously corrects the deformity through two different elements: A posterior convex Torsional Spring Implant (TSI) that provides a derotational torque at the apex, and a concave Spring Distraction System (SDS), which provides posterior, concave distraction to restore thoracic kyphosis. PURPOSETo determine whether the DSR components are able to correct an induced idiopathic-like scoliosis and to compare correction realized by the TSI alone to correction enforced by the complete DSR implant. STUDY DESIGN/SETTINGPreclinical randomized animal cohort study. PATIENT SAMPLETwelve growing Göttingen minipigs. OUTCOME MEASURESCoronal Cobb angle, T10-L3 lordosis/kyphosis, apical axial rotation, relative anterior lengthening. METHODSAll mini-pigs received the TSI with a contralateral tether to induce an idiopathic-like scoliosis with apical rotation (mean Cobb: 20.4°; mean axial apical rotation: 13.1°, mean lordosis: 4.9°). After induction, the animals were divided into two groups: One group (N=6) was corrected by TSI only (TSI only-group), another group (N=6) was corrected by a combination of TSI and SDS (DSR-group). 3D spinal morphology on CT was compared between groups over time. After 2 months of correction, animals were euthanized. RESULTSBoth intervention groups showed excellent apical derotation (TSI only-group: 15.0° to 5.4°; DSR-group: 11.2° to 3.5°). The TSI only-group showed coronal Cobb improvement from 22.5° to 6.0°, while the DSR-group overcorrected the 18.3° Cobb to -9.2°. Lordosis was converted to kyphosis in both groups (TSI only-group: -4.6° to 4.3°; DSR-group: -5.2° to 25.0°) which was significantly larger in the DSR-group (p<.001). CONCLUSIONSThe TSI alone realized strong apical derotation and moderate correction in the coronal and sagittal plane. The addition of distraction on the posterior concavity resulted in more coronal correction and reversal of induced lordosis into physiological kyphosis. CLINICAL SIGNIFICANCEThis study shows that dynamic spring forces could be a viable method to guide the spine towards healthy alignment, without fusing it or inhibiting its growth.

Design and implementation of knee-ankle exoskeleton for energy harvesting and walking assistance

The increasing requirement of powering portable electronic devices can be potentially met by recycling the biomechanical energy generated during the human joint motion through a knee-ankle exoskeleton. In this paper, a knee-ankle exoskeleton is designed to recycle the negative work from the wearer’s knee extension and ankle dorsiflexion. The exoskeleton can convert the mechanical energy into electrical energy for energy harvesting and assist the knee flexion and ankle plantarflexion to reduce the wearer’s metabolic cost during walking. It is mainly composed of two torsion springs, two one-way transmission mechanisms, a gear train, and a generator. The torsion springs can store the elastic energy when the wearer’s ankle and knee joints do negative work and release it to assist walking when positive work is required. The one-way transmission mechanisms are employed to filter the knee flexion and ankle plantarflexion and to convert the knee extension and ankle dorsiflexion into the one-way rotation of the generator by symmetrically arranging the gear train. Finally, experiments are conducted to evaluate the performance of the developed knee-ankle exoskeleton. The experimental results indicate that the exoskeleton can generate an average electrical power of 0.49 W and a maximum instantaneous electrical power of 1.8 W at a walking speed of 5.5 km h−1 during a gait cycle, and reductions of 3.48% ± 0.33%, 9.50% ± 0.29%, and 4.54% ± 0.47% of the average muscle activities of the semitendinosus, soleus, and gastrocnemius during a gait cycle are observed, respectively.

An Interactive Rehabilitation Mechanism Design System for Kinematic and Kinetostatic Synthesis With Expandable Solution Space

Abstract Compared to manual therapy, robot therapy can provide more intensive and accurate rehabilitation training. However, most current devices are built on bulky and complex multi-degree-of-freedom (multi-DOF) mechanisms. Recently, 1-DOF mechanisms have gained popularity due to their portability and simplicity. Existing synthesis methods for 1-DOF mechanisms focus primarily on computing the optimal mechanism dimensions such that kinematic error between the task and the mechanism output is minimized. In cases where the kinematically feasible solutions become impractical under engineering circumstances, designers may need a handle to intervene in the synthesis process; moreover, the force interactions between the mechanism and users should also be considered to encourage the active participation of users for effective physical recovery. In this paper, we combine kinematic and kinetostatic synthesis to develop an interactive rehabilitation mechanism design system, taking into account task specifications on rehabilitation motion and gravity balancing. To enable interactive design, users are invited to manage the task movement via kinematic tolerance-oriented variation, thus providing the flexibility to address practical constraints. To compensate the gravity, torsional springs are attached to the actuated joints of the mechanism and human limb, and designed based on the principle of static balancing. For presenting a systematic, general, and defect-free design methodology for 1-DOF rehabilitation mechanisms, the synthesis model is formulated in a Fourier way to better accommodate different mechanism types and continuous limb motion. Examples of the upper- and lower-limb rehabilitation mechanism design are given in the end to demonstrate the validity of the proposed method.

Influence of brake-disc friction characteristics on anti-skid braking control system of aircraft

The low-frequency landing gear walk of aircraft during braking processis studied. Firstly, by virtual of LMS Virtual.Lab motion software, the multi-body dynamic model of the landing gear is established, the motion pair and internal and external loads are applied, and the torsion spring is set at the connection between the landing gear and the fuselage to simulate the flexibility of the landing gear. Then, the variation of friction coefficient of brake discis considered in the model of braking pressure and torque. When the braking control system works, if the braking pressure is less than the limit value, the gear walk is less affected by the friction characteristics of the brake disc. If the braking pressure reaches the limit value, the law of gear walk is the same as that of the pilot's manual control of the braking pressure. At this time, the gear walk is only affected by the positive and negative slope of the friction coefficient of the brake disc. If the friction coefficient curve of the brake disc presents a negative slope, it may cause gear walk, and the greater the absolute value of the slope, the more obvious the gear walk is. Improving the friction characteristics of brake discs can provide a new strategy forgear walk control.

A novel variable stiffness actuator based on a rocker-linked epicyclic gear train

• A novel variable stiffness actuator based on a rocker-linked epicyclic gear train is proposed. • The simultaneous relocations of the pivot and torsion spring permit a wide-range stiffness adjustment. • The energy efficiency is improved by introducing a linear guide and a cam follower. • A dynamic single-neuron adaptive PID controller is presented for trajectory tracking. This paper presents a novel variable stiffness actuator based on a rocker-linked epicyclic gear train (REGT-VSA). The stiffness adjustment principle of the actuator is to change the lever ratio of force by converting the differential motion of the planetary gear train into the linear motion of the elastic element. The unique design of the rocker-linked epicyclic gear train ensures the compactness of structure and the accuracy of transmission. The simultaneous relocations of the pivot and torsion spring permit a wide-range stiffness adjustment. By introducing a linear guide and a cam follower, the internal friction is reduced, and the energy efficiency is improved. A prototype and its trajectory tracking controller are developed to evaluate the performance of REGT-VSA. An exponential function is used to train the neuron proportion coefficient of the conventional single-neuron adaptive proportional-integral-derivative (PID) controller to compensate for the position error in real time, thus creating the dynamic single-neuron adaptive PID controller. The stiffness identification and trajectory tracking experiments under different conditions prove the feasibility of the actuator and the proposed algorithm.

A novel torsion instrument for miniaturized components based on the flexural pivot

A universal torsion instrument with a broad torque capacity and a high resolution for small-scale components is constructed. A high-sensitivity torque transducer based on the flexural pivot with a wide measurement range is addressed. The torque transducer consists of a cylindrical flexural pivot acting as the elastic element, and an optical angle detector involving dual laser displacement sensors. The instrument can measure the torque accurately using the flexural pivot with a known torsional spring constant. By selecting suitable pivots, it allows for a torque capacity ranging from 1.94 × 10-4 to 1.91 × 10-2 N∙m, corresponding to a resolution ranging from 1.94 × 10-9 to 1.91 × 10-7N∙m. The relative uncertainty for the torque measurement is less than 0.8%. Torsion tests on Nylon 6 filaments, copper wires, and soft ribbons were performed with the developed instrument. It shows that the instrument is a helpful tool for characterizing the torsional properties of miniaturized components.

SurgGrip: a compliant 3D printed gripper for vision-based grasping of surgical thin instruments

The online version contains supplementary material available at 10.1007/s11012-022-01594-6.