Optimal Stiffness Research Articles

A hybrid hydrogel encapsulating human umbilical cord mesenchymal stem cells enhances diabetic wound healing

BackgroundDiabetic wound is a severe complication of diabetes. Stem cell is considered as a promising therapy for diabetic skin wounds. Hydrogel can supply niche for cells adhesion and survival to improve the efficacy of stem cell therapy, but the development of hydrogel with suitable properties remains a great challenge. Thus, our study was conducted to combine an optimized hydrogel with stem cell to improve complex diabetic wound treatment.MethodsThis study constructed a hydrogel with low toxicity and adjustable mechanical properties from gelatin methacrylate (GelMA) and chitosan-catechol (Chi-C), and encapsulated human umbilical cord-mesenchymal stem cells (hUMSCs) to repair full-thickness diabetic wound.ResultsWe explored the relationship between mechanical stiffness and cell proliferation and differentiation potency, and found 10% GelMA hydrogel with an optimal stiffness improved hUMSCs adhesion, proliferation, and differentiation potency maintenance in vitro. Assistant with optimized hydrogel encapsulating hUMSCs, diabetic wound healing process was greatly accelerated, including accelerated wound closure, inhibited secretion of inflammatory factors TNF-α and IL-1β, promoted vascular regeneration and collagen deposition after treatment of hUMSCs.ConclusionsThe optimized hydrogel encapsulating hUMSCs improved diabetic wound healing, and has a broad implication for the treatment of diabetic complication.Diabetic wound is a severe complication of diabetes. Stem cell is considered as a promising therapy for diabetic skin wounds. Hydrogel can supply niche for cells adhesion and survival to improve the efficacy of stem cell therapy. This study constructed a hydrogel with low toxicity and adjustable mechanical properties from gelatin methacrylate (GelMA) and chitosan-catechol (Chi-C), and encapsulated human umbilical cord-mesenchymal stem cells (hUMSCs) to repair full-thickness diabetic wound. Hydrogel of 10% GelMA with an optimal stiffness improved hUMSCs adhesion, proliferation, and differentiation potency maintenance in vitro. Assistant with optimized hydrogel encapsulating hUMSCs, diabetic wound healing process was greatly accelerated, including accelerated wound closure, inhibited secretion of inflammatory factors TNF-α and IL-1β, promoted vascular regeneration and collagen deposition after treatment of hUMSCs. The study supplies an alternative treatment for diabetic complication. Hydrogel-hUMSCs combined treatment accelerates wound closure in diabetic mice. A. Representative images of wounds during 21-day in vivo experiments. B. Quantification of wound closure rate (%) over 21-day period. C. HE staining of wounds at days 7, 14 and 21. The bar corresponds to 200 μm.

The Utility of Myotonometry in Musculoskeletal Rehabilitation and Human Performance Programming.

Myotonometry is a relatively novel method used to quantify the biomechanical and viscoelastic properties (stiffness, compliance, tone, elasticity, creep, mechanical relaxation) of palpable musculotendinous structures with portable mechanical devices called myotonometers. Myotonometers obtain these measures by recording the magnitude of radial tissue deformation that occurs in response to the amount of force that is perpendicularly applied to the tissue through a device's probe. Myotonometric parameters such as stiffness and compliance have repeatedly demonstrated strong correlations with force production and muscle activation. Paradoxically, individual muscle stiffness measures have been associated with both superior athletic performance and higher incidence of injury. This suggest there may be optimal stiffness levels that promotes athletic performance while too much or too little may lead to an increased risk of injury. Numerous studies suggest that myotonometry may assist practitioners in the development of performance and rehabilitation programs that improves athletic performance, mitigates injury risk, guides therapeutic interventions, and optimizes return to activity decision making. Thus, the purpose of this narrative review is to summarize the potential utility of myotonometry as a clinical tool that assists musculoskeletal clinicians with the diagnosis, rehabilitation, and prevention of athletic injuries.

Directed cell migration towards softer environments.

How cells sense tissue stiffness to guide cell migration is a fundamental question in development, fibrosis and cancer. Although durotaxis-cell migration towards increasing substrate stiffness-is well established, it remains unknown whether individual cells can migrate towards softer environments. Here, using microfabricated stiffness gradients, we describe the directed migration of U-251MG glioma cells towards less stiff regions. This 'negative durotaxis' does not coincide with changes in canonical mechanosensitive signalling or actomyosin contractility. Instead, as predicted by the motor-clutch-based model, migration occurs towards areas of 'optimal stiffness', where cells can generate maximal traction. In agreement with this model, negative durotaxis is selectively disrupted and even reversed by the partial inhibition of actomyosin contractility. Conversely, positive durotaxis can be switched to negative by lowering the optimal stiffness by the downregulation of talin-a key clutch component. Our results identify the molecular mechanism driving context-dependent positive or negative durotaxis, determined by a cell's contractile and adhesive machinery.

Influence of Supraphysiologic Biomaterial Stiffness on Ventricular Mechanics and Myocardial Infarct Reinforcement

Injectable intramyocardial biomaterials have promise to limit adverse ventricular remodeling through mechanical and biologic mechanisms. While some success has been observed by injecting materials to regenerate new tissue, optimal biomaterial stiffness to thicken and stiffen infarcted myocardium to limit adverse remodeling has not been determined. In this work, we present an in-vivo study of the impact of biomaterial stiffness over a wide range of stiffness moduli on ventricular mechanics. We utilized injectable methacrylated polyethylene glycol (PEG) hydrogels fabricated at 3 different mechanical moduli: 5 kPa (low), 25 kPa (medium/myocardium), and 250 kPa (high/supraphysiologic). We demonstrate that the supraphysiological high stiffness favorably alters post-infarct ventricular mechanics and prevents negative tissue remodeling. Lower stiffness materials do not alter mechanics and thus to be effective, must instead target biological reparative mechanisms. These results may influence rationale design criteria for biomaterials developed for infarct reinforcement therapy. Statement of significanceAcellular biomaterials for cardiac application can provide benefit via mechanical and biological mechanisms post myocardial infarction. We study the role of biomaterial mechanical characteristics on ventricular mechanics in myocardial infarcts. Previous studies have not measured the influence of injected biomaterials on ventricular mechanics, and consequently rational design criteria is unknown. By utilizing an in-vivo assessment of ventricular mechanics, we demonstrate that low stiffness biomaterial do not alter pathologic ventricular mechanics. Thus, to be effective, low stiffness biomaterials must target biological reparative mechanisms. Physiologic and supra-physiologic biomaterials favorably alter post-infarct mechanics and prevents adverse ventricular remodeling.

Anterior to Posterior Bone Plug Suture Tunnels Provide Optimal Biomechanics for Bone−Patellar Tendon−Bone Anterior Cruciate Ligament Graft

PurposeTo evaluate different bone−patellar tendon−bone (BPTB) plug suture configurations for pull through strength, stiffness, and elongation at failure in a biomechanical model of suspensory fixation.MethodsForty nonpaired, fresh-frozen human cadaveric BPTB allografts with an average age of 65.6 years were tested. Tensile testing was performed with the use of a custom-designed fixture mounted in a dynamic tensile testing machine. A preload of 90 N was applied to the graft and held for 5 minutes. Following this, a tensile load-to-failure test was performed. The ultimate failure load, elongation at failure, and mode of failure were recorded, and the resulting load–elongation curve was documented.ResultsThe drill tunnel through the cortical surface (anterior to posterior) was found to be significantly stronger than the drill tunnel through the cancellous surface (medial to lateral). There were no significant differences found when comparing the strength of the suture augmentation through the tendon and the drill tunnel alone (P = .13 among cancellous groups, P = .09 among cortical groups). The cortical drill tunnel with suture augmentation through the tendon showed significantly greater elongation values (13.7 ± 3.2) at failure when compared with either the cancellous or cortical drill tunnel only test groups (P = .0003 compared with cancellous alone, P = .009 when compared with cortical alone). Conclusions: The BPTB suture configuration with an anterior to posterior–directed suture tunnel without a suture through tendon augmentation provides the optimal strength and stiffness while minimizing graft elongation after fixation in a biomechanical model. This configuration is best for preventing suture pull through and failure when passing sutures through the BPTB plug.Clinical RelevanceThis study biomechanically evaluates the optimal suture configuration in the proximal bone plug for suspensory fixation in the setting of BPTB grafts.

Planar Multi-Closed-Loop Hyper-Redundant Manipulator Using Extendable Tape Springs: Design, Modeling, and Experiments

This letter describes the development of a planar multi-closed-loop hyper-redundant manipulator. The proposed manipulator consists of two extendable tape springs and several inner tube rods. As the tape springs can be wound, the manipulator achieves a large workspace with a small footprint. The inner tube rods are arranged between the two tape springs, providing the manipulator with a triangular-lattice structure in which the inner tube rods and tape springs are subjected to purely axial loads. By controlling the two fixed drive components and eight mobile drive components in the manipulator, various redundant configurations can be produced. The kinematic model of this manipulator is established, and a configuration planning approach based on optimal stiffness is proposed. Simulations are conducted for three different cases, and a prototype is fabricated and tested to validate the proposed design and method.

Optimization of Spring Constant of a Pneumatic Artificial Muscle-Spring Driven Antagonistic Structure

Pneumatic artificial muscles (PAMs) have been widely applied to robotic systems, especially assistive devices, which could benefit from PAMs’ intrinsic viscoelasticity. However, nonlinearity and hysteresis make it challenging to achieve high-accuracy control. Using pre-tensioned springs to replace one side PAMs in an antagonistic structure is one efficient way to improve control accuracy. However, in the previous study, the selection method for spring, especially the range of spring constant has not been sufficiently investigated. This study designed a method to find the optimal spring constant based on gradient descent algorithm; and verified it with prototype and simulation experiments. Results showed that the group with optimal spring constant leads to a faster response time, smaller overshoot, and lower steady-state error, which indicated that the proposed method could find optimal spring constant. Moreover, the sensitivity of PAMs dynamic model parameters to the optimal spring stiffness was investigated. This study provides insights to practical use of soft actuators.

Operating characteristics of a 15 W free-piston Stirling generator

Free-piston Stirling generators (FPSGs) show great potential in portable power sources for the advantages of high reliability, high efficiency, low noise, compact structure, long lifetime, etc. An FPSG aimed at 15 W electric power output is numerically and experimentally studied. By adopting the second method of Lyapunov, the onset characteristics of the FPSG are analyzed based on a thermodynamic model. The effects on the onset conditions of the interaction between the displacer and power piston are explored. It is shown that the optimal operating pressure and spring stiffness corresponding to the lowest onset heating temperature are 6.2 MPa and 5500 N/m, and the FPSG is easier to start when the damping of the displacer and power piston is smaller and the mass of the displacer and power piston is well matched. The experimental results of the effects of the pressure and spring stiffness on the onset temperature agree well with the calculated results. The FPSG can generate 15.5 W electric power with a thermal-to-electric efficiency of 16.0% in the experiment when the heating and chilling water temperatures are 820 K and 300 K, respectively. And the relative errors between the calculated and experimental PV power and their efficiencies are about 2.1%–6.8% and 24.4%–26.9%, respectively. This work can lay a good foundation for studying the onset characteristics and stable operating characteristics of FPSGs.

On the Characteristics and Practical Parameters Selection of a Quasi-Zero-Stiffness Isolator

Quasi-zero-stiffness (QZS) isolators, characterized by high-static-low-dynamic stiffness (HSLDS), have attracted interest in the field of low-frequency vibration isolation. An existing QZS isolator, using horizontal springs in series with rigid oblique rods as a negative stiffness mechanism, has been proposed to obtain desirable low-frequency isolation performance. However, it is unknown if the rigid oblique rods will obtain the optimal isolation performance for the existing QZS isolation system. In this research, considering that the oblique rods are flexible rather than rigid, the effects of the stiffness of the springs and the rods on mechanical characteristics and isolation performance of this QZS isolator are investigated to answer the above question and to guide design of the QZS isolator. The QZS conditions ensuring the QZS characteristics of the proposed QZS isolator are derived, and the parametric analysis on QZS characteristics is conducted. Further, amplitude-frequency response of the QZS isolation system is obtained by the average method and the numerical methods; the following parametric analysis indicates that the optimal stiffness ratio of horizontal spring to vertical spring should be slightly greater than 0.5 to obtain a reasonable compromise between the peak amplitude control and peak force transmissibility reduction. Meanwhile, when the stiffness ratio of the oblique rod to the vertical spring is greater than 2, the QZS isolator with finite-stiffness oblique rods has similar isolation performance as that of the existing QZS isolator with rigid oblique rods. Therefore, designers could select oblique rods with finite stiffness to avoid excessive size or non-negligible weights of the rods.

A Study on Preparation and Property Evaluations of Composites Consisting of TPU/Triclosan Membranes and Tencel®/LMPET Nonwoven Fabrics.

This study investigated eco-friendly antibacterial medical protective clothing via the nonwoven process and characteristic evaluations. Firstly, Tencel® fibers and low melting point polyester (LMPET) fibers (re-sliced and granulated from recycled PET bottles) were mixed at different ratios and then needle punched at diverse needle rolling depths. The influences of manufacturing parameters on the Tencel®/LMPET nonwoven fabrics were examined in terms of mechanical properties, water vapor transmission rate, and stiffness. Next, Tencel®/LMPET nonwoven fabrics were combined with thermoplastic polyurethane (TPU)/Triclosan antibacterial membranes that contained different contents of triclosan using melt processing technology. The resulting Tencel®/LMPET/TPU/Triclosan composites were characterized via different measurements; an optimal bursting strength of 86.86 N, an optimal horizontal tensile strength of 41.90 N, and an optimal stiffness along the MD and CD of 8.60 cm were recorded. Furthermore, the Tencel®/LMPET/TPU/Triclosan composites exhibited a distinct inhibition zone in the antibacterial measurement, and the hydrostatic pressure met the requirements of the EN 14126:2003 and GB 19082-200 disposable medical protective gear test standards.

Topology optimization including a model of the layer-by-layer additive manufacturing process

A topology optimization formulation including a model of the layer-by-layer additive manufacturing (AM) process is considered. Defined as a multi-objective minimization problem, the formulation accounts for the performance and cost of both the final and partially manufactured designs and allows for considering AM-related issues such as overhang and residual stresses in the optimization. The formulation is exemplified by stiffness optimization in which the overhang is limited by adding mechanical or thermal compliance as a measure of the cost of partially manufactured designs. Convergence of the model as the approximate layer-by-layer model is refined is shown theoretically, and an extensive numerical study indicates that this convergence can be fast, thus making it a computationally viable approach useful for including AM-related issues into topology optimization. The examples also show that drips and sharp corners associated with some geometry-based formulations for overhang limitation can be avoided. The codes used in this article are written in Python using only open sources libraries and are available for reference.

Vibration characteristics analysis and suspension parameter optimization of tractor/implement system with front axle suspension under ploughing operation condition

To improve the riding comfort and driving safety of the tractor system, it’s necessary to build a vibration model of wheeled tractor/implement system to analyze its corresponding vibration characteristics. A discrete element model of plough-soil coupling system was developed in this work to obtain the tillage resistance and its effectiveness is verified through experiment. Then, the vibration model of wheeled tractor/implement system with front axle suspension under ploughing condition was constructed and the corresponding vibration characteristics of the tractor system under road transportation, farmland transportation and plough operation conditions were simulated. It’s demonstrated that the simulated vibration responses agree well with the measured data and the validity of the proposed model is proved. The simulation results show that the natural frequency of the tractor system almost remains constant under the three working conditions above and the natural frequencies of vertical vibration for front axle, cabin, driver seat and implement are 2.09 Hz, 2.84 Hz, 2.84 Hz and 2.09 Hz, respectively. The existence of front axle suspension will deteriorate the ride comfort of driver but improve the handing stability obviously. The farmland road roughness and tillage resistance can reduce the vibration responses of the wheeled tractor/implement system with front axle suspension significantly. With the increase of tillage speed or depth, the vibration responses of the tractor system rise tremendously. When the tillage speed or depth is constant, the largest vertical vibration acceleration exists on the front axle. In addition, the multi-objective optimization of stiffness and damping parameters for the front axle suspension is implemented through particle swarm algorithm and the optimal stiffness and damping are recommended to be 60 kNm−1 and 8.919 kNsm−1, respectively.

Freezing transitions of Brownian particles in confining potentials

We study the mean first passage time (MFPT) to an absorbing target of a one-dimensional Brownian particle subject to an external potential v(x) in a finite domain. We focus on the cases in which the external potential is confining, of the form v(x) = k|x − x 0| n /n, and where the particle’s initial position coincides with x 0. We first consider a particle between an absorbing target at x = 0 and a reflective wall at x = c. At fixed x 0, we show that when the target distance c exceeds a critical value, there exists a nonzero optimal stiffness k opt that minimizes the MFPT to the target. However, when c lies below the critical value, the optimal stiffness k opt vanishes. Hence, for any value of n, the optimal potential stiffness undergoes a continuous ‘freezing’ transition as the domain size is varied. On the other hand, when the reflective wall is replaced by a second absorbing target, the freezing transition in k opt becomes discontinuous. The phase diagram in the (x 0, n)-plane then exhibits three dynamical phases and metastability, with a ‘triple’ point at (x 0/c ≃ 0.171 85, n ≃ 0.395 39). For harmonic or higher order potentials (n ⩾ 2), the MFPT always increases with k at small k, for any x 0 or domain size. These results are contrasted with problems of diffusion under optimal resetting in bounded domains.

Analysis and Optimization of Suspension Spring Stiffness for Improving Frequency Response Characteristics of the Vehicle

The work puts forward a way to research the kinematics of front double wishbone suspension by virtue of analytical method. A way of discussing the kinematics of rear five-link suspension is put forward by means of space coordinate transformation. The influence of suspension spring stiffness on the suspension characteristics is analyzed. The vehicle frequency response index is deduced in view of theoretical model of equivalent handling stability. The relationship between the vehicle frequency characteristic index and the frequency of the steering wheel angle under the variation of spring stiffness is gained, and the influence mechanism of spring stiffness on the vehicle frequency characteristics is explained. The suspension spring stiffness is the optimization variable, the vehicle frequency characteristic index is the optimization objective, and genetic algorithm is used to optimize the vehicle frequency characteristic.

Efficient electromagnetic micropunching technology for producing well-ordered, high-density micropits

ABSTRACT Micropits are favorable for interfacial lubrication and cell culturing. This study developed an AC electromagnetic-driven high-speed micropunching mechanism capable of rapidly fabricating a large-numbered array of well-ordered micropits. The designed mechanism converts 60-Hz AC into 120-Hz electromagnetic force, which in turn drives a punching-shaft to complete a high-speed punching movement at 120-Hz. The micropunching mechanism is installed on a desktop gantry framework to create a stable, high-speed CNC micropunching system. Combining an eddy current sensor with an oscilloscope determines optimal spring stiffness for the system. A micropunching experiment is performed using a micropunching tool comprised of electrically conductive polycrystalline composite diamond (ECPCD) and an annealed aluminum alloy workpiece. The results revealed that a 120-Hz punching-frequency, a spring stiffness of 2.7 N/mm, and a workpiece moving speed of 2160 mm/min generate micropits with a high-integrity profile. It takes only 3.4 seconds to complete 400 high-integrity, well-organized micropits, with a depth of 23.0–23.3 μm that are burr-free and almost chipless, indicating the proposed high-speed electromagnetic micropunching technology is highly precise and efficient while also being energy-saving.

Stiffness-Oriented Placement Optimization of Machining Robots for Large Component Flexible Manufacturing System

A large component flexible manufacturing system provides more application scenarios for industrial robots, and, in turn, these robots exhibit competitive advantages in machining applications. However, the structural characteristic of low stiffness is the main obstacle for the industrial robot. Aiming at obtaining sufficient stiffness in the whole machining process, this paper focuses on robot placement optimization in the flexible manufacturing of large components. The geometric center of the machined feature is selected as, firstly, the base point, and the center-reachable placement space of the robot base is obtained by establishing the kinematic model considering a variety of motion constraints. Then, according to the reachability of the machining feature contour, the global placement space meeting all machining boundaries is further extracted. The mapping relationship between joint force and posture is established, and the most suitable robot placement is selected based on the criterion of global stiffness optimization. A series of numerical and finite element simulations verify the correctness and effectiveness of the proposed optimization strategy. The developed stiffness-oriented placement planning algorithm can provide beneficial references for robotic machining applications.

A new layout optimization method for stiffened panels based on ground stiffener structure (GSS) and thickness penalty

The stiffener layout has a crucial impact on the load-bearing performance of stiffened panels. It is difficult for existing methods to directly obtain a stiffener layout design that meets the manufacturing requirements without post-processing. In this paper, a new layout optimization method for stiffened panels is proposed, in which the ground stiffener structure is pre-modeled and the optimal stiffener layout is obtained by optimizing the thickness of each stiffener, where the intermediate thickness is penalized to ensure that a clear stiffener layout is acquired. The enrichment constraint and its KS function are derived to restrict the local excessive concentration of stiffeners in the final optimization results, so as to ensure the manufacturability of the obtained stiffener layout. Moreover, the explicit and clear stiffener layout design scheme can be obtained from the pre-modeled ground stiffener structure, which can be imported directly into the CAD system, so no additional post-processing such as geometric reconstruction is required. Through eight typical examples, the effectiveness of the proposed method is verified, which will be a meaningful supplement to existing layout optimization methods of thin-walled stiffened structures.

Prosthetic forefoot and heel stiffness across consecutive foot stiffness categories and sizes.

Prosthetic foot stiffness plays a key role in the functional mobility of lower limb prosthesis users. However, limited objective data exists to guide selection of the optimal prosthetic foot stiffness category for a given individual. Clinicians often must rely solely on manufacturer recommendations, which are typically based on the intended user's weight and general activity level. Availability of comparable forefoot and heel stiffness data would allow for a better understanding of differences between different commercial prosthetic feet, and also between feet of different stiffness categories and foot sizes. Therefore, this study compared forefoot and heel linear stiffness properties across manufacturer-designated stiffness categories and foot sizes. Mechanical testing was completed for five types of commercial prosthetic feet across a range of stiffness categories and three foot-sizes. Data were collected for 56 prosthetic feet, in total. Testing at two discrete angles was conducted to isolate loading of the heel and forefoot components, respectively. Each prosthetic foot was loaded for six cycles while force and displacement data were collected. Forefoot and heel measured stiffness were both significantly associated with stiffness category (p = .001). There was no evidence that the relationships between stiffness category and measured stiffness differed by foot size (stiffness category by size interaction p = .80). However, there were inconsistencies between the expected and measured stiffness changes across stiffness categories (i.e., magnitude of stiffness changes varied substantially between consecutive stiffness categories of the same feet). While statistical results support that, on average, measured stiffness is positively correlated with stiffness category, force-displacement data suggest substantial variation in measured stiffness across consecutive categories. Published objective mechanical property data for commercial prosthetic feet would likely therefore be helpful to clinicians during prescription.

Dynamics identification and stability analysis in turning of slender workpieces with flexible boundary constraints

The exact implementation of the turning stability analysis mainly depends on the realistic prediction model and reliable dynamical parameters. However, the workpiece located in the chuck-workpiece-tailstock dynamical system is generally regarded as a combination of a cantilever and a simply-supported beam. The effect of boundary conditions is ignored in the prediction of structural dynamics and stability limits. Hence, in this paper a model for slender workpieces with flexible boundary constraints is first built to improve the prediction accuracy of the turning stability. In this model, a two-dimensional (2D) compliance of the tool and part as well as the effect of the tool nose radius are incorporated in the dynamic force modeling, and the dynamical characteristic of slender workpieces in the chuck-workpiece-tailstock dynamical system is calculated according to the continuum theory. Then a novel strategy is proposed to identify the connection stiffness acting on the joint interface of the turning machine. According to the mathematical relation of workpiece dynamics induced by boundary conditions, a further theoretical derivation for the best selection of characteristic parameters, which is the critical part of the identification strategy, is developed on this basis. The optimal connection stiffness is determined by minimizing the deviation between the experimental and simulated values of characteristic parameters. The measured results of structural dynamics indicate that the connection stiffness identified from partial working conditions is also applicable to other working conditions. Finally, a series of turning experiments are conducted on this basis to verify the position-dependent stability limits considering flexible boundary constraints. The prediction result shows a good agreements with the experimental result. It proves that the proposed method has a unique advantage for the dynamics identification and stability analysis of the slender workpiece.

Collaborative optimization of bushing installation angle and bushing stiffness of torsion beam suspension to improve the handing stability of the whole vehicle

Both the bushing installation angle and bushing stiffness of torsion beam suspension have important and complex effects on suspension characteristics and vehicle handling stability. For improving the vehicle handling stability by optimizing the two, this paper systematically analyzes the influence mechanism of the bushing installation angle and bushing stiffness of the torsion beam suspension on the suspension C characteristic. The nonlinear relationship between the bushing installation angle and the steady-state characteristics index in the local design space is discussed. The influence mechanism of the bushing installation angle and bushing stiffness on the frequency response characteristics is deeply analyzed, the variation relationship of the frequency characteristic index at the low frequency of 0.5 Hz under different bushing installation angles and bushing stiffnesses is obtained. Finally, the bushing stiffness, which has a great influence on the frequency characteristics, and the bushing installation angle are taken as the optimization variables, and the frequency characteristic index is taken as the optimization goal, and the multi-objective collaborative optimization of the frequency characteristic is carried out with the help of genetic algorithm. From the comparative analysis of transient and steady-state characteristics before and after optimization, it can be seen the vehicle handling stability has been improved.