Motion System Research Articles

Memory effects in colloidal motion under confinement and driving

The transport of individual particles in inhomogeneous environments is complex and exhibits non-Markovian responses. The latter may be quantified by a memory function within the framework of the linear generalised Langevin equation (GLE). Here, we exemplify the implications of steady driving on the memory function of a colloidal model system for Brownian motion in a corrugated potential landscape, specifically, for one-dimensional motion in a sinusoidal potential. To this end, we consider the overdamped limit of the GLE, which is facilitated by separating the memory function into a singular (Markovian) and a regular (non-Markovian) part. Relying on exact solutions for the investigated model, we show that the random force entering the GLE must display a bias far from equilibrium, which corroborates a recent general prediction. Based on data for the mean-square displacement (MSD) obtained from Brownian dynamics simulations, we estimate the memory function for different driving strengths and show that already moderate driving accelerates the decay of the memory function by several orders of magnitude in time. We find that the memory may persist on much longer timescales than expected from the convergence of the MSD to its long-time asymptote. Furthermore, the functional form of the memory function changes from a monotonic decay to a non-monotonic, damped oscillatory behaviour, which can be understood from a competition of confined motion and depinning. Our analysis of the simulation data further reveals a pronounced non-Gaussianity, which questions the Gaussian approximation of the random force entering the GLE.

Students' Critical Thinking Skills on Motion System Material in Elementary School

Students' Critical Thinking Skills on Motion System Material in Elementary School

Fuzzy Neural Network Control for a Reaction Force Compensation Linear Motor Motion Stage

Technological progress and market expansion in the semiconductor industry require ultra-precise and high-speed processing and motion systems. However, even though reaction force compensation (RFC) linear motor motion stages help reduce the transmitted reaction force, the residual vibration of the movable magnet track after motion acts as a disturbance, affecting settling time and tracking performance. To address this issue, this study introduces a fuzzy neural network controller for an RFC linear motor motion stage. Since non-linear factors, such as frictional forces from guide rails, make it difficult to accurately model the system, a Nonlinear Autoregressive Neural Network (NARX) is used to identify the nonlinearity from displacement and servo control outputs. The fuzzy logic controller, which takes into account the error and error rate, is then combined with the inverse model controller of NARX. Finally, the fuzzy neural network controllers are integrated with the existing PIV (proportional-integral-velocity) control in feedforward configurations. The experiments demonstrate the potential performance improvements of the proposed approach over the PIV controllers.

Design of a Wind Tunnel Nozzle Section Trolley Control System Based on Backstepping Method

Abstract To accommodate different types of supersonic wind tunnel tests, frequent replacements of nozzle sections and test sections are required, involving multiple complex technical processes. To optimize operational procedures and improve efficiency, a control system for the wind tunnel nozzle section trolley based on the backstepping method was designed. The system uses radio frequency identification (RFID) signals for station positioning and intelligently adjusts the speed and direction of the control motor, thus driving the trolley to move back and forth automatically. Through the simulation of the motor motion control model, the system effectively reduces random disturbances in the motion system caused by load changes, achieves precise positioning of wind tunnel plugins and nozzle assemblies, enhances system operating accuracy, reduces production cycle times, and realizes a one-button positioning function for all components, playing a significant role in improving wind tunnel test efficiency and operational quality.

Design, modeling and feedforward control of a hybrid extruder for material extrusion additive manufacturing

Material extrusion (MatEx) is the one of the most widely utilized additive manufacturing (AM) methods. The key to high printing quality in MatEx lies in the synchronization between the fast motion system and the slow extrusion system. However, the synchronization is challenged by the slow response of the extrusion system. In MatEx, there are two main types of extrusion systems: Bowden and direct-drive (DD), based on different extruder-hot end arrangements. DD systems have the extruder installed directly above the hot end, providing a relatively fast extrusion response but adding more inertia to the print head. In contrast, Bowden systems position the extruder on the printer’s frame, feeding the filament to the hot end through a long Bowden tube. As a result, this setup leads to a sluggish extrusion response due to the elasticity of the long segment of filament but has a lower print head’s inertia, offering a higher positioning accuracy compared to the DD system. To leverage the advantages of both extrusion systems, this paper proposes a hybrid extrusion system design that combines a Bowden extruder with a low-mass DD extruder for filament feeding. To optimize the design and control of the extruder, a low-order model that characterizes the hybrid extruder dynamics is proposed. The model is used to design a feedforward (FF) controller that minimizes the force exerted by the DD extruder motor in the hybrid extruder while achieving the desired extrusion accuracy. The effectiveness of the proposed extruder and the FF controller is validated experimentally by demonstrating transient responses as fast as those of the standard DD extruder with up to 65% less force required from the DD extruder motor. Data collected from motor torque–mass specifications of three motor series from three different manufacturers indicate that the torque/force reduction could yield up to a 69% mass reduction in the motor used for the DD extruder, adding only 32.5% extra weight of the hot end to the print head. Hence it holds the potential to achieve the same extrusion accuracy as standard DD extruders while significantly reducing print head inertia, hence the resulting vibration of the printer, as demonstrated using a case study.

Development of Mini Silk Screen Printing Machine

The research aims to develop and design a mini semi-automatic screen-printing system that can be easily controlled. The objectives of this project are to create a suitable design for the mini semi-auto screen printing system and to develop it accordingly. The type of study conducted is the development of a real project, which is the production of a mini silk screen printing machine. The development of this project involves 4 phases: design and fabrication phase, motor wiring system, mould production and testing process. In this project, a mechanical setup will be created to execute the printing process. This setup will include a conveyor mechanism to hold the paper, a lifting arrangement, a wiping setup, and cutters. To control the printing operation and semi-automate the screen-printing setup, a power panel will be utilized. The setup will encompass a control system and a motion system, which will consist of a gear assembly and servo motors. The testing conducted is the functional process of the system regarding machine operation. As a conclusion, the development of mini silk screen printing successfully develops for student in Mechanical Engineering Department in POLIMAS. Keywords: Silk screen printing, printing process, control system

The impact of shoes versus ankle-restricted orthoses on sit-to-stand kinematics and centre of mass trajectories in adults with myelomeningocele

BackgroundIndividuals with myelomeningocele (MMC) present with neurological and orthopaedic deficiencies, requiring orthoses during walking. Orthoses for counteracting dorsiflexion may restrict activities such as rising from a chair. Research questionHow are sit-to-stand (STS) movements performed with ankle joint-restricted ankle-foot orthoses (AFO) and knee-ankle-foot orthoses with a free-articulated knee joint (KAFO-F)? MethodsTwenty-eight adults with MMC, mean age 25.5 years (standard deviation: 3.5 years), were divided into an AnkleFree group (no orthosis or a foot orthosis) and an AnkleRestrict group (AFOs or KAFO-Fs). Study participants performed the five times STS test (5STS) while their movements were simultaneously captured with a three-dimensional motion system. Centre of mass (CoM) trajectories and joint kinematics were analysed using statistical parametric mapping. ResultsThe AnkleRestrict group performed the STS slower than the AnkleFree group, median 8.8 s (min, max: 6.9, 14.61 s) vs 15.0 s (min, max: 7.5, 32.2 s) (p = 0.002), displayed reduced ankle dorsiflexion (mean difference: 6°, p = 0.044) (74–81 % of the STS cycle), reduced knee extension (mean difference: 14°, p = 0.002) (17–41 % of the STS cycle), larger anterior pelvic tilt angle (average difference: 11°, p = 0.024) (12–24 % of the STS cycle), and larger trunk flexion angle (on average 4°, p = 0.029) (6–15 % of the STS cycle). SignificanceThe differences between the AnkleFree and AnkleRestrict groups in performing the STS seem consistent with the participants functional ambulation: community ambulation in the AnkleFree group, and household and nonfunctional ambulation with less hip muscle strength in the majority of the AnkleRestrict group. No differences in the 5STS CoM trajectories or the kinematics were found with respect to the AFO and KAFO-Fs groups. Because orthoses are constructed to enable walking, the environment needs to be adjusted for activities in daily living such as the STS movement.

Coarse-graining Hamiltonian systems using WSINDy

Weak form equation learning and surrogate modeling has proven to be computationally efficient and robust to measurement noise in a wide range of applications including ODE, PDE, and SDE discovery, as well as in coarse-graining applications, such as homogenization and mean-field descriptions of interacting particle systems. In this work we extend this coarse-graining capability to the setting of Hamiltonian dynamics which possess approximate symmetries associated with timescale separation. A smooth ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon$$\\end{document}-dependent Hamiltonian vector field Xε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_\\varepsilon$$\\end{document} possesses an approximate symmetry if the limiting vector field X0=limε→0Xε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X_0=\\lim _{\\varepsilon \\rightarrow 0}X_\\varepsilon$$\\end{document} possesses an exact symmetry. Such approximate symmetries often lead to the existence of a Hamiltonian system of reduced dimension that may be used to efficiently capture the dynamics of the symmetry-invariant dependent variables. Deriving such reduced systems, or approximating them numerically, is an ongoing challenge. We demonstrate that WSINDy can successfully identify this reduced Hamiltonian system in the presence of large perturbations imparted in the ε>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon >0$$\\end{document} regime, while remaining robust to extrinsic noise. This is significant in part due to the nontrivial means by which such systems are derived analytically. WSINDy naturally preserves the Hamiltonian structure by restricting to a trial basis of Hamiltonian vector fields. The methodology is computationally efficient, often requiring only a single trajectory to learn the global reduced Hamiltonian, and avoiding forward solves in the learning process. In this way, we argue that weak-form equation learning is particularly well-suited for Hamiltonian coarse-graining. Using nearly-periodic Hamiltonian systems as a prototypical class of systems with approximate symmetries, we show that WSINDy robustly identifies the correct leading-order system, with dimension reduced by at least two, upon observation of the relevant degrees of freedom. While our main contribution is computational, we also provide a contribution to the literature on averaging theory by proving that first-order averaging at the level of vector fields preserves Hamiltonian structure in nearly-periodic Hamiltonian systems. This provides theoretical justification for our approach as WSINDy’s computations occur at the level of Hamiltonian vector fields. We illustrate the efficacy of our proposed method using physically relevant examples, including coupled oscillator dynamics, the Hénon–Heiles system for stellar motion within a galaxy, and the dynamics of charged particles.

Analysis of sampled-data hybrid integrator-gain systems: A discrete-time approach

Hybrid integrator-gain systems (HIGS) are hybrid control elements used to overcome fundamental performance limitations of linear time-invariant feedback control, and have enjoyed recent successes in engineering applications such as high-precision motion systems. However, despite the relevance of digital implementations, the creation of sampled-data versions of HIGS and their formal analysis have not been addressed in the literature so far, and will form the topic of the present paper. Thereto, we present discrete-time HIGS elements, which preserve the main philosophy behind the operation of HIGS in continuous time. Moreover, stability criteria are presented that can be used to certify input-to-state stability of discrete-time and sampled-data HIGS-controlled systems based on both (i) (measured) frequency response data, and (ii) linear matrix inequalities (LMIs). A comparison between these stability criteria is presented as well. A numerical case study is provided to illustrate the application of the main results.

Modelling and analysis of a superconducting magnetic coupler used for cryogenic pump

AbstractIt is difficult to achieve low heat leakage and leak‐free rotary sealing for conventional small‐ and medium‐sized cryogenic liquid pumps (CLPs). This is because the motor in a room‐temperature environment is connected to the pump impeller (in a cryogenic environment) via a long transmission shaft. An axial flux‐concentration superconducting magnetic coupler (AFCSMC) is proposed for CLP to eliminate the transmission shaft. Firstly, the structure and the operation mechanism of AFCSMC are described. Then, a 2D electromagnetic modelling method for AFCSMC is established based on the H‐φ formulation and also validated experimentally in terms of the prediction on the levitation force and the guidance force. Thus, the 2D numerical simulations of AFCSMC are performed in an equivalent static system instead of the actual double rotor motion system in which the moving mesh is quite complicated. It is investigated that dependences of the transmission torque on the key electromagnetic structural parameters, such as permanent magnet arrangement, number of pole‐pairs, ferromagnetic yoke, operating slip, and so on. The results indicate that the average transmitting torque is less affected by the operating slip, and AFCSMC can start asynchronously and operate in steady state with a synchronous speed. With the advantages of low loss, risk‐free of desynchronising, and overload protection, the proposed AFCSMC can provide a competitive candidate for mechanical power transmission technologies in cryogenic engineering.

Stochastic evaluation of quasi-zero stiffness magnetic spring using a reluctance-corrected analytical model

—In state of the art high-precision motion systems, which utilize magnetic levitation, a quasi-zero stiffness gravity compensation is one of the essentials to improve dynamic performance, eliminate position dependency and thus simplify controller design. Special configurations of permanent magnets, such as Halbach magnet arrays, can realize magnetic levitation as a form of magnetic spring. However, unlike conventional permanent magnet machines with large stiffness, the quasi-zero stiffness magnetic spring requires higher modeling accuracy for force estimation, which is affected by the nonlinear reluctance effect of permanent magnets. In this study, we propose an accurate magnetic modeling method for the quasi-zero stiffness magnetic spring. By correcting the reluctance effect of magnets, the proposed magnetic model achieves superior accuracy estimating levitation force and stiffness to the conventional surface current model. Using the reluctance-corrected magnetic model, tolerance analysis was performed to identify dominant geometric parameters affecting the uncertainty of the Halbach array magnetic spring performance. A Monte-Carlo simulation was used to estimate the overall tolerance of magnetic forces and stiffness. The experimental results fit in the tolerances.

Quantifying the traverse: a comprehensive kinematic analysis of climbing technique

Biomechanical analysis plays a pivotal role in enhancing performance and preventing injuries in rock climbing. Despite a recent increase in popularity, there remains a lack of research quantifying full-body movements, resulting in uncertainty regarding biomechanical demands and variability. It should be noted that there is a scarcity of data in climbing research to quantify optimal techniques, particularly for traverses. This study aims to address this gap by examining the demands of a traverse in a controlled setting using Vicon marker-based three-dimensional (3D) motion capture. Fourteen experienced climbers (32 ± 13 years, 70 ± 9 kg) with varying skill levels (intermediate to advanced) and climbing backgrounds (sport climbing, trad climbing and bouldering) completed a two-minute standardised traverse on a custom-built Lattice circuit (2440 × 2440 × 1220 mm). A twelve-camera (200 Hz, Vantage) motion analysis system (Vicon, Motion Systems Ltd. Oxford, United Kingdom) acquired kinematic data. Retroreflective markers were attached to anatomical landmarks of the upper and lower body. The trials were preceded by a 10-minute self-selected warmup. This data will be analysed to assess the degree of inter-participant variability, observing if there is the possibility of quantifying an optimal traversing technique. Intra-participant variability will be assessed, to measure the effect of fatigue on the climbing movement. Previous literature has alluded to the possibility of fatigue increasing the use of the legs when climbing as compensation. Comparing the beginning of the traverse to the end, data should further substantiate this claim. This research will offer insights into the kinematic demands of rock climbing, laying the groundwork for further studies on a larger scale to assess the possibility of optimising technique, performance, and injury strategies. This study contributes to bridging the vast gap between biomechanical research and practical applications in the climbing community, facilitating a more evidence-based approach to performance.

EnderScope: a low-cost 3D printer-based scanning microscope for microplastic detection.

Low-cost and scalable technologies that allow people to measure microplastics in their local environment could facilitate a greater understanding of the global problem of marine microplastic pollution. A typical way to measure marine microplastic pollution involves imaging filtered seawater samples stained with a fluorescent dye to aid in the detection of microplastics. Although traditional fluorescence microscopy allows these particles to be manually counted and detected, this is a resource- and labour-intensive task. Here, we describe a novel, low-cost microscope for automated scanning and detection of microplastics in filtered seawater samples-the EnderScope. This microscope is based on the mechanics of a low-cost 3D printer (Creality Ender 3). The hotend of the printer is replaced with an optics module, allowing for the reliable and calibrated motion system of the 3D printer to be used for automated scanning over a large area (>20 × 20 cm). The EnderScope is capable of both reflected light and fluorescence imaging. In both configurations, we aimed to make the design as simple and cost-effective as possible, for example, by using low-cost LEDs for illumination and lighting gels as emission filters. We believe this tool is a cost-effective solution for microplastic measurement. This article is part of the Theo Murphy meeting issue 'Open, reproducible hardware for microscopy'.

Проблема движения в философии Махмуда Ша­бистари

The article is dedicated to the interpretation of the problem of motion by Mahmud Shabistari – one of the prominent medieval Persian Sufi thinkers. The main source for the study was his philosophical treatise “Haqq al-Yaqin fi Ma’rifat Rabb al-’Alamin”. The article includes the first translation into a European language (Russian) of a chapter from this treatise – “On the Manifestation of Movement and the Renewal of Manifesta­tions”. Ancient authors also dealt with the problem of motion comprehension. The inves­tigation of the way Shabistari solves this problem is particularly interesting because, striving for the affirmation of strict monotheism, he proposed a monistic model of the uni­verse where only the One First Principle exists. He considered the existence of everything else as an illusion. However, such a statement makes any change impossible, and conse­quently movement as well. Meanwhile, Shabistari, on the contrary, states the constant circular motion of the First Principle with itself as the center. It generates its numerous virtual images in non-being, that move constantly around the One. These images include everything – from the Universal Reason to the individual human being. Shabistari con­structs a system of virtual images motion based on a fractal principle: the circle around the point of the One represents the motion trajectory of the first creature – the Universal Reason. Each point of this circle is the Universal Reason’s manifestation at each individ­ual moment in the form of one of the forty existence levels. In its turn, each level of exis­tence becomes also a center of the circular motion of its virtual copies – individual things.

Development of robot motion direction based on microcontroller with compass sensor

This research brings innovation to the motion and navigation system of the ‘DK-ONE’ robot. In the 2021 Indonesian ‘Search and Rescue’ robot contest, the ‘DK-ONE’ robot faced difficulties moving towards the target room. The issue was attributed to an unbalanced frame construction and friction between the robot’s legs and the arena floor, leading to leg slippage. This resulted in a mismatch between the programmed number of steps for the robot and the desired path to the target space, causing errors in the robot’s system. To address these problems, researchers conducted a study aimed at enabling the ‘DK-ONE’ robot to accurately determine its direction of motion. This research followed the waterfall method, involving stages such as system analysis, design, coding, testing, and supporting phases. The study was carried out in the integrated laboratory of the Department of Electrical Engineering Education. The development of the robot’s motion direction using a compass sensor significantly improved stability while walking on straight, flat, and uneven paths. The robot no longer experienced errors in its motion direction and remained on the intended path. As a result, the increased efficiency in robot motion also positively impacted the structural efficiency and energy consumption of the robot.

All inkjet-printed organic solar cells on 3D objects

Drop-on-demand inkjet printing is a promising and commercially relevant technology for producing organic electronic devices of arbitrary shape on a wide variety of different substrates. In this work we transfer the inkjet printing process of organic photovoltaic devices from 2D to 3D substrates, using a 5-axis robot system equipped with a multi-nozzle inkjet printing unit. We present a ready-to-use 3D printing system for industrial application, using a 5-axis motion system controlled by commercial 3D motion software, combined with a commonly used multi-nozzle inkjet print head controlled by the corresponding printing software. The very first time inkjet-printed solar cells on glass/ITO with power conversion efficiencies (PCEs) of up to 7% are realized on a 3D object with surfaces tilted by angles of up to 60° against the horizontal direction. Undesired ink flow during deposition of the inkjet-printed layers was avoided by proper ink formulation. In order to be able to print organic (opto-)electronic devices also on substrates without sputtered indium tin oxide bottom electrode, the bottom electrode was inkjet-printed from silver nanoparticle (AgNP) ink, resulting in the first all inkjet-printed (i.e. including bottom electrode) solar cell on a 3D object ever with a record PCE of 2.5%. This work paves the way for functionalizing even complex objects, such as cars, mobile phones, or ‘Internet of Things’ applications with inkjet-printed (opto-)electronic devices.

Self-powered porous polymer sensors with high sensitivity for machine learning-assisted motion and rehabilitation monitoring

Muscle contraction and relaxation inherently contains valuable information crucial for monitoring physical states, rehabilitation, and injury prevention. However, the majority of flexible wearable devices struggle to offer customizable sensors with high sensitivity, durability, and stability, resulting in suboptimal biofeedback performance. Herein, the machine learning-assisted smart motion and rehabilitation monitoring system (SMRMS) is demonstrated for full-body motion recognition and rehabilitation assessment using a designed porous triboelectric nanogenerator (TENG) array. A theoretical model of porous materials is built to demonstrate the effect mechanism of porosity on TENG output. Through pore design on the tribolayer, theoretical simulation and experimental are performed to determine the key features of porous TENG sensors with high sensitivity (1.76 kPa−1), fast response time (50 ms) and high durability (over 100,000 cycles). A ring-shaped TENG (RS-TENG) is fabricated based on the porous TENG sensor, enabling real-time recording of leg/arm force without additional attachment. By integrating the RS-TENG array with a multichannel signal acquisition system, an SMRMS is designed to capture motion information during human subjects’ exercise and rehabilitation training. These data are then fused for machine learning analytics, resulting in significantly improved accuracy in motion pattern recognition (98.75 %) and rehabilitation monitoring (100 %). The simple, precise and durable porous sensors could help mitigate the risk of excessive exercise-induced muscle injuries, expanding self-powered wearable functionalities and adaptabilities.

Self-Powered Hybrid Motion and Health Sensing System Based on Triboelectric Nanogenerators.

Triboelectric nanogenerator (TENG) represents an effective approach for the conversion of mechanical energy into electrical energy and has been explored to combine multiple technologies in past years. Self-powered sensors are not only free from the constraints of mechanical energy in the environment but also capable of efficiently harvesting ambient energy to sustain continuous operation. In this review, the remarkable development of TENG-based human body sensing achieved in recent years is presented, with a specific focus on human health sensing solutions, such as body motion and physiological signal detection. The movements originating from different parts of the body, such as body, touch, sound, and eyes, are systematically classified, and a thorough review of sensor structures and materials is conducted. Physiological signal sensors are categorized into non-implantable and implantable biomedical sensors for discussion. Suggestions for future applications of TENG-based biomedical sensors are also indicated, highlighting the associated challenges.

Dynamic Separation Model-Based Sliding Mode Control with Adaptive Neural Network Compensators for a Reluctance Actuator Motion System

Dynamic Separation Model-Based Sliding Mode Control with Adaptive Neural Network Compensators for a Reluctance Actuator Motion System

Unified framework for geometric error compensation and shape-adaptive scanning in five-axis metrology systems

In response to the escalating demand for precise shape metrology of complex optical surfaces, this study unveils a unified geometric error compensation and trajectory planning framework tailored for high-accuracy five-axis scanning metrology systems, which remains a notably underexplored field compared to error compensation in machine tools. Founded on a unified geometric model, the proposed framework seamlessly integrates a versatile shape-adaptive trajectory planning strategy, a thorough global error sensitivity analysis approach, and an exhaustive geometric error compensation scheme. Leveraging inverse kinematics, an innovative shape-adaptive scanning trajectory generation strategy is mathematically formulated, thereby facilitating adaptable measurement trajectory generation for diverse surface geometries. Employing forward kinematics, an exhaustive geometric error model is established to extensively address the 53 distinct geometric errors in the metrology system. This proposed error model fundamentally augments conventional geometric error models in machine tool by managing not only the geometric errors from the motion system, but also those from the probe and workpiece. To streamline the error compensation procedure, a novel global error sensitivity analysis approach is introduced, identifying both system-oriented and process-oriented sensitive geometric errors for targeted compensation. Experimental validation using a standard ball, which achieved an exceptional 89.35% reduction in the root mean square of the measurement errors, further confirms the feasibility and effectiveness of the proposed framework. By offering an universal trajectory planning, sensitivity analysis and error compensation trinity for five-axis scanning metrology systems, this study sets the stage for precision advancements and design optimization across diverse configurations of metrology systems.