Kinematic Principles Research Articles

Study on a Novel Reseeding Device of a Precision Potato Planter

In order to address the problem of a high miss-seeding rate in mechanized potato planting work, a novel reseeding device is designed and analyzed. Based on dynamic and kinematic principles, the seed potato’s motion analysis model in the seed preparation process was constructed. The analysis results indicate that the seed preparation performance is positively related to the seed preparation opening length l1 and inclination angle of the seed-returning pipe θ. Then, the potato’s motion analysis model in the reseeding process was constructed. The analysis showed that the displacement of seeding potatoes in the horizontal direction ds is influenced by the initial seeding potato’s speed , dropping height hs, and the angle between the seeding pipe and the horizontal ground βs. The horizontal moving distance xr of the reseeding potatoes is influenced by the angle between the bottom of the reseeding pipe and horizontal ground βs2, the distance from its centroid to the reseeding door d, and the dropping height of the potato hr. The analysis results indicated that the reseeding potato can be effectively discharged into the furrow. Then, a prototype of a reseeding control system was constructed based on the STM32 microcontroller, electric pushers, and through-beam laser sensors. The simulation analysis was conducted to verify the theoretical analysis by using EDEM2020 software. The simulation results indicated that with the increase in the seeding chain speed, the seed preparation success rate initially increased slowly and then decreased gradually. The seed preparation performance can be increased by increasing the seed preparation opening length or decreasing the seed-returning pipe inclination angle. The impact on the successful seed preparation rate is ranked by significance as follows: seed preparation opening length > seed-returning pipe inclination angle > chain speed. Then, the prototype reseeding device and the corresponding seed metering device were manufactured and a series of bench tests and field tests were conducted. The bench test results showed an average successful seed preparation rate of 93.6%. The average qualified-seeding rate, miss-seeding rate, and multi-seeding rate in the field test were 89.6%, 2.46%, and 7.94%, respectively. This study can provide a theoretical reference for the design of potato reseeding devices.

Research on the Measurement and Estimation Method of Wheel Resistance on a Soil Runway

In view of the fact that there is no suitable measurement method for tire driving resistance during the operation of a transporter on soil pavement, this paper proposes a simple measurement and estimation method for driving resistance on a soil runway based on the Bekker settlement model. In this paper, using the driving resistance equation based on the Bekker model, a simplified equation of driving resistance related to mass is proposed. Using the principle of kinematics, a simple test device for driving resistance was developed, and the test data of the test device were used to determine the parameters of the driving resistance estimation equation of the road surface. The driving resistance of the wheel running state was tested by the simulated aircraft load loading vehicle through the mechanical sensor, and the consistency between the theoretical value and the actual value of the driving resistance value under 8T, 10T, and 12T loads was verified. This research shows that the test method and estimation method have low cost and good accuracy and are suitable for wide promotion. The results of this paper provide a new idea and method for estimating the driving resistance of a wheel when a transporter runs on a soil road and also provide a reference for designing the length of a soil runway.

A novel method for measuring three-axis dynamic centrifugal acceleration field: the matrix transformation method

Abstract When a three-axis dynamic centrifuge is used to test the performance of inertial equipment (accelerometer, gyroscope, gyro-accelerometer, etc.), accurate estimating of the acceleration at the sensing position of the tested sensors is a key step. To solve the problem of the lack of relevant suitable methods, first, the principle of rigid body kinematics is used to prove that the acceleration of each point on a rigid body changes linearly with respect to the position. Subsequently, a matrix transformation method for accurately measuring the acceleration field on the three-axis dynamic centrifuge is presented. In this method, the distribution law (expressed by a 3×3 matrix) of the acceleration field is calculated based on the measured acceleration at multiple positions. After that the acceleration estimation value at any point on the centrifuge can be calculated. Finally, the uncertainty of the estimated acceleration value is analysed, and a verification experiment is carried out. The results show that the accuracy of this method is mainly limited by the accuracy of the acceleration measurements. The preliminary verification experiment system shows that the mean deviation of the estimated value error obtained by this method is less than 0.024 g, the standard uncertainty is less than 0.015 g, the left and right endpoints of the 95% probability inclusion interval are less than -0.026 g and 0.036 g, respectively, and the half width of the interval is less than 0.028 g. In all, this paper provides a powerful tool for examining the precision performance of inertial equipment on a three-axis dynamic centrifuge, and can also be used for calibration of this kind of centrifuge.

Vehicle Turning Carbon Emissions and Highway Planar Alignment Design Indicators

The carbon emitted by vehicles traveling on curved roads is greatly affected by the alignment of the route, yet the mechanism behind this is not yet clear, leading to current horizontal alignment designs being unable to avoid this problem. To clarify the principles and indicator thresholds of low-carbon design for planar geometry, this study takes the carbon emission of traveling on curved routes as the research object, and establishes a relationship model between carbon emissions and design indicators based on the principles of vehicle dynamics and kinematics. Field tests were conducted to validate the quantitative relationship model. The model shows that both radius and superelevation are negatively correlated with carbon emissions, while the lateral force coefficient is positively correlated with carbon emissions. The contribution of radius to carbon emissions is greater than that of superelevation. This study clarifies the recommended values of low-carbon design indicators by assessing carbon emissions according to the current route design specification, outlines the principles of superelevation settings, and proposes a methodology to deal with the relationship between superelevation and the lateral friction coefficient. The research findings promote the quantification and standardization of low-carbon highway design, contributing to the early mitigation of high-carbon emissions from curved traffic during the design phase.

Game psychotherapy intervention based on entertainment interactive robots for preventing depression in university students

This study designs an entertainment interactive robot system for gaming psychotherapy intervention and evaluates its effectiveness in preventing depression in students. In terms of the architecture and hardware of the entertainment interactive robot system, the robot adopts high-performance processors and sensors to achieve the ability to quickly respond and accurately perceive user actions. In terms of software, a mathematical model was established based on the structure and kinematic principles of the robot to describe its motion. Preprocess user gesture data by analyzing the features and patterns of user gestures, extracting key action information, and using machine learning algorithms or deep learning models to classify and recognize gestures to determine user intent and action types. Evaluate action recognition and effectiveness, and verify the accuracy and reliability of the gesture interaction module through comparison and testing with actual user gestures. The study designed an entertainment interactive robot assisted game that provides a fun and interactive experience to attract students’ attention and stimulate positive emotions. Through game design and behavioral pattern evaluation, the research team evaluated the preventive effect of entertainment interactive robot assisted games on depression and proposed optimization strategies.

Impact of kinematic parameters on lapping uniformity

ABSTRACT Kinematic principle in lapping process is an essential theoretical foundation to achieve high lapping accuracy. The motion path of abrasive grains determines the machined area on workpiece, thereby affecting the surface accuracy. To improve lapping uniformity, this paper established a kinematic model of swing fixed-abrasive lapping (SFAL) and investigated the effect of kinematic parameters (rotational speed ratio, swing ratio, swing angle) on lapping uniformity. Non-uniformity coefficient (NUC) was adopted to evaluate the lapping uniformity, and the impact mechanism of kinematic parameters on the trajectory of abrasive grains were revealed by Taguchi experiments and numerical simulation. Furthermore, response surface experiments were employed to optimize the parameter combination, and a prediction model for NUC was developed. This work provides theoretical guidance for the selection of kinematic parameters in SFAL process, and has reference significance for improving the lapping accuracy.

Conventionally instrumented inverse kinematic alignment for total knee arthroplasty: How is it done?

For primary total knee arthroplasty (TKA), there is an increasing trend towards patient-specific alignment strategies such as kinematic alignment (KA) and inverse kinematic alignment (iKA), which by restoring native joint mechanics may yield higher patient satisfaction rates. Second, the most recent Australian joint registry report describes favourable revision rates for conventionally instrumented TKA compared to technology-assisted techniques such as those using navigation, robotics or custom-cutting blocks. The aim of this technique article is to describe in detail a surgical technique for TKA that: (1) utilises the principles of iKA and (2) uses conventionally instrumented guided resections thereby avoiding the use of navigation, robotics or custom blocks. A TKA technique is described, whereby inverse kinematic principles are utilised and patient-specific alignment is achieved. Additionally, the patellofemoral compartment of the knee is restored to the native patellofemoral joint line. The sequenced technical note provided may be utilised for cemented or cementless components; cruciate retaining or sacrificing designs and for fixed or rotating platforms. An uncomplicated, robust and reproducible technique for TKA is described. Knee arthroplasty surgeons may wish to harness the emerging benefits of both a conventionally instrumented technique and a patient-specific alignment strategy. Level V.

Comprehensive analysis of rotor edgewise whirling mode interaction with rotor speed harmonics

This paper presents a model that investigates the interaction between rotor edgewise whirling modes and rotor speed harmonics in wind turbines. The model is based on kinematic and dynamic principles, with a focus on the multi-blade coordinate transformation, which is critical for simulating the behaviour of the rotor whirling modes in wind turbines. The research has two objectives: to investigate the interaction between the rotor edgewise whirling modes and the rotor speed harmonics, and to provide clearer graphs that explain the complex nature of this non-intuitive rotor dynamics. The paper concludes by highlighting the practical implications of the research findings, in particular the effectiveness of visualisation techniques in identifying and explaining unexpected interactions.

Kinematics-Based Design Method and Experimental Validation of Internal Meshing Screw for High-Viscosity Fluid Mixing

The challenge of mixing high-viscosity materials is a common issue encountered in the manufacturing process of food materials. The advantages of the internal meshing screw mixer have led to its adoption in various manufacturing processes, but it has yet to be implemented in the food industry. The paper presents a design method for an internal meshing screw mixer based on kinematic principles. The mixer features a helical chamber created by alternating volumes formed by the stator and rotor, establishing an extension-dominated environment for mixing high-viscosity fluids. A kinematic model based on the internal cycloid principle was established, providing trajectories and equations for key points on the rotor, simulating both its rotation and revolution processes, and revealing the velocity variations at different points on the rotor. Based on the kinematic analysis results, a stator and rotor design method was developed according to relevant functional divisions. To achieve the desired motion effects, transmission and support devices were designed, and the relationship between the transmission device and the internal cycloid surface of the fixed rotor was established. The mixer’s application and mixing effectiveness in the food industry were validated using corn syrup and flour. Experimental results showed that the extensional mixer described in the paper effectively mixed high-viscosity fluids while also efficiently blending fine powders. Slurry viscosity was tested with a rheometer at different speeds with an eccentric rotor mixer. Results showed that viscosity decreased with increasing shear rate, with a more pronounced decrease at higher shear rates. The apparent viscosity trend remained consistent at different speeds, although variations were observed at lower shear rates, especially concerning speed. The non-Newtonian fluid index exhibited minimal variations at different speeds, while the consistency coefficient showed significant fluctuations. The mixing uniformity index of the slurry was used to evaluate the mixing uniformity and dispersion uniformity of this extensional mixer. At different rotational speeds, the density of the slurry changes little. The uniformity index of mixing decreases gradually with the increase of rotational speed, reaching its maximum at 15 r/min. The overall trend of the uniformity index decreases with increasing rotational speed, indicating a decrease in density uniformity. A peak appears at 45 r/min, possibly due to the maximum values of elongation rate and shear rate at this speed. As the rotational speed increases, the residence time of the material in the mixer decreases, which may be the main reason for the decrease in mixing uniformity. These findings provide valuable insights into the design and utilization of extension-dominated screw mixers within the food industry, laying a solid foundation for future research and practical applications in this field.

Electro-Hydraulic Servo-Pumped Active Disturbance Rejection Control in Wind Turbines for Enhanced Safety and Accuracy

Aiming at the high accuracy and high robustness position control of servo pump control in the pitch system of a wind turbine generator, this paper proposes an active disturbance rejection controller (ADRC). The ADRC considers pitch angular velocity and acceleration limits. According to the kinematics principle of the pump-controlled pitch system, the relationship between the pitch angular velocity and acceleration limit and the displacement of the hydraulic cylinder is established. Through the method of theoretical analysis, the nonlinear relationship expression between pitch angle and hydraulic cylinder displacement is obtained, and the linearization of pitch angular velocity control is realized; the formula for b0 (the estimated value of the input gain of the system) of the pump-controlled pitch system is obtained by the method of modeling and analysis, b0 is the key parameter for the design of the ADRC; the stability of the controller parameters is proved through the stability analysis and simulation analysis, and the design of the self-immobilizing controller with pitch angular velocity and acceleration limitation is the completed ADRC design. Finally, a joint simulation platform of AMESim and MATLAB as well as a physical experiment platform of electro-hydraulic servo pump-controlled pitch control is constructed, and the effectiveness of the proposed control method is verified through simulation and experiment. The results show that compared with the unrestricted ADRC and PID, the velocity-acceleration-limited ADRC can effectively improve the control effect of the angular velocity and acceleration of the paddle, smooth the startup process, improve the safety of the system, and have better position control accuracy and anti-jamming ability.

Integrating a Physical Model with Multi-Objective Optimization for the Design of Optical Angle Nano-Positioning Mechanism

In light of recent advancements in synchrotron radiation technology and nano-technology, there has been a marked increase in the need for ultra-precision nano-positioning mechanisms. This paper presents a method that integrates physical models with multi-objective optimization for developing an optical angle nano-positioning mechanism. We begin by examining the actual motion law of the mechanism, based on kinematic principles. The outcomes from this kinematic analysis facilitate a static analysis of the flexible hinge, identified as a critical component of the mechanism. Subsequently, we establish a dynamic model for the entire mechanism. By employing the physical model as a base and combining it with the optimization algorithm, we identify the optimal design parameters for the mechanism. The design achieves a resolution of 50 nrad and meets the specified requirements. The first-order inherent frequency of the mechanism is approximately 43.75 Hz. There is a discrepancy of 2.63% from the finite element modal analysis results and a 3.33% difference from the theoretical analysis results, validating the reliability of the design method proposed in this study.

KINEMATIC ANALYSIS OF CROSS ON TRAINING AND COMPETITION RINGS: COMPARISON BETWEEN ELITE AND INTERNATIONAL LEVEL GYMNASTS

Auxiliary devices are used to train gymnastics skills. Based on the principles of training specificity, this study aimed to investigate the effectiveness of a training device for the static cross posture on Men’s Artistic Gymnastics rings through kinematic analysis. Twelve national team gymnasts were divided into two groups, based on their competitive results: the elite group (age: 21.8±3.2 years) and the international group (age: 19.3±3.3 years) performed the cross three times under both conditions: standard competition rings, and training rings with an auxiliary device. The videos were digitised and analysed with shoulder angles as trunk and arm segments. The variables included the right and the left shoulder angles in the frontal plane, as well as any asymmetry of those angles. Two-way ANOVA (conditions versus groups) and individual t-test statistics were conducted. Both groups performed the cross on training rings with increased abduction at both right (p<0.001) and left (p<0.001) shoulders and reduced asymmetry (p=0.01) than on competition rings. These kinematic improvements would translate into competition-typical score improvements of 0.1 to 0.3 points, and enhanced shoulder joint stability. Hence, the training rings with an auxiliary device effectively replicate skill-specific joint angles, adhering to the kinematics principles of training specificity for the static cross posture on rings, thus benefiting both elite and international-level gymnasts.

Correcting for asymmetry of the proximal tibial epiphysis is warranted to determine postoperative alignment deviations in kinematic alignment from planned alignment of the tibial component on the native tibia

BackgroundIn total knee arthroplasty, unrestricted kinematic alignment aims to restore pre-arthritic lower limb alignment and joint lines. Joint line orientations of the contralateral healthy proximal tibia might be used to evaluate accuracy of tibial component alignment post-operatively if asymmetry is minimal. Our objective was to evaluate left-to-right asymmetry of the proximal tibial epiphysis in posterior tibial slope and varus-valgus orientation as related to unrestricted kinematic alignment principles. MethodsHigh resolution CT images (0.5 mm slice thickness) were acquired from bilateral lower limbs of 11 skeletally mature subjects with no skeletal abnormalities. Images were segmented to generate 3D tibia models. Asymmetry was quantified by differences in orientations required to shape-match the proximal epiphysis of the mirror 3D tibia model to the proximal epiphysis of the contralateral 3D tibia model. FindingsSystematic and random differences (i.e. mean ± standard deviation) in tibial slope and varus-valgus orientation were − 0.8° ± 1.2° and − 0.2° ± 0.8°, respectively. Ninety five percent confidence intervals on the means included 0° indicating that systematic differences were minimal. InterpretationSince random differences due to asymmetry are substantial in relation to random surgical deviations from pre-arthritic joint lines previously reported, post-operative computer tomograms of the contralateral healthy tibia should not be used to directly assess accuracy of tibial component alignment on a group level without correcting for differences in tibial slope and varus-valgus orientation due to asymmetry.

Distributed Fixed-Time Control for Leader-Steered Rigid Shape Formation With Prescribed Performance.

Resorting to the principle of rigid body kinematics, a novel framework for a multirobot network is proposed to form and maintain an invariant rigid geometric shape. Unlike consensus-based formation, this approach can perform both translational and rotational movements of the formation geometry, ensuring that the entire formation motion remains consistent with the leader. To achieve the target formation shape and motion, a distributed control protocol for multiple Euler-Lagrange robotic vehicles subject to nonholonomic constraints is developed. The proposed protocol includes a novel prescribed performance control (PPC) algorithm that addresses the second-order dynamics of the robotic vehicles by employing a combination of nonsingular sliding manifold and adaptive law. Finally, the effectiveness of the proposed formation framework and control protocol is demonstrated through the numerical simulations and practical experiments with a team of four robotic vehicles.

Kinematics and trajectory analysis of swinging fixed abrasive plane lapping: Effect of swinging mode on the lapping uniformity

The relative motion between the workpiece and the fixed abrasive pad (FAP) determines the abrasive trajectories and the distribution of abrasives' sliding distance (ASD), and further affects the surface accuracy of the lapping process. To improve the surface accuracy of the swinging fixed abrasive plane lapping (SFAPL), the influence of the workpiece's swinging modes on the lapping uniformity was studied in this paper. The kinematics model of SFAPL was established by the coordinate transformation method based on the kinematical principle of the crank-rocker mechanism. The numerical simulation method was adopted to investigate the abrasive trajectories and the ASD on the workpiece surface in different swinging modes. Furthermore, the regional meshing and statistical methods were applied to visualize the simulation results, and the non-uniformity coefficient (NUC) and root mean square (rms) were employed to quantitatively evaluate the lapping uniformity. Finally, the verification experiments were carried out. Results indicated that the additional swinging could avoid the periodic distribution of material removal on the workpiece surface. The swinging mode significantly affected the lapping efficiency and lapping uniformity. Compared with the traditional lapping method, the lapping uniformity was optimal when the workpiece swung out of the FAP from the bottom and inner sides, and the lapping uniformity could be improved by 44.3 %; The lapping efficiency was the highest when the workpiece swung out of the FAP from the bottom side, and the material removal rate could be increased by 45.23 %. The appropriate swinging mode should be selected based on different processing requirements in SFAPL.

Machine learning–driven self-discovery of the robot body morphology

The morphology of a robot is typically assumed to be known, and data from external measuring devices are used mainly for its kinematic calibration. In contrast, we take an agent-centric perspective and ponder the vaguely explored question of whether a robot could learn elements of its morphology by itself, relying on minimal prior knowledge and depending only on unorganized proprioceptive signals. To answer this question, we propose a mutual information–based representation of the relationships between the proprioceptive signals of a robot, which we call proprioceptive information graphs (π-graphs). Leveraging the fact that the information structure of the sensorimotor apparatus is dependent on the embodiment of the robot, we use the π-graph to look for pairwise signal relationships that reflect the underlying kinematic first-order principles applicable to the robot’s structure. In our discussion, we show that analysis of the π-graph leads to the inference of two fundamental elements of the robot morphology: its mechanical topology and corresponding kinematic description, that is, the location and orientation of the robot’s joints. Results from a robot manipulator, a hexapod, and a humanoid robot show that the correct topology and kinematic description can be effectively inferred from their π-graph either offline or online, regardless of the number of links and body configuration.

Fabrication of the curved Fresnel lens array on the spherical surface by 6-axis diamond ruling

The curved Fresnel lens array on the spherical surface owns exceptional optical performance and meets the growing demand for smart home and security alarm systems. However, the intricate three-dimensional microstructure of such optical component is typically considered impossible to be directly fabricated by diamond machining. In this paper, a novel 6-axis diamond ruling method is proposed to fabricate the complex optics utilizing a commercial 6-axis ultra-precision machine tool. The kinematic principle and tool path generation algorithm of this method are presented. A varying-angle sampling strategy is employed in the proposed algorithm to reduce the acceleration and following error in the rotation of the A-axis. Novel trial cutting processes are introduced to figure out the tool setting errors induced by visual inspection, which need to be compensated in the tool path. Based on the proposed tool path generation algorithm and cutting processes, this method enables the efficient processing of precise curved Fresnel lenses. There is no interference between the diamond tool and the curved microstructure in the 6-axis synchronized motions. Finally, the feasibility and superiority of this method are experimentally verified by analyzing the surface roughness and shape accuracy of the machined component. It can indeed generate high-quality curved Fresnel lenses on the spherical surface by the proposed 6-axis diamond ruling method.

Stability Analysis and Navigational Techniques of Wheeled Mobile Robot: A Review

Wheeled mobile robots (WMRs) have been a focus of research for several decades, particularly concerning navigation strategies in static and dynamic environments. This review article carefully examines the extensive academic efforts spanning several decades addressing navigational complexities in the context of WMR route analysis. Several approaches have been explored by various researchers, with a notable emphasis on the inclusion of stability and intelligent capabilities in WMR controllers attracting the attention of the academic community. This study traces historical and contemporary WMR research, including the establishment of kinetic stability and the construction of intelligent WMR controllers. WMRs have gained prominence in various applications, with precise navigation and efficient control forming the basic prerequisites for their effective performance. The review presents a comprehensive overview of stability analysis and navigation techniques tailored for WMRs. Initially, the exposition covers the basic principles of WMR dynamics and kinematics, explaining the different wheel types and their associated constraints. Subsequently, various stability analysis approaches, such as Lyapunov stability analysis and passivation-based control, are discussed in depth in the context of WMRs. Starting an exploration of navigation techniques, the review highlights important aspects including path planning and obstacle avoidance, localization and mapping, and trajectory tracking. These techniques are carefully examined in both indoor and outdoor settings, revealing their benefits and limitations. Finally, the review ends with a comprehensive discussion of the current challenges and possible routes in the field of WMR. The discourse includes the fusion of advanced sensors and state-of-the-art control algorithms, the cultivation of more robust and reliable navigation strategies, and the continued exploration of novel WMR applications. This article also looks at the progress of mobile robotics during the previous three decades. Motion planning and path analysis techniques that work with single and multiple mobile robots have been discussed extensively. One common theme in this research is the use of soft computing methods to give mobile robot controllers cognitive behaviors, such as artificial neural networks (ANNs), fuzzy logic control (FLC), and genetic algorithms (GAs). Nevertheless, there is still a dearth of applications for mobile robot navigation that leverage nature-inspired algorithms, such as firefly and ant colony algorithms. Remarkably, most studies have focused on kinematics analysis, with a small number also addressing dynamics analysis.

Design and characterization of a novel motion conversion element: curved groove ball bearing without retainer

An unconventional and innovative mechanical transmission component, the curved groove ball bearing without retainer (CGBBR), is introduced in this article to facilitate the conversion between rotational and reciprocating motion. The CGBBR boasts several advantages over conventional motion conversion mechanisms, including a streamlined and compact structure, as well as the mitigation of high-order vibrations. This article delves into the design methodology, structural attributes, kinematic principles, and dynamic response properties of the CGBBR. A novel design method named closed curve envelopment theory is proposed to generate the distinctive spatial surface structure of the CGBBR. Moreover, a design scheme is presented that employs the concept of diameter-stroke ratio for CGBBR implementation. A calculation methodology is also introduced for determining the number of rolling elements within the CGBBR, which serves as the foundation for subsequent optimization design. This article deeply analyzes the kinematics principle of CGBBR and provides a new insight of motion conversion in mechanism.

Research on topological grinding of bionic structured scale surface for reducing contact friction and fluid drag resistance

The structured scale surface is an important functional surface that reduces the drag resistance of fluids and contact friction resistance. In order to grind the bionic scale structure on the workpiece, based on the topological theory and the principle of grinding kinematics, a novel topological grinding strategy was proposed. To this end, the topological feature vectors of the structured scale surface and the grinding wheel surface were established by analyzing the biomimetic structured scale surface; The Topological space of grinding process is constructed and the topological mapping equation of grinding process is established; The feasibility of this grinding strategy was verified through simulation and grinding experiments. The research results indicate that the established topological mapping equation is correct; Under the condition of maintaining design parameters, the errors of the feature parameters of the ground structured scale surface are between 2.8% and 8%; As the grinding parameters change, the feature parameters of the ground scale surface will also change, but they can still maintain the same topological attributes as the designed scale surface. Therefore, the proposed topology grinding strategy is feasible.