Search Results (374)

Time-fractional diffusion equations describe subdiffusive transport in heterogeneous media, but their numerical treatment is complicated by the nonlocal Caputo derivative and by the weak singularity that the solution develops at the initial time. We study a global-in-time discretization that combines spectral collocation in time—on the fractional power basis ${\left\{t^{\mathsf{\ell }\alpha }\right\}}_{\mathsf{\ell }=0}^N$, evaluated at Chebyshev–Gauss–Lobatto nodes, which reproduces the leading terms of the singular expansion of the solution—with a second-order conservative finite-difference stencil in space that uses harmonic averaging of the diffusivity at the cell faces and therefore remains accurate across discontinuous media. The resulting fully discrete problem is a large, nonsymmetric, dense-in-time linear system whose two-norm condition number grows like the inverse square of the spatial mesh size, so that Krylov subspace iteration without preconditioning stalls under refinement. Exploiting the Kronecker sum structure of the discrete operator, we build a preconditioner by fast diagonalization of the spatial factor through the discrete sine transform. For constant diffusivity the preconditioner reproduces the operator exactly and yields a direct solver; for variable diffusivity it is spectrally equivalent to the operator, and we prove that the eigenvalues of the preconditioned system cluster in a disk centered at one whose radius depends only on the coefficient contrast, and not on the mesh, the number of temporal degrees of freedom, or the fractional order. Numerical experiments in one and two space dimensions confirm second-order spatial accuracy and a preconditioned iteration count that stays flat—twelve iterations from $M=32$ up to $M=1024$ in one dimension and eleven up to $M=256$ per direction in two—while the unpreconditioned count grows by more than two orders of magnitude. In time, the accuracy is spectral until round-off in the ill-conditioned Vandermonde matrix of the power basis takes over: the barrier is reached at $N=9,10,13$ for $\alpha =0.3,0.5,0.7$, where the attainable error is about ${10}^{-6}$. A benchmark against the L1 scheme on uniform and graded meshes, the Alikhanov L2-$1_{\sigma }$ scheme and Grünwald–Letnikov convolution quadrature quantifies when the global approach pays: on forced problems and on modes with $\kappa \lambda T^{\alpha }\lesssim 2$ it reaches a prescribed accuracy one to two orders of magnitude faster and with several times less memory, while for strongly damped modes the fractional power basis converges only algebraically and graded time marching is preferable below a relative error of ${10}^{-2}$. Full article

The modern energy transition has outpaced the control and optimization frameworks built to govern it. As power and energy systems fragment into webs of renewable generators, storage operators, flexible loads, and carbon-constrained firms, the deterministic, single-optimizer models that once sufficed buckle against nonlinearity, bounded rationality, and strategic conflict among parties who learn and revise as they go. Evolutionary game theory (EGT), which traces how strategies propagate through populations by imitation and selection rather than instantaneous optimization, offers a route through this difficulty—one this review develops across three scales of low-carbon coordination central to cleaner production: enterprise-level industrial symbiosis, system-level smart energy operation, and market-level carbon governance. We synthesize three decades of theory alongside the recent fusion of EGT with artificial intelligence, where deep reinforcement learning approximates high-dimensional payoffs, federated learning lets rival firms co-train models without surrendering proprietary data, and blockchain underwrites decentralized mechanism execution. The synthesis is accompanied by two illustrative numerical case studies, constructed for this review rather than drawn from the surveyed literature, whose quantitative outputs are reported below as demonstrations of modeled behavior rather than as empirical measurements. In the first of these, cooperative emergence in industrial symbiosis hinges on critical thresholds that travel from 0.15 to 0.75 as subsidies and transaction costs vary, with anchor-enterprise targeting accelerating cooperation 2.4-fold while cutting outcome variance 3-fold. In smart energy coordination, AI-enhanced learning buys 32 to 41% faster convergence, yet pays 25 to 39% larger oscillations—a speed–stability tension whose resolution lives in a narrow learning-rate band near 0.08 to 0.12, outside which either sluggishness or instability takes hold. Carbon-market behavior turns on price thresholds: emitters switch abruptly from buying quotas toward investing in abatement once the clearing price clears firm-specific triggers, a discrete state switch that smooth equilibrium analysis misses entirely. Across all three domains, fragmented data, path dependence, and regime-switching dynamics recur as the binding constraints on modeling and on governance alike. Four mechanisms prove invariant to scale—the decisive weight of initial conditions, the catalytic leverage of well-positioned anchor agents, the equilibrium-shaping force of institutional design, and the computational reach added by AI integration—which suggests that insight earned in one domain transfers to the others. We close by mapping open problems in heterogeneity modeling, verification under deep uncertainty, and the still-unrealized coupling of digital twins with privacy-preserving learning. EGT emerges not as retrospective description but as prospective guidance for the cooperative transitions on which credible decarbonization depends. Full article

Floating tidal platforms provide a flexible solution for offshore tidal–stream energy exploitation, but their wave-induced motions may affect platform stability, turbine operation and power performance. Integrating wave energy converters (WECs) with a floating tidal platform provides a potential approach to absorb wave energy and modify platform motions. However, the dynamic role of a WEC array attached to a floating tidal platform remains insufficiently understood, especially with respect to array layouts, power take-off (PTO)-induced coupling and absorbed power. This study investigates the effects of WEC array layout on the motion response and absorbed power of a catamaran-type floating tidal platform under irregular wave excitation. Three representative WEC array layouts, namely longitudinal, transverse and hybrid arrangements, were compared with a baseline platform without WECs. A coupled numerical model was established by combining frequency-domain radiation-diffraction analysis and time-domain simulations of mooring system and PTO dynamics based on ANSYS AQWA 2023R2. The hydrodynamic model was verified through code-to-code comparisons with OrcaWave 11.6, and the PTO power model was checked against published numerical results. The results show that the WEC array layout has a significant influence on both platform response and power absorption. Among the investigated layouts, the transverse array provides the most effective overall motion suppression, with average reductions of 36.83% in heave responses and 52.62% in pitch responses compared with the baseline platform. Frequency-domain results indicate that pure multi-body hydrodynamic interaction has a limited influence on the platform response amplitude operators (RAOs) and wave-excited forces, whereas time-domain results reveal much stronger layout-dependent responses once PTO coupling was included. The WECs’ absorbed power was strongly affected by the geometric relationship between the PTO rotation plane and the dominant platform motion plane. When these two planes were aligned in coplanarity, platform motion enhances the relative PTO rotation and increases output power. These findings indicate that, for floating tidal platforms with relatively small displacement, WEC arrays should be treated as distributed dynamic subsystems rather than only as energy-harvesting add-ons. The results can provide useful guidance for the layout design and coupled dynamic assessment of floating hybrid tidal–wave energy converters (HTWEC). Full article

Global restoration frameworks, such as the Bonn Challenge and Forest Landscape Restoration, have endorsed multistakeholder engagement in agroforestry as key to reversing land degradation at scale. This paper follows shifts in how stakeholders have been organised, coordinated and steered since 2010 when Rwanda’s National Forestry Policy came into force, a year ahead of Rwanda’s pledge to the Bonn Challenge. The specific focus is on Bugesera District, representing a national policy shift from focusing on restoration in highland areas only. Bugesera is a lowland area facing complex socio-ecological and livelihood challenges including high rates of deforestation, recurrent drought and rapid population fluctuations. This paper analyses these changes by investigating which stakeholders were involved, how they were engaged (modes of participation) and why they participated (drivers of participation). Conceptually, this follows stakeholder mapping, Reed’s theory of participation and multi-level governance theory. Through thematic analysis, we triangulated data from 15 policy-related documents with semi-structured interviews with representatives from 24 organisations. Our findings show that both before and after 2010, stakeholder engagement has remained top-down. However, since 2010 this has been qualified by an asymmetrical form of collaboration that increasingly takes the form of top-down deliberation. Changes were observed in participation patterns, engagement approaches, and governance arrangements, driven by contextual conditions, power relations, process design, and spatial–temporal dynamics. Within a centrally coordinated government system, shaped by the post-genocide political context and culturally embedded structures such as Umuganda and Ubudehe, multistakeholder restoration initiatives have largely remained state-led, with structured approaches to coordination and implementation that have varied in the extent of local stakeholder engagement. Trust emerged as an important factor influencing stakeholder interactions. Despite more diverse and expanded institutional arrangements over time, variations in levels of participation and influence among stakeholders persist, with differences in how engagement and decision-making power are distributed. We conclude that effective stakeholder engagement is contingent on existing governance structures, the political will to engage with a diversity of actors at different levels, contextual conditions including spatial-temporal dynamics, and opportunities provided by global and regional restoration frameworks. Full article

Background: Team sports often involve high-intensity unilateral actions that can lead to neuromuscular asymmetries, increasing injury risk and reducing performance, particularly in young female athletes. Methods: This study quantified and compared inter-limb asymmetries in single-leg countermovement jumps (slCMJ) across sexes and sports in 96 youth elite athletes (16.42 ± 1.03 years; 1.83 ± 0.09 m; 74.36 ± 8.69 kg) from basketball, handball, and volleyball. Using a force plate, asymmetries were assessed, and statistical analyses (t-test, ANOVA) identified differences. Results: Females showed greater asymmetry in jump height (9.64 ± 6.43% vs. 6.48 ± 4.87%, p = 0.01, d = 0.59), whereas males exhibited higher asymmetry in time to take-off (10.32 ± 7.5% vs. 6.4 ± 4.7%, p = 0.003, d = 0.63). Volleyball players displayed the lowest asymmetry in jump height (7.05 ± 4.9%) compared to basketball (8.73 ± 7.2%) and handball (11.88 ± 9.7%, p = 0.05), and in relative maximum power (4.63 ± 3.7%) compared to basketball (7.75 ± 5.3%, p = 0.04) and handball (6.51 ± 4.7%). Conclusions: These findings highlight sex- and sport-specific neuromuscular asymmetry patterns, emphasizing their relevance for injury prevention and performance strategies. However, asymmetries are highly variable, influenced by multiple factors. Full article

Vertical take-off and landing (VTOL) configurations incur a structural weight penalty that reduces payload fraction and endurance compared to conventional fixed-wing and multirotor aircraft of comparable gross weight. To extend the endurance of VTOL UAVs, this work presents the design, analysis and control of a novel unmanned tilt trirotor aircraft with tandem wings, named Gong-H, featuring VTOL capability and high aerodynamic efficiency. A prototype of this aircraft was built with the rotor system mounted between tandem wings with a high wing coverage rate, which can achieve a more compact structure than other VTOL aircraft. The control forces and torques are provided not only by the rotor system in VTOL flight mode and the two tandem wings in cruise mode, but also by both the rotor system and wings in transition mode. Additionally, Computational Fluid Dynamics (CFD) simulations are conducted to optimize the wing configuration to improve the efficiency of cruise mode. Moreover, an airspeed-scheduled hybrid control framework based on incremental nonlinear dynamic inversion (INDI) and PID is adopted for different flight modes to improve the robustness of control and the stability of flight mode switching. Hover experiments confirm improved power efficiency compared to tilt quadrotor configuration, which extends endurance time and increases range. Additionally, complete flight cycle field experiments were conducted to demonstrate the aerodynamic feasibility of the prototype, including VTOL flight, cruise flight, and transition flight modes. Control surface redundancy tests and comparative INDI-PID validation under asymmetric disturbances further verify the practical robustness of the control framework. This work provides a design concept of VTOL aircraft and a practical solution for VTOL applications. Full article

This paper delves into the free vibration analysis of a rotating non-uniform functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beam with symmetric material distribution, taking into account boundary relaxation. Three common carbon nanotube (CNT) distributions, namely FG-X, UD, and FG-O, are considered. The governing equations of a rotating FG-CNTRC beam with variable cross-section and boundary relaxation are formulated via Hamilton’s principle. Some factors, including the centrifugal force induced by rotation, boundary relaxation, cross-section gradient, and others, substantially complicate the boundary conditions, making it challenging to directly obtain an analytical solution with variable coefficients. To address this, a novel power series solution based on the differential transformation method (DTM) is introduced to discretize the vibration equation and obtain the natural frequency of the rotating FG-CNTRC beam, which forms the core novelty of this study. Comprehensive numerical calculations are carried out, and the reliability of the DTM results is fully verified via comparisons with finite element (FEM) outputs and published reference data. Full article

The distinct engineering advantages of Oscillating Water Column (OWC) systems have driven substantial academic interest lately. This work examines the onshore U-shaped OWC (U-OWC), selected for its cost-effective installation integrated with existing coastal infrastructure and its superior broadband response to diverse wave climates. Time-domain CFD simulations, incorporating the scaling-rematched approach, were conducted to quantify key hydrodynamic and air-compressibility coefficients, including the amplitude of the wave exciting force, fluid damping coefficient, added mass, absorption factor, and the effective PTO (power take-off) damping and air-compressibility coefficients. These parameters collectively elucidate the underlying hydrodynamics and how they are interwoven with the compressibility of the air in the plenum chamber, thereby impacting the U-OWC’s energy-capture performance under incident waves. A principal finding is the identification of a C+ interval wherein air compressibility enhances capture performance in the lower wave-period range examined (<8.0 s). The added mass of the present U-OWC exhibits a remarkably pronounced decrease around the wave period of 8.0 s, which can be verified by a simple resonance formula of heave buoys to underline its strong near-resonance behavior. Full article

The traditional urbanization path based on scale expansion is unsustainable in karst mountainous regions due to fragmented topography and ecological fragility. Taking Guiyang City as a case study, this paper constructs two evaluation indicator systems for urban–rural development and environmental support. Employing the entropy method, coupled coordination degree model, Grey relational analysis, Geodetector, and multi-source spatial analysis methods to examine the evolutionary trajectory, driving mechanisms, and spatial responses of the human–land system from 2000 to 2024. The results show three main findings. First, the comprehensive score of Guiyang’s urban–rural human–land system increased from 0.054 to 0.826, and the coupling coordination degree rose from 0.223 (relative imbalance) in 2000 to 0.903 (high-quality coordination) in 2024, while the environmental support system deviated from the classic environmental Kuznets curve. Second, the driving force has shifted from economic scale to green well-being. The interaction analysis using Geodetector shows that all interaction types fall under the category of two-factor enhancement, among which the interaction coefficient between the number of broadband internet subscribers and other driving factors has the highest explanatory power, with a q-value of 0.949. Third, spatially, the light center distribution stabilized after 2015, and the land use ecological transition index dropped from 0.162 to 0.050 while the D-value continued rising, showing a significant negative correlation (r = −0.89, p < 0.05). Construction land was concentrated in low-slope (0–6°) and mid-elevation (1000–1400 m) basin areas, overlapping with high-quality farmland, and the synchronization rate between economically active areas and construction expansion was 50%. These findings reveal a digital–ecological co-evolution path in karst regions and provide an empirical basis for urban–rural integration governance. Full article

Cycloidal propellers are known for their omnidirectional vectored thrust, enabling smooth transitions between hovering and forward flight, making them ideal for unmanned aerial vehicles (UAVs) and electric vertical take-off and landing (eVTOL) aircraft. However, cycloidal propellers tend to have lower hovering efficiency than screw propellers at the unmanned aerial vehicle (UAV) scale. Adding end plates to the blade tips can improve hovering efficiency by suppressing blade tip vortices. But the impact of these end plates have not been thoroughly studied. This paper aims to seek the designs with enhanced hovering efficiency and develop design guidelines for cycloidal propellers with end plates. Comprehensive force measurement experiments are performed on designs with and without end plates, and designs with rotating and static end plates. Complementary high-fidelity numerical analysis is performed to gain deeper insights into the complex 3D flow structures and the role of end plates in suppressing induced power losses. Our study reveals that end plates can effectively suppress the efficiency degradation typically associated with low aspect ratio blades. We demonstrate that even with a blade aspect ratio of 1.5, a cycloidal propeller equipped with end plates can achieve high hovering efficiency, thereby establishing a new design guideline for lightweight, high-performance propulsion systems. The designs with stationary end plates are superior to those with rotating end plates because rotation introduces additional torque caused by the friction force. Designs featuring thick end plates (${\overline{t}}_e=0.056$) outperform those with thin end plates (${\overline{t}}_e=0.004$), as the rounded edges can eliminate end plate vortices. A comprehensive parametric study is conducted, evaluating blade chord-to-radius ratios from 0.26 to 0.65, aspect ratios from 0.5 to 3.0, pitching amplitudes from 10° to 50°, as well as end plate configurations (stationary vs. rotating, and thin vs. thick). From this parameter space, the best design was identified as featuring stationary thick end plates (${\overline{t}}_e=0.056$), a chord-to-radius ratio of 0.65, and a large pitching amplitude of 40 degrees. It achieves a hovering efficiency of 0.72 with a blade aspect ratio of 3, which is comparable to that of sub-scale rotors with similar Reynolds number. In contrast, for the cases without end plates, the highest hovering efficiency is lower than 0.6. Full article

Against the coordinated advancement of building a maritime power, high-quality development of marine tourism and ecological civilization construction, realizing positive interaction between marine resource conservation and tourism industrial development has emerged as a pivotal issue for high-quality growth in coastal regions. Taking 11 coastal provincial-level administrative regions in China spanning 2008 to 2024 as the research sample, this paper first establishes an evaluation indicator system covering marine resources and the tourism industry. It further adopts an integrated empirical framework encompassing the coupling coordination degree model, spatial Markov chain model, obstacle degree model, fixed-effect model and geographically and temporally weighted regression (GTWR) model to systematically unpack the spatiotemporal differentiation characteristics, internal restrictive obstacle factors and external driving determinants of the two-system coupling coordination. On this basis, a marine resource compensation mechanism for tourist destinations is formulated. Empirical results demonstrate four core findings: (1) In terms of temporal evolution, the overall coupling coordination level keeps rising and goes through three phases: initial development, rapid improvement and post-shock recovery. After a short-term decline triggered by the pandemic, the index rebounds markedly after 2023, showing that the two systems can recover and stabilize. (2) In terms of spatial layout, a persistent stratified spatial pattern featuring “higher coordination in southern coast versus lower coordination in northern coast with three-tier hierarchical differentiation” is identified; high-level neighboring regions exert prominent positive spatial spillover effects, whereas low-level adjacent areas are prone to fall into development lock-in traps. (3) For internal constraint obstacles, the marine resource subsystem is persistently restricted by resource exploitation limits and coastal spatial scarcity, while the dominant bottleneck of the tourism industrial subsystem shifts from insufficient market scale to inadequate human capital supply. (4) Regarding external driving forces, the proportion of tertiary industry and the digital infrastructure constitute core driving contributors, whereas marketization progress and opening-up degree act as primary restrictive factors, with pronounced spatial heterogeneity existing across all driving indicators. Finally, in line with the quasi-public-good attribute and ecological externality of marine resources, this study constructs a differentiated and synergistic marine resource compensation mechanism from three dimensions: stakeholder identification, compensation implementation pathways and institutional guarantee systems. The proposed framework provides theoretical references and practical policy options to facilitate high-level coupling and coordinated development between marine resource preservation and the coastal tourism industry. The marginal contribution of this research lies in integrating coupling coordination measurement, obstacle factor diagnosis, driving mechanism identification and compensation mechanism design into an integrated analytical framework, which delivers theoretical foundations and operable policy solutions for coastal marine resource protection, tourism industrial upgrading and differentiated compensation system construction. Full article

Interior permanent magnet synchronous motor (IPMSM) has advantages with high power density, wide speed range, small size, and high efficiency, and is widely used in the drive system of electric vehicles. Compared to other types of motors, permanent magnet synchronous motors (PMSMs) have some irreplaceable advantages, but there are also some disadvantages. As a type of PMSM, IPMSMs have problems with large fluctuations in permanent magnet (PM) magnetic field and demagnetization. At present, irreversible demagnetization of PMs is the most serious problem faced by IPMSMs. Once irreversible demagnetization of PMs occurs, it can cause a decrease in the performance of IPMSMs and can even damage the entire drive system. This paper takes an IPMSM with 48 slots, 8 poles, and 66 kW as the research object. Based on the reasons for PM demagnetization, a PM demagnetization model is established to obtain the demagnetization law of PMs. Firstly, the magnetic properties of PM materials were described based on their characteristic curves. The demagnetization mechanism of PMs was analyzed, and the demagnetization process of PMs was studied in combination with the reasons for demagnetization. Secondly, the basic parameters and torque performance of IPMSMs were calculated and analyzed. We analyzed the demagnetization curves of PM materials at different temperatures, calculated the operating points of PMs under various working conditions, and analyzed whether PMs undergo irreversible demagnetization based on the relationship between the operating points of PMs and the knee points of demagnetization curves. A high-fidelity electromagnetic–thermal coupling simulation model has been established, combined with the characteristics of electric vehicle driving conditions, to accurately characterize the temperature rise distribution and electromagnetic parameter changes of IPMSMs under different operating conditions and achieve multi-physics field collaborative analysis. Finally, a finite element model is adopted to simulate uniform and local demagnetization of PMs, and the changing characteristics of motor performance parameters under demagnetization are summarized. Different magnitudes of d-axis reverse current are applied as demagnetization excitation to analyze PM behaviors under various demagnetization degrees. The variations in magnetic flux density, output torque, and no-load back electromotive force (EMF) before and after demagnetization are simulated and analyzed. For the investigated motor and specific magnet grade, this work summarizes the irreversible demagnetization characteristics and corresponding practical judgment references. Full article

To improve the energy capture efficiency of wave energy converters (WECs), various control strategies based on adjustable power take-off (PTO) systems have been developed. However, such approaches often impose stringent requirements on PTO structural design and generator performance. To address this issue, this paper proposes a novel variable-stiffness point-absorber wave energy converter (VSPAWEC). In the proposed system, a stiffness regulator (SR) composed of a magnetorheological damper (MRD) and a spring mechanism is introduced as a frequency-tuning device, enabling stiffness compensation of the point absorber within a certain operating range. Based on the SR mechanism, a frequency-tracking resonance control strategy is further developed. Specifically, a sliding mode control algorithm is employed to regulate the MRD in real time, allowing the piston rod to track a reference position signal generated from the known dominant wave frequency. In this way, the spring force applied to the buoy can be adjusted adaptively, so that resonance between the buoy and the incident waves can be achieved. Finally, numerical simulations are conducted to evaluate the variable-stiffness characteristics of the proposed VSPAWEC and to verify the effectiveness of the developed frequency-tracking control strategy. The results demonstrate the feasibility of the proposed concept for resonance tuning and wave energy capture enhancement. Full article

This article presents a new combined post-processing concept to improve the quality of laser powder bed fusion (LPBF) of 17-4PH stainless steel (SS) cylindrical parts fabricated from N₂-atomised LaserForm 17-4PH (B) powder. The concept is based on consecutive heat treatment procedures and diamond burnishing (DB) processes. A two-stage study was conducted. The first stage was an LPBF process experiment. The following combination of LPBF parameter values was selected after optimisation: a laser power of $\mathrm{P}=150 \mathrm{W}$, laser scanning speed of v = 1200 mm/s, and layer thickness of $\mathrm{t}=40 \mathsf{\mu }\mathrm{m}$. In the second stage, this combination was used to evaluate the effects of two heat treatment procedures (HT1 and HT2) and two DB processes (using burnishing forces of 100 N and 300 N) on the tensile properties and surface integrity of LPBF 17-4PH SS cylindrical samples. The HT2 procedure, including annealing $({1200}^{\circ }$, $4 \mathrm{h})$, solution treatment (${1060}^{\circ }$, $1 \mathrm{h})$, cooling (${-70 }^{\circ }\mathrm{C},2 \mathrm{h}$), and ageing (${482}^{\circ }$, $4 \mathrm{h}$) led to yield limit, tensile strength, and Vickers hardness values of $\mathrm{Y}\mathrm{L}=1071 \mathrm{M}\mathrm{P}\mathrm{a}$, $\mathrm{T}\mathrm{S}=1410 \mathrm{M}\mathrm{P}\mathrm{a}$, and $523 \mathrm{H}\mathrm{V},$ respectively. The concept presented takes advantage of the combination of the transformation, precipitation and strain-hardening effects. The combined effect was most pronounced in the samples subjected to the HT2 procedure and subsequent DB (300 N), for which a retained austenite fraction of 6.93%, surface microhardness of ${563 \mathrm{H}\mathrm{V}}_{0.05}$ and the maximum values of the compressive axial and hoop RSs of $-1426.3 \mathrm{M}\mathrm{P}\mathrm{a}$ and $-1095.9 \mathrm{M}\mathrm{P}\mathrm{a}$, respectively, were measured. Full article

A comprehensive numerical method was developed to ensure energy-efficient operating modes of a linear motion module powered by an induction motor. The proposed approach is based on minimizing inertial torque, accounting for the inertial properties of the drive components and the load carriage, followed by structural-parametric optimization and dynamic modeling. For the optimization of the drive system, comprising an intermediate gear stage and a primary ball screw mechanism, a normalization-based method combined with numerical parameter sweep was employed. The optimization process yielded optimal values of the screw lead and the number of gear teeth, which were further validated in terms of Pareto optimality. The carriage design was optimized with respect to mass, strength constraints, and dynamic stiffness using the finite element method. For the developed linear motion module, dynamic behavior was simulated by means of a system of nonlinear differential equations, taking into account the electromagnetic characteristics of the induction motor and the nonlinearities of the gear mesh. As a result of the comprehensive approach, the kinematic, force, and energy characteristics of the linear motion module, which was optimized at the design stage, were determined. Full article