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The database generation for planar 2-DOF fractionated multiple-joint kinematic chains 平面 2-DOF 分段式多关节运动学链的数据库生成
Pub Date : 2024-04-15 DOI: 10.1115/1.4065321
Peng Huang, Tingting Liu, Huafeng Ding, Yuqian Zhao
According to fractionation concept and whether containing a multiple-joint, planar kinematic chains (KCs) are primarily categorized as non-fractionated simple-joint kinematic chains (NFS-KCs), fractionated simple-joint kinematic chains (FS-KCs), non-fractionated multiple-joint kinematic chains (NFM-KCs), and fractionated multiple-joint kinematic chains (FM-KCs). Currently, there is a noticeable research gap on the enumeration of FM-KCs, whereas comprehensive investigations have been conducted on the enumeration of the other three types of KCs. Aiming at addressing this research gap, the present study develops a heuristic approach for enumerating all planar 2-DOF FM-KCs. To this end, the composition of 2-DOF FM-KCs is initially analyzed to acquire their basic two classifications. Then, utilizing the characteristic graph generation methods for NFM-KCs and NFS-KCs, the combined characteristic graph and its corresponding combined characteristic number string of a 2-DOF FM-KC are created for solving the isomorphic problem in enumeration procedure. Finally, all non-isomorphic 2-DOF FM-KCs with 9, 11, 13, 15 and 17 links are enumerated and the corresponding database is established.
根据分馏概念和是否含有多关节,平面运动链(KCs)主要分为非分馏单关节运动链(NFS-KCs)、分馏单关节运动链(FS-KCs)、非分馏多关节运动链(NFM-KCs)和分馏多关节运动链(FM-KCs)。目前,关于 FM-KCs 列举的研究存在明显空白,而关于其他三种类型 KCs 列举的研究则已全面展开。针对这一研究空白,本研究开发了一种启发式方法,用于枚举所有平面 2-DOF FM-KC。为此,首先分析了 2-DOF FM-KC 的组成,以获得其基本的两种分类。然后,利用 NFM-KC 和 NFS-KC 的特征图生成方法,创建 2-DOF FM-KC 的组合特征图及其相应的组合特征数串,以解决枚举过程中的同构问题。最后,枚举出具有 9、11、13、15 和 17 个链接的所有非同构 2-DOF FM-KC 并建立相应的数据库。
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引用次数: 0
Positioning error estimation models for horizontal-distributed PUU parallel mechanism 水平分布 PUU 并行机制的定位误差估计模型
Pub Date : 2024-04-15 DOI: 10.1115/1.4065320
J. Ke, Yu-Jen Wang, Jhy-Cherng Tsai
In this paper, two models were proposed to estimate the positioning error of a 3-translational prismatic-universal-universal parallel kinematic mechanism. The two models were a kinematic error model (KEM) and a backpropagation neural network (BPNN) model, respectively. The KEM was constructed by incorporating three translational joint errors into the ideal kinematic model to describe the errors that occur during machining or assembly. Additionally, a sensitivity analysis was presented for each error parameter. The BPNN model was constructed to establish the relationship between the position of the end effector, the posture of each link, and the positioning error of the end effector using a neural network approach. Moreover, a hybrid method was proposed to decrease the final estimated residual error. The average errors of the KEM and BPNN model were 35% and 15% of the original error, respectively. The hybrid model reduced the final average error to less than 10% of its original value.
本文提出了两个模型来估算三跨棱柱-通用-通用并联运动机构的定位误差。这两个模型分别是运动误差模型(KEM)和反向传播神经网络(BPNN)模型。KEM 是通过将三个平移关节误差纳入理想运动学模型来构建的,以描述加工或装配过程中出现的误差。此外,还对每个误差参数进行了灵敏度分析。构建了 BPNN 模型,利用神经网络方法建立了末端效应器的位置、每个链接的姿态和末端效应器定位误差之间的关系。此外,还提出了一种混合方法来减少最终估计的残余误差。KEM 和 BPNN 模型的平均误差分别为原始误差的 35% 和 15%。混合模型则将最终平均误差降低到原始误差的 10%以下。
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引用次数: 0
A Cable-Based Haptic Interface with a Reconfigurable Structure 基于电缆的可重构结构触觉界面
Pub Date : 2024-04-15 DOI: 10.1115/1.4065318
Bastien Poitrimol, Hiroshi Igarashi
Cable robots have been used as haptic interfaces for several decades now, with the most notable examples being the SPIDAR and its numerous iterations throughout the years, as well as the more recent IPAnema 3 Mini manufactured by Fraunhofer IPA. However, these robots still have drawbacks, particularly their high number of cables required to maintain a high workspace-to-installation-space ratio. Using a hybrid-structure cable robot (HSCR) could prevent some collisions that occur between the cables and the user's body. More specifically, some applications requiring multimodal feedback could benefit from the flexibility that a reduced number of cables offers. Therefore, this paper presents a novel SPIDAR-like VSCR and its sensor-less force control method based on motor current. The purpose of this work is to clarify the advantages that a variable structure can provide for haptic interaction. In this regard, experimental results regarding the device's workspace and its force feedback capabilities are presented. Additionally, since real-time high-frequency updates are required for haptic display, we provide additional data regarding the control algorithm's runtime. Lastly, another experiment was conducted to study changes in user performance when using both the variable and the usual cable configuration. The results showed that feedback accuracy is maintained, and there are no drawbacks to using hybrid configurations.
缆线机器人用作触觉界面已有几十年的历史,其中最著名的例子是 SPIDAR 及其多年来的多次迭代,以及最近由 Fraunhofer IPA 制造的 IPAnema 3 Mini。然而,这些机器人仍然存在缺点,特别是需要大量电缆来保持较高的工作空间与安装空间比。使用混合结构电缆机器人(HSCR)可以避免电缆与用户身体之间发生碰撞。更具体地说,一些需要多模态反馈的应用可以从减少缆线数量所带来的灵活性中获益。因此,本文介绍了一种新型的类 SPIDAR VSCR 及其基于电机电流的无传感器力控制方法。这项工作的目的是阐明可变结构可为触觉交互带来的优势。为此,我们介绍了有关设备工作空间及其力反馈能力的实验结果。此外,由于触觉显示需要实时高频更新,我们还提供了有关控制算法运行时间的额外数据。最后,我们还进行了另一项实验,以研究使用可变电缆配置和常规电缆配置时用户性能的变化。结果表明,反馈精度得以保持,而且使用混合配置没有任何缺点。
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引用次数: 0
Design and analysis of a symmetric overconstrained compliant tilt/tip stage based on a hybrid transmission ratio model 基于混合传动比模型的对称过约束顺应倾斜/尖端平台的设计与分析
Pub Date : 2024-04-03 DOI: 10.1115/1.4065258
Jian Yang, Peng Yan
Developing a compliant mechanism that have potential in parasitism suppression and cross-axis decoupling is a major challenge to meet the requirement of spatial micro-/nano positioning. This work introduces a compliant tilt/tip stage design with a symmetric and overconstrained configuration that is equipped with four reverse-bridge-notch-flexure amplifiers(RBNFAs) and five revolute notch flexure hinges as multiaxis decoupled structures. A hybrid transmission ratio model is developed to describe the mechanical behavior of this stage using elastic beam and pseudo-rigid-body theories. Finite element analysis(FEA) confirmed the analytical model results. A comprehensive study is performed based on FEA model to validate the influence of a particular configuration on parasitic motion and decoupling effect. A prototype stage is 3D-printed and experimentally tested, which confirmed the predictions of the analytical hybrid model. Additionally, further analysis was conducted to examine the static mechanical characteristics and parasitic behavior of the stage.
要满足微米/纳米空间定位的要求,开发具有寄生抑制和跨轴去耦潜力的顺应式机构是一项重大挑战。这项工作介绍了一种具有对称和过约束配置的顺应倾斜/尖端平台设计,它配备了四个反向桥式缺口挠性放大器(RBNFA)和五个外旋缺口挠性铰链作为多轴解耦结构。利用弹性梁和假刚体理论建立了一个混合传动比模型来描述该平台的机械行为。有限元分析(FEA)证实了分析模型的结果。在有限元分析模型的基础上进行了综合研究,以验证特定配置对寄生运动和去耦效应的影响。对原型平台进行了 3D 打印和实验测试,证实了混合分析模型的预测结果。此外,还进行了进一步分析,以检查平台的静态机械特性和寄生行为。
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引用次数: 0
Analytic Centre Based Tension Distribution for Cable-Driven Platforms (CDPs) 基于分析中心的缆索驱动平台(CDP)张力分布
Pub Date : 2024-04-02 DOI: 10.1115/1.4065244
Vincenzo Di Paola, Alexandre Goldsztejn, Matteo Zoppi, Stéphane Caro
A redundant Cable-Driven Platform (CDP) is composed of m cables that exceed the Degree of Freedom (DOF) of the end-effector. The choice of tension along the cables admits infinite solutions. This paper proposes the use of the Analytic Centre to solve the tension distribution problem. Adopting this technique allows finding tensions far from the tension limits namely, textit{robust} as well as tension profiles continuous and differentiable in time. The continuity, differentiability and uniqueness of the solution is also proven. Moreover, the possibility of including non-linear constraints acting on the tensions (e.g. friction) is a further contribution. The computational time with the proposed approach is compared to the existing techniques to asses its real-time applicability. Finally, several simulations using several CDPRs' architectures are reported to demonstrate the method's capabilities.
冗余缆索驱动平台(CDP)由超过末端执行器自由度(DOF)的多根缆索组成。沿缆索张力的选择存在无限解。本文建议使用分析中心来解决张力分布问题。采用这种技术可以找到远离张力极限的张力,即textit{robust}以及在时间上连续且可微分的张力曲线。解的连续性、可微性和唯一性也得到了证明。此外,将作用于张力的非线性约束条件(如摩擦力)包括在内的可能性也是一大贡献。为了评估该方法的实时适用性,我们将该方法的计算时间与现有技术进行了比较。最后,报告了使用几种 CDPR 架构进行的几次模拟,以证明该方法的能力。
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引用次数: 0
Redundant Non-Serial Implicit Manipulator Kinematics and Dynamics 冗余非串行隐式机械手运动学和动力学
Pub Date : 2024-04-02 DOI: 10.1115/1.4065234
Edward J. Haug
Redundant non-serial manipulators that encompass a broad spectrum of parallel and non-parallel heavy load bearing construction and material handling equipment are treated, using foundations of differential geometry. Kinematics of this category of manipulator are defined in configuration space by algebraic equations in input and output coordinates that cannot be explicitly solved for either set of coordinates as a function of the other. New sets called assembly components of manipulator configuration space are defined that partition the space into disjoint topological components whose assembled configurations cannot be connected by continuous trajectories. Forward and inverse kinematically singular configurations are characterized by criteria that partition each assembly component into singularity free assembly components in which equations of kinematics and dynamics are well behaved. Three typical applications and associated simplified model problems are studied throughout the paper to illustrate methods and results presented. Singularity free differentiable configuration space manifolds are parameterized by both input and operational coordinates, leading to well posed ordinary differential equations of manipulator dynamics in both input and operational coordinates. It is shown that generalized inverse velocity kinematic equations that are problematic for serial manipulators are likewise plagued with problems for non-serial implicit manipulators that can be avoided using the methods presented.
利用微分几何学的基础,对包括各种平行和非平行重型承重建筑和材料处理设备的冗余非串行机械手进行了研究。这类机械手的运动学是通过输入和输出坐标中的代数方程在配置空间中定义的,而这两组坐标中的任何一组都无法作为另一组的函数明确求解。我们定义了被称为机械手配置空间装配组件的新集合,将空间划分为互不相交的拓扑组件,这些组件的装配配置不能通过连续轨迹连接。正向和逆向运动学奇异配置的特征是通过标准将每个装配组件划分为无奇异的装配组件,其中的运动学和动力学方程表现良好。本文研究了三个典型应用和相关的简化模型问题,以说明本文介绍的方法和结果。无奇点可变的配置空间流形由输入坐标和操作坐标参数化,从而在输入坐标和操作坐标中得出机械手动力学方程。结果表明,对于串行操纵器而言存在问题的广义速度反向运动方程,对于非串行隐式操纵器而言同样存在问题,而这些问题都可以通过所介绍的方法加以避免。
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引用次数: 0
Online Self-Calibration of Cable-Driven Parallel Robots Using Covariance-Based Data Quality Assessment Metrics 使用基于协方差的数据质量评估指标对电缆驱动并联机器人进行在线自我校准
Pub Date : 2024-04-02 DOI: 10.1115/1.4065236
Ryan Caverly, Sze Kwan Cheah, Keegan R. Bunker, Samir Patel, Niko Sexton, Vinh L. Nguyen
This paper presents an algorithm to perform self-calibration of cable-driven parallel robots (CDPRs), where the CDPR's end-effector pose is estimated in conjunction with the calibration of biases in the CDPR's measurements. Two new metrics, known as the position dilution of precision (PDOP) and orientation dilution of precision (ODOP) are introduced as a means to quantify the quality of data collected with regards to self-calibration. These metrics are based on a covariance matrix that is computed online as part of the proposed self-calibration algorithm, which results in the PDOP and ODOP directly corresponding to the standard deviation of the position and orientation errors, respectively. These metrics are used to intuitively select which data points contribute to improved calibration, resulting in a computationally-efficient algorithm requiring few data points to maintain accurate calibration. Additionally, the PDOP and ODOP provide a means to assess when sufficient calibration data has been collected. Numerical results involving an inverse kinematic simulation with rigid cables and a dynamic simulation with flexible cables indicate that the proposed algorithm is capable of performing self-calibration in a computationally-efficient manner. Moreover, the simulation results indicate that the proposed PDOP and ODOP metrics result in smaller position and orientation errors when used to prune the data set compared to the observability indices found in the literature. Accuracy of the proposed algorithm is also confirmed through experiments when compared to ground-truth pose data.
本文提出了一种对缆索驱动并联机器人(CDPR)进行自我校准的算法,在校准 CDPR 测量偏差的同时估算 CDPR 的末端执行器姿态。本文引入了两个新指标,即位置精度稀释(PDOP)和方向精度稀释(ODOP),作为量化自校准方面所收集数据质量的一种方法。这些指标基于协方差矩阵,该矩阵是作为拟议自校准算法的一部分进行在线计算的,其结果是 PDOP 和 ODOP 分别直接对应于位置误差和方向误差的标准偏差。这些指标用于直观地选择哪些数据点有助于改进校准,从而产生一种计算效率高的算法,只需很少的数据点就能保持精确的校准。此外,PDOP 和 ODOP 还提供了一种方法,用于评估何时已收集到足够的校准数据。使用刚性电缆进行反运动学模拟和使用柔性电缆进行动态模拟的数值结果表明,所提出的算法能够以计算效率高的方式进行自我校准。此外,仿真结果表明,与文献中的可观测性指数相比,提议的 PDOP 和 ODOP 指标用于剪切数据集时,位置和方向误差较小。通过与地面实况姿态数据进行比较,实验也证实了所提出算法的准确性。
{"title":"Online Self-Calibration of Cable-Driven Parallel Robots Using Covariance-Based Data Quality Assessment Metrics","authors":"Ryan Caverly, Sze Kwan Cheah, Keegan R. Bunker, Samir Patel, Niko Sexton, Vinh L. Nguyen","doi":"10.1115/1.4065236","DOIUrl":"https://doi.org/10.1115/1.4065236","url":null,"abstract":"\u0000 This paper presents an algorithm to perform self-calibration of cable-driven parallel robots (CDPRs), where the CDPR's end-effector pose is estimated in conjunction with the calibration of biases in the CDPR's measurements. Two new metrics, known as the position dilution of precision (PDOP) and orientation dilution of precision (ODOP) are introduced as a means to quantify the quality of data collected with regards to self-calibration. These metrics are based on a covariance matrix that is computed online as part of the proposed self-calibration algorithm, which results in the PDOP and ODOP directly corresponding to the standard deviation of the position and orientation errors, respectively. These metrics are used to intuitively select which data points contribute to improved calibration, resulting in a computationally-efficient algorithm requiring few data points to maintain accurate calibration. Additionally, the PDOP and ODOP provide a means to assess when sufficient calibration data has been collected. Numerical results involving an inverse kinematic simulation with rigid cables and a dynamic simulation with flexible cables indicate that the proposed algorithm is capable of performing self-calibration in a computationally-efficient manner. Moreover, the simulation results indicate that the proposed PDOP and ODOP metrics result in smaller position and orientation errors when used to prune the data set compared to the observability indices found in the literature. Accuracy of the proposed algorithm is also confirmed through experiments when compared to ground-truth pose data.","PeriodicalId":508172,"journal":{"name":"Journal of Mechanisms and Robotics","volume":"17 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140754847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Kinematic Synthesis Methodology for P-Drivable Spatial Single Degree of Freedom Mechanisms to Avoid Singularities 避免奇异性的可 P 驱动空间单自由度机构运动合成方法学
Pub Date : 2024-04-01 DOI: 10.1115/1.4065237
Mohammad Z. Khan, Jian Liu, D. Myszka, Andrew P. Murray
For a single degree of freedom spatial mechanism, a reference frame attached to any of its links produces a continuous motion of this frame. Given the progression of this frame from the start through the end of the mechanism's motion, this paper seeks to identify specific points relative to this moving reference frame. The points of interest are those that can be coupled with a second point determined in the fixed frame to act as the end joint locations for a spherical-prismatic-spherical (SPS) driving chain. If the selection of the point pair is made such that the change in distance between them as the mechanism moves is strictly monotonic, then the SPS chain they define is potentially capable of driving the mechanism over the desired range of motion. This motion is referred to as locally P-drivable because a global solution is not ensured by the process proposed herein. This synthesis process can avoid singularities encountered by actuating the mechanism at one of its original joints. The proposed approach enables the dimensional synthesis of a single degree-of-freedom mechanism to focus on creating circuit-defect-free solutions without concern for potential singular positions. The actuating chain can then be determined as a separate step in the synthesis process. This paper also considers motions that are not P-drivable and the specialization to planar systems with the synthesis of a P-drivable RPR chain.
对于单自由度空间机构而言,连接到其任何一个环节的参照系都会产生连续的运动。考虑到该参照系从机构运动的开始到结束的过程,本文试图确定相对于该运动参照系的特定点。这些点可以与固定框架中确定的第二个点耦合,作为球面-棱镜-球面(SPS)驱动链的末端关节位置。如果选择的点对在机构运动时它们之间的距离变化是严格单调的,那么它们定义的 SPS 链就有可能在所需的运动范围内驱动机构。这种运动被称为局部 P 可驱动运动,因为本文提出的流程并不能确保获得全局解决方案。这种合成过程可以避免在机构的一个原始关节处驱动机构所遇到的奇异现象。所提出的方法可使单自由度机构的尺寸合成专注于创建无电路缺陷的解决方案,而无需考虑潜在的奇异位置。然后,执行链可作为合成过程中的一个单独步骤来确定。本文还考虑了不可 P 驱动的运动以及平面系统的特殊化,并合成了可 P 驱动的 RPR 链。
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引用次数: 0
Bistable Aerial Transformer (BAT): A Quadrotor Fixed-Wing Hybrid that Morphs Dynamically via Passive Soft Mechanism 双稳态空中变压器 (BAT):通过被动软机制动态变形的四旋翼固定翼混合动力机
Pub Date : 2024-03-25 DOI: 10.1115/1.4065159
Jessica Weakly, Xuan Li, Tejas Agarwal, Minchen Li, Spencer Folk, Chenfanfu Jiang, Cynthia Sung
Aerial vehicle missions require navigating trade-offs during design, such as the range, speed, maneuverability, and size. Multi-modal aerial vehicles enable this trade-off to be negotiated during flight. This paper presents a Bistable Aerial Transformer (BAT) robot, a novel morphing hybrid aerial vehicle (HAV) that switches between quadrotor and fixed- wing modes via rapid acceleration and without any additional actuation beyond those required for normal flight. The design features a compliant bistable mechanism made of thermoplastic polyurethane (TPU) that bears a large mass at the center of the robot's body. When accelerating, inertial forces transition the vehicle between its stable modes, and a four-bar linkage connected to the bistable mechanism folds the vehicle's wings in and out. The paper includes the full robot design and a comparison of the fabricated system to the elastodynamic simulation. Successful transitions between the two modes in mid-flight, as well as sustained flight in each mode indicate that the vehicle experiences higher agility in the quadrotor mode and higher flight efficiency in the fixed-wing mode, at an energy equivalent cost of only 2 s of flight time per pair of transitions. The vehicle demonstrates how compliant and bistable mechanisms can be integrated into future aerial vehicles for controllable self-reconfiguration for tasks such as surveillance and sampling that require a combination of maneuverability and long-distance flight.
航空飞行器在执行任务时,需要在设计过程中进行权衡,如航程、速度、机动性和尺寸。多模式航空飞行器可以在飞行过程中进行这种权衡。本文介绍的双稳态空中变压器(BAT)机器人是一种新型变形混合飞行器(HAV),可通过快速加速在四旋翼和固定翼模式之间切换,除正常飞行所需的驱动外无需任何额外驱动。该设计的特点是采用热塑性聚氨酯(TPU)制成的顺应式双稳态机构,在机器人身体中心承载一个大质量。加速时,惯性力会使飞行器在稳定模式之间转换,而与双稳态机构相连的四杆连杆则会使飞行器的机翼折叠或收起。论文包括完整的机器人设计以及制造系统与弹性动力学模拟的比较。飞行中期两种模式之间的成功转换以及每种模式下的持续飞行表明,飞行器在四旋翼模式下具有更高的灵活性,在固定翼模式下具有更高的飞行效率,而每对转换的能量等效成本仅为 2 秒钟的飞行时间。该飞行器展示了如何将顺从和双稳态机制集成到未来的航空飞行器中,实现可控的自我重新配置,以完成监视和采样等需要机动性和长距离飞行相结合的任务。
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引用次数: 0
Hydrodynamic performance research of underwater oscillating fin with the compound locomotion of two modes 双模复合运动水下振动鳍的水动力性能研究
Pub Date : 2024-03-19 DOI: 10.1115/1.4065137
Qian Yin, Ming-hai Xia, Wen-bin Zhang, Yuan Luo, Jianzhong Shang, Zirong Luo
The fish-like propulsion robot is becoming a profound intelligent equipment due to its excellent swimming ability and good environmental adaptability. In this paper, we propose the oscillating fin based on the fish-swimming mechanism which compounded with the locomotion modes of sway and yaw. The kinematic and dynamic models are established to study the locomotion mechanism of the oscillating fin. The hydrodynamic performance of the underwater locomotion is investigated to analyze the velocity, the propulsive force, the pressure, the propulsive efficiency and the vortices property. Finally, the experimental measurements of the robot with oscillating fin propulsion are carried out to analyze the underwater propulsion of the oscillating fin and the unsteady fluid flow with Strouhal Number. The results illustrate that the propulsive force is fluctuating and the velocity is increasing to the maximum value. The underwater propulsion velocity could reach 1.2 m/s in the period time of 0.4s. Besides, the high and low pressure regions change alternatively and the fin deforming process which illustrate the vortices property and the locomotion mechanism analyses. The propulsive efficiency of the oscillating fin with compound waves is increased by 11% compared with that of the one without deformation. The experiments of the robot prototype verifies the numerical simulation and the propulsive velocity with the period of 0.4s is two times larger than that of the period of 0.8s. The Strouhal Number of each motion mode is obtained through theoretical and experimental analyses.
鱼类推进机器人因其卓越的游泳能力和良好的环境适应性,正在成为一种深层次的智能装备。本文基于鱼类的游泳机理,提出了摇摆鳍的运动模式。本文建立了运动学和动力学模型来研究摆动鳍的运动机理。研究了水下运动的水动力性能,分析了速度、推进力、压力、推进效率和涡流特性。最后,对摆动鳍推进机器人进行了实验测量,分析了摆动鳍的水下推进力和具有斯特劳哈尔数的非稳态流体流动。结果表明,推进力是波动的,推进速度不断增加,直至达到最大值。在 0.4 秒的时间内,水下推进速度可达 1.2 m/s。此外,高低压区交替变化和鳍片变形过程说明了涡旋特性和运动机理分析。与没有变形的鳍相比,带有复合波的振荡鳍的推进效率提高了 11%。机器人原型的实验验证了数值模拟,周期为 0.4s 的推进速度是周期为 0.8s 的推进速度的两倍。通过理论和实验分析得出了每种运动模式的斯特劳哈尔数。
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引用次数: 0
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