Output Stiffness Research Articles

Development of an elliptic vibration mechanism for wire electrochemical micromachining

A novel flexure-based mechanism driven by two piezoelectric actuators was developed to generate elliptic vibration at the tool cathode in the wire electrochemical micromachining, which presented higher machining quality. The flexure-based mechanism adopted lever type and half bridge-type amplification mechanisms to enlarge the output of the piezoelectric actuator, the cathode wire was installed on the vibration platform through a 3D-printed insulating clamp. In order to predict the output property of the elliptic vibration mechanism, the theoretical analysis including output stiffness, kinematic modelling, and finite element analysis were implemented. A semi-closed loop controller based on the strain measurement of piezoelectric actuators was established to improve the output precision. The experimental setup of the elliptic vibration mechanism was constructed to examine the correctness of the stiffness and kinematic models, the elliptic vibration trajectory was successfully generated on the cathode wire. Furthermore, the elliptic vibration mechanism was used in the wire electrochemical micromachining, the experimental results indicated that the elliptic vibration of the cathode wire effectively improved the machining quality.

A hybrid summation and multiplication displacement amplification mechanism for piezoelectric actuators

Abstract This paper reports a novel amplified piezoelectric actuator featuring compliant displacement amplification mechanism of hybrid summation and multiplication. The hybrid amplification mechanism uses the concept of nesting a pair of Scott–Russell linkages into a toggle linkage to realize the hybrid amplification functions of summation and multiplication. Also, compliant amplification mechanisms with double output ports are designed, enhancing the flexibility of designs and applications. The hybrid displacement amplification principle is mathematically explained in detail. It is demonstrated based on finite element simulations that the displacement amplification ratio, output stiffness and resonance frequency of the proposed hybrid amplification mechanism of summation and multiplication outperform those of the classic rhombus-type and bridge-type compliant mechanisms. The experimental testing results of a prototype show that the amplified piezoelectric actuator is capable of providing 315 μm strokes with the displacement amplification ratio of 16.2. The fundamental resonance frequency with piezoelectric stacks mounted is 1218 Hz. Comparison to typical designs in literature shows well comprehensive performances of statics and dynamics, verifying the advantages of such a hybrid amplification mechanism of summation and multiplication.

Design of a variable stiffness actuator based on a multi-pulley system with a spring

This paper presents a variable stiffness actuator (VSA) based on a multi-pulley system with a linear spring. In this design, twelve pairs of outer pulleys and six pairs of inner pulleys are evenly arranged around a center and are serially connected to a spring through a cable. When the inner pulleys rotate about the center point, the spring is extended to generate an elastic force exerted on the cable and then transmitted to the output link as an output torque, resulting in an output stiffness. The significance of the proposed design is that it can quickly vary the output stiffness by adjusting the positions of the inner pulleys using a cam disk. Also, all the components are adequately arranged, making the design compact. In this work, the design concept, analysis, and a numerical example are provided to illustrate the proposed VSA and its performance. It is shown that the VSA can offer a maximum output torque of 30 N-cm with a maximum deflection of 40 degrees. These parameters can demonstrate the wide application and high adaptability of the proposed actuator to various environments.

Linear and nonlinear analytical equations for fast design of three types of triangular-amplified compliant mechanisms

Compliant amplification mechanisms based on the triangular principle have attracted considerable applications in precision and other engineering fields due to their compactness and efficient amplification capacity. However, a fast engineering design for geometric nonlinearity of large strokes is still much challenging. We report herein a series of analytical equations of nonlinear amplification ratio, input and output stiffness for three commonly-used triangular-amplified compliant mechanisms, namely the rhombus, diamond and bridge types. The pronounced geometric nonlinearities of axially-loaded stiffening and kinematics-arching effects are explicitly formulated. The proposed nonlinear formulas can be directly degenerated as the linear models by vanishing the nonlinear terms, which enables a comprehensive analysis of linear and nonlinear kinetostatics, and hence offers a straightforward way for the fast performance evaluation and size synthesis/optimization. This relieves an engineer's experience and knowledge for an ab initio modeling process. The prediction error is discussed and some insights into the linear and nonlinear characteristics of the three commonly-used triangular-amplified compliant mechanisms are outlined that confirms the advantage of analytical equations bringing to a fast engineering analysis and design.

A Lightweight Series Elastic Actuator With Variable Stiffness: Design, Modeling, and Evaluation

This article proposes a lightweight variable stiffness actuator (LVSA) driven by a novel mechanism with four sliders on a shared crank (FS2C). The FS2C mechanism allows the LVSA to simultaneously regulate the preload of four springs using only one motor and hence achieves a wider-range continuous stiffness adaption with reduced weight. A cable transmission system is developed to remotely place motors and further reduce the influence of the LVSA on the mass distribution. A dynamics model is established to study the torque-deflection and the stiffness-deflection relations. Based on the model, a torque-stiffness controller is proposed. Experiments are carried out to validate the performance of the dynamics model, the controller, and the LVSA. The results indicate that the LVSA provides a range of stiffness from 0 to 988 Nm/rad with a weight of 0.412 kg, and the controller is accurate in adjusting the output torque and stiffness at relatively high speeds. The proposed actuator provides a solution for actuation systems that have to be lightweight with variable stiffness, such as wearable robotics and assistive exoskeletons.

Development of a novel piezoelectric-driven non-resonant elliptical vibrator with adjustable characteristics.

Aiming at the fabrication of a micro-textured surface, a novel piezoelectric-driven non-resonant elliptical vibrator is proposed in this paper; the output characteristics could be adjusted by the length change of the tool holder. The flexible mechanism is the primary structure of the vibrator, which includes a lever type mechanism, an enhanced Scott-Russell mechanism, and a T-shaped mechanism. The former two mechanisms are used to enlarge the output of the piezoelectric actuator, and the T-shaped mechanism is applied to transfer the parallel movements to the elliptical trajectory. The theoretical models including the elliptical trajectory, output stiffness, and resonant frequencies are established to investigate the impacts of the tool holder and controlling signals on the output characteristics of the vibrator, which are further validated using the finite element analysis method. A prototype is developed by integrating the non-resonant elliptical vibrator assembly and controlling system. Some experiments are carried out to verify the basic performance and the adjustable properties of the vibrator.

Design of a redundant actuated 4-PPR planar 3-DOF compliant nanopositioning stage

The compliant planar positioning stage actuated by voice coil motors can obtain nanoscale motion accuracy within a millimeter motion range and has received increasing attention in precision engineering. However, there is always a contradiction between the actuation force and the output stiffness in the design of the stage. This study presents the design of a novel redundant actuated planar 3-DOF-compliant nanopositioning stage. A redundant actuated configuration can increase the output stiffness of the stage and decrease the peak actuating force. The analytical stiffness model, kinetostatic model, and dynamic model of the stage are established, which illustrate the high force transmission efficiency and dynamic decoupling feature of the stage. The geometric parameters were optimized based on the established models, and model validation and performance evaluation of the stage were conducted via finite element analysis. Finally, a prototype positioning stage is fabricated. Experimental results show that the proposed stage can achieve a motion range of up to ±2.5 mm × ±2.5 mm × ±2.5° with a resolution of 80 nm and 0.28″, and the tracking error ratio for a composite Lissajous trajectory is within 0.102%.

Design and Analysis of a Hybrid Displacement Amplifier Supporting a High-Performance Piezo Jet Dispenser

In this study, a compliant amplifier powered by a piezoelectric stack is designed to meet high-performance dispensing operation requirements. By studying the issue of low frequency bandwidth on the traditional bridge-type amplifier mechanism, we propose a displacement amplifier mechanism, hybrid bridge-lever-bridge (HBLB), that enhances its dynamic performance by combining the traditional bridge-type and lever mechanism. A guiding beam is added to further improve its output stiffness with a guaranteed large amplification ratio. An analytical model has been developed to describe the full elastic deformation behavior of the HBLB mechanism that considers the lateral displacement loss of the input end, followed by a verification through a finite element analysis (FEA). Results revealed that the working principle of the HBLB optimizes the structural parameters using the finite element method. Finally, a prototype of the displacement amplifier was fabricated for performance tests. Static and dynamic test results revealed that the proposed mechanism can reach a travel range of 223.2 μm, and the frequency bandwidth is 1.184 kHz, which meets the requirements of a high-performance piezo jet dispenser.

Switchable compliant actuator with fast stiffness modulation and energy efficient power transmission

This article presents the design of a switchable compliant actuator (Swi-CA), capable of fast stiffness modulation over a wide range and energy-efficient equilibrium position control. Compliant actuators are designed to have a variable stiffness to generate a restoring force upon displacement. In previous studies, such actuators provided compliance by changing both output stiffness and equilibrium position using a clutch to switch between two modes. We implemented a bifurcation-based switching mechanism to shift between stiffness modulation and equilibrium position control modes via mechanical integration of a variable stiffness spring with a parallel elastic unit without the use of an additional clutch. The distinctive features of the proposed Swi-CA are threefold. First, the central bending of a leaf spring widens the range of modulated stiffness and increases the average stiffness modulation speed. Second, the developed slider-crank mechanism has high power transmission efficiency and fast stiffness modulation. Lastly, an optimized elliptical cam generated negative stiffness during output and enabled switching between the two modes without the use of a controllable clutch. Analytical models and experimental validation of the proposed design clearly demonstrated its advantages for applications requiring fast stiffness modulation and energy-efficient operation, such as some robotics applications.

Design and optimization of two-degree-of-freedom parallel four pure-slide- and four parallel quadrilateral-pair precision positioning platform.

Aiming at the complex structure, small output displacement, and low positioning accuracy of the two-degree-of-freedom (2-DOF) precision positioning platform, theoretical analyses and experimental tests are carried out so that the platform has the characteristics of compact structure, large output stroke, and high positioning accuracy. First, to optimize the structural parameters of the positioning platform, a modeling method to improve the modeling accuracy of the compliant mechanism of the positioning platform is proposed. A static model of the positioning platform based on Euler-Bernoulli beam theory and the sixth-order compliance matrix method is established, and the accuracy of the model is verified by simulation. In addition, the single-objective genetic optimization algorithm is used to optimize the structural size parameters of the positioning platform, and the optimal solution set of the structural size parameters of the positioning platform is obtained by taking the displacement amplification rate of the positioning platform as the optimization target. Finally, according to theoretical and simulation analysis and optimization results, an experimental prototype was fabricated, and a series of experimental tests were carried out on the working stroke, displacement magnification, and output stiffness. The experimental results show that the displacement magnification of the positioning platform reaches 3.39, the positioning stroke is 89.2 × 85.9 µm2, and the displacement resolutions of the x-axis and y-axis are 35 and 31nm, respectively. The positioning platform designed in this paper meets the requirements of large output stroke and high positioning accuracy.

Design and Analysis of Pneumatic Downforce Regulating Device for No-Till Corn Planter

To avoid the issues of undesired soil compaction and seeding depth variation caused by the downforce fluctuation of the corn no-till planter, the influence of the structural parameters of the air spring on the downforce was researched in this paper, by establishing the gas–solid coupling simulation model of the air spring. The downforce test bench was built to verify the simulation model; the test showed that the vertical output force error of the simulation model was 4.79%, the pitch diameter error was 0.76%, and the pressure error was 5.07%. The cord angle, piston angle and piston diameter were used as influencing factors to carry out single-factor experiments. The influences of structural parameters on downforce were analyzed from four aspects: the vertical output force, the vertical stiffness, the pressure difference and the deformation rate. The results showed that the cord angle reduced the effective area and its change rate during deformation by limiting the radial deformation of the bellow. When the cord angles were 30°, 45° and 60°, the deformation rates were 65.6%, 20.3% and 4.8%, respectively. The cord angle had a positive effect on the vertical output force when the cord angle was in the range of 30~56°, and it had a negative impact in the range of 56~60°. As the cord angle increased, the vertical stiffness decreased. As the piston angle increased, the effective area of the air spring decreased, and the change in internal pressure decreased, reducing its vertical output force and stiffness. The piston diameter had little effect on the internal pressure and deformation rate. It increased the vertical output force and stiffness by increasing the effective area. The structural parameters of the air spring had a significant impact on the stability of the downforce; the structure of the air spring should be optimized according to the downforce demand of the corn no-till planter.

Design, modeling, and control of a variable stiffness elbow joint

New technological advances are changing the way robotics are designed for safe and dependable physical human–robot interaction and human-like prosthesis. Outstanding examples are the adoption of soft covers, compliant transmission elements, and motion control laws that allow compliant behavior in the event of collisions while preserving accuracy and performance during motion in free space. In this scenario, there is growing interest in variable stiffness actuators (VSAs). Herein, we present a new design of an anthropomorphic elbow VSA based on an architecture we developed previously. A robust dynamic feedback linearization algorithm is used to achieve simultaneous control of the output link position and stiffness. This actuation system makes use of two compliant transmission elements, characterized by a nonlinear relation between deflection and applied torque. Static feedback control algorithms have been proposed in literature considering purely elastic transmission; however, viscoelasticity is often observed in practice. This phenomenon may harm the performance of static feedback linearization algorithms, particularly in the case of trajectory tracking. To overcome this limitation, we propose a dynamic feedback linearization algorithm that explicitly considers the viscoelasticity of the transmission elements, and validate it through simulations and experimental studies. The results are compared with the static feedback case to showcase the improvement in trajectory tracking, even in the case of parameter uncertainty.

Development and assessment of a novel two-degree-of-freedom vibration generator for generating and hiding optical information

Nanostructure-induced optical information is useful in everyday life, such as information communication and display. However, the machining methods of nanostructures still face several challenges, such as low machining efficiency and low surface quality. Therefore, this paper proposes a two-degree-of-freedom vibration generator to solve these issues. Firstly, the mechanical structure of this device is designed based on the compound bridge-type amplification mechanism. Then, the output stiffness, input stiffness, and dynamic features of this device are theoretically modeled. To mathematically establish the relationship between the nanostructure dimension and the optical information, the generation and hiding principles of optical information are next illustrated. Finally, experiments verify the effectiveness of this device. A quick response code that stores the website information is successfully machined on the workpiece. Besides, an optical number “2021” can be hidden by controlling the facet spacings of nanostructures. This developed vibration generator promotes the functional application of nanostructures, which can be used in information storage and protection.

Optimized design of a compact multi-stage displacement amplification mechanism with enhanced efficiency

Mechanically amplifying micro-stroke of actuators such as piezoelectric stacks through compliant mechanisms is an effective solution for use in micro/nano manipulation, precision positioning, gripping and manufacturing with large enough workspaces. This paper proposes a novel type of hybrid three-stage compliant displacement amplifier with a compact structure by synthesizing bridge-type and lever-type compliant mechanisms. A new index is introduced to measure its displacement amplification efficiency by considering the whole size and input stiffness. To facilitate design, the dynamic stiffness model is also derived to capture its kinetostatics and dynamics on both time and frequency domain. Then, the key structural parameters are efficiently optimized with the Pareto multi-objective optimization strategy. The capacity curve in terms of the resonance frequency, displacement amplification ratio and load capacity (output stiffness) is provided as well in a form of the Pareto optimal solution set. Experimental tests of two prototypes indicate a high displacement amplification efficiency of the current design, of which one prototype exhibits the output displacement of 0.7 mm and the resonance frequency of 874 Hz with a compact size of only 57 mm × 50 mm × 10 mm.

Hybrid explicit–implicit topology optimization method for the integrated layout design of compliant mechanisms and actuators

Increasing the working stroke of compliant mechanisms in a limited space has always been an important topic in mechanics. One effective method is to develop a more fundamental design model that considers the multi-physical coupling characteristics of compliant mechanisms and actuators. This paper presents a new method for the integrated design of compliant mechanisms and piezoelectric actuators, which incorporates the projective transformation-based moving morphable components method with the parametric level set method (PMMC-PLS), based on the use of explicit and implicit topology optimization methods to drive the layout evolution of the embedded actuator and host structure, respectively. The extended finite element method (XFEM) is adopted to accurately capture the boundary of the multi-component system, thereby increasing the accuracy of the structural response and sensitivity analysis. To circumvent defacto hinges and thin wall features, a global manufacturability constraint is proposed by applying the minimum length scale control to the host structure and a non-overlap constraint to embedded actuators. Moreover, the output stiffness is considered to enhance the mechanical performance of the mechanism. The effectiveness of the proposed method is verified considering numerical examples.

Cable Decoupling and Cable-Based Stiffening of Continuum Robots

Cable-driven continuum robots, which are robots with a continuously flexible backbone and no identifiable joints that are actuated by cables, have shown great potential for many applications in unstructured, uncertain environments. However, the standard design for a cable-driven continuum robot segment, which bends a continuous backbone along a circular arc, has many compliant modes of deformation which are uncontrolled, and which may result in buckling or other undesirable behaviors if not ameliorated. In this paper, we detail an approach for using additional cables to selectively stiffen planar cable-driven robots without substantial coupling to the actuating cables. A mechanics-based model based on the planar Cosserat equations is used to find the design conditions under which additional cables can be routed without coupling of the cable lengths for small deformations. Simulations show that even for relatively large deformations, coupling remains small. A prototype is evaluated, and it is demonstrated that the compliance of the robot is substantially modified relative to the same robot without stiffening cables. Additional stiffening cables are shown to increase the end-effector output stiffness by a factor of approximately 10 over a typical design with actuating cables.

Isolated Joint Block Progression Training Improves Leaping Performance in Dancers.

The purpose of this study was to investigate the effect of a 12-week ankle-specific block progression training program on saut de chat leaping performance [leap height, peak power (PP), joint kinetics and kinematics], maximal voluntary isometric plantar flexion (MVIP) strength, and Achilles tendon (AT) stiffness. Dancers (training group n = 7, control group n = 7) performed MVIP at plantarflexed (10◦) and neutral ankle positions (0◦) followed by ramping isometric contractions equipped with ultrasound to assess strength and AT stiffness, respectively. Dancers also performed saut de chat leaps surrounded by 3-D motion capture atop force platforms to determine center of mass and joint kinematics and kinetics. The training group then followed a 12-week ankle-focused program including isometric, dynamic constant external resistance, accentuated eccentric loading, and plyometric training modalities, while the control group continued dancing normally. We found that the training group's saut de chat ankle PP (59.8%), braking ankle stiffness (69.6%), center of mass PP (11.4%), and leap height (12.1%) significantly increased following training. We further found that the training group's MVIP significantly increased at 10◦ (17.0%) and 0◦ (12.2%) along with AT stiffness (29.6%), while aesthetic leaping measures were unchanged (peak split angle, mean trunk angle, trunk angle range). Ankle-specific block progression training appears to benefit saut de chat leaping performance, PP output, ankle-joint kinetics, maximal strength, and AT stiffness, while not affecting kinematic aesthetic measures. We speculate that the combined training blocks elicited physiological changes and enhanced neuromuscular synchronization for increased saut de chat leaping performance in this cohort of dancers.

Cu2Se-based thermoelectric cellular architectures for efficient and durable power generation

Thermoelectric power generation offers a promising way to recover waste heat. The geometrical design of thermoelectric legs in modules is important to ensure sustainable power generation but cannot be easily achieved by traditional fabrication processes. Herein, we propose the design of cellular thermoelectric architectures for efficient and durable power generation, realized by the extrusion-based 3D printing process of Cu2Se thermoelectric materials. We design the optimum aspect ratio of a cuboid thermoelectric leg to maximize the power output and extend this design to the mechanically stiff cellular architectures of hollow hexagonal column- and honeycomb-based thermoelectric legs. Moreover, we develop organic binder-free Cu2Se-based 3D-printing inks with desirable viscoelasticity, tailored with an additive of inorganic Se82− polyanion, fabricating the designed topologies. The computational simulation and experimental measurement demonstrate the superior power output and mechanical stiffness of the proposed cellular thermoelectric architectures to other designs, unveiling the importance of topological designs of thermoelectric legs toward higher power and longer durability.

A Human-Inspired Soft Finger with Dual-Mode Morphing Enabled by Variable Stiffness Mechanism

Elevating stiffness without compromising compliance and agility is a key problem for soft finger applications, especially for articulate ones. Inspired by human finger, a multijoint soft finger with dual morphing through active/passive variable rigidity is proposed. The fabricated soft finger weighs 27.4 g. Conductive thermoplastic starch polymers (CTPSs) are embedded in a U-shape-joint pneumatic soft actuator segmentally like biological phalanges. Their stiffness can be independently adjusted utilizing customized thermomechanical property. Yoshimura origami imitating ligaments can passively match deformation and stiffness of the joints. Through electrothemal activation of CTPSs, the finger can realize dual independent articulate morphing: stiffened phalanges (mode 1) for dexterous manipulation and heavy load, softened phalanges (mode 2) for large deformation contact and light load. Comparative experiments of bending angle, output force, and stiffness are carried out between the active and passive stiffness adjustment of mode 1 and mode 2. The results show that the output force and stiffness of the finger adopting mode 1 can be improved more than two times and five times, and its compliance using mode 2 is almost similar, compared with the pure soft one. To further demonstrate performances of dual-mode morphing, a three-fingered gripper is assembled for grasping and manipulating targets with different shapes, sizes, rigidity, and weight, including playing card, unshelled raw egg, grapes, and unscrewing the bottle cap. It can successfully lift a dumbbell weighing 1460 g with a 7.6 load/weight ratio through a two-mode switch.

Current Insights in the Age-related Decline in Sports Performance of the Older Athlete.

The higher performance level of master athletes compared to non-athletes is often associated with better health throughout life. However, even the physical performance of master athletes declines with age, and this decline accelerates from about the age of 70 years onwards. A progressive loss of muscle mass, declines in force- and power-generating capacity, decreased flexibility, and the concomitant decline in specific tension characterize the muscular changes underlying performance declines. In the cardiovascular system, declines in stroke volume and cardiac output, and cardiac and vascular stiffness contribute to decreasing performance. Recent studies have shown that long-term endurance exercise in master athletes does not only have positive effects, but is associated with an increased incidence of atrial fibrillation, atherosclerotic plaques, and aortic dilation, and even more so in men than in women. Recently, larger longitudinal datasets were analysed and showed that the age-related decline in performance was similar in longitudinal and cross-sectional data. In conclusion, regular physical activity enhances the exercise capacity, and hence quality of life in old age, but it is not without risks.