Search Results (64)

This paper addresses the data-driven identification of open-chain robot morphology from finite windows of heterogeneous signals, including commanded joint references, measured joint states, and end-effector pose observations. Unlike conventional calibration procedures that assume a known kinematic topology, the proposed formulation estimates both discrete structural quantities and continuous kinematic coordinates: the number of active joints, the revolute/prismatic token sequence, Product-of-Exponentials (POE) screw axes, and the home pose of the end effector. A temporal transformer encoder is used as the main estimator and compared with a gated recurrent unit (GRU) baseline on the same dataset, with the same output heads and a multitask physics-aware objective. The continuous target is expressed in POE coordinates rather than as a Denavit–Hartenberg table because POE directly represents spatial joint axes and avoids several frame-assignment ambiguities. Simulated results on a noisy benchmark of 48 serial-robot families show that both sequence models recover the discrete structure on the tested in-library trajectories, while their continuous reconstruction errors reveal different trade-offs in screw-axis, home-pose, and trajectory reconstruction accuracy. The study also discusses inactive-slot masking, out-of-library behavior, synthetic-to-real limitations, persistent excitation, and the role of the learned model as an initialization for subsequent calibration refinement. Full article

Geometric errors in CNC machine tools accumulate along the tool path and directly affect machining accuracy. Traditional serial-chain-based volumetric error models, such as those based on the homogeneous transformation matrix (HTM) or screw theory, often exhibit ambiguous geometric definitions, weak traceability to measurement points, and increased computational cost due to repeated coordinate transformations and inverse mappings, limiting their suitability for real-time control. To overcome these challenges, this study proposes a parallel-type unified error vector transfer (EVT) framework, based on the Abbe and Bryan principles. In this framework, axis error motions are directly expressed as vectors and transferred to the tool center point (TCP), where they are superimposed to obtain total error contributions. Building on this principle, a unified normal volumetric error model (NVEM) is formulated using survival and sign factors. The unified NVEM is applicable to various types of three-axis machining centers, including horizontal configurations. In other words, differences in coordinate system definitions can be reconciled through coordinate transformation, allowing the unified NVEM to be consistently applied. Furthermore, a real-time error compensation controller (RECC) is embedded into the CNC kernel to compute compensation values within each interpolation cycle, ensuring deterministic and low-latency operation without external computation. Experimental validations on an XYFZ-type vertical machining center demonstrate that the proposed framework improves positioning accuracy by more than 72% and machining accuracy by 60.4%. These results confirm the feasibility, efficiency, and universality of the parallel-type unified EVT framework for real-time volumetric error compensation. Here, ‘parallel-type’ denotes the parallel superposition of independent error vector contributions, rather than a parallel kinematic mechanism. Full article

The main difficulty of pitch diameter calculation arises during the determination of the coordinates of the probing element and screw surface contact. This paper proposes a mathematical model for pitch diameter calculation of thread gauges using a two-ball stylus for internal thread calibration and three wires for external thread calibration. To describe the geometry of the thread and probing element, a non-linear equation system has been established and solved numerically. The solution of this system gives the actual contact points of the probing element with the thread profile. Pitch diameter is calculated directly without any further corrections. This mathematical model can be applied to parallel threads without any restrictions regarding lead and flank angles. Calculation of the rake correction is therefore avoided completely. The authors provide functional PHP/HTML code that can be easily integrated into any PHP-based website. Additionally, an open-access web tool has been developed that enables the direct calculation of thread pitch diameter from measured values, as well as the coordinates of the actual contact points between the thread profile and the measuring elements. Full article

A spatial system of cantilever bars is considered; the bars are fixed at one end and have the other end in common. The bars are straight ones. A given system of forces and torques acts on the bar system. The displacement of the common end is determined in the form of three linear displacements and three angular displacements. The calculation is carried out in screw coordinates. Various cases where certain components of the common end displacement have minimal values are also discussed. A numerical example is studied for different possibilities of the bar parameters. A particular case is that of a planar bar system. An extension of the problem is the case where, instead of the common end of the bars, the existence of a rigid body to which all the bars are connected is considered. Full article

A symmetric redundant-actuated 4-PSS compliant parallel micro-motion mechanism is proposed to meet the high requirements for stiffness and motion precision in micro-nano manipulation. First, the screw theory is employed to confirm that the mechanism possesses spatial three translational (3T) degrees of freedom along the X, Y and Z axes. On this basis, the global compliance model of the mechanism is constructed by combining the compliance matrix method with coordinate transformation technology, and the kinetostatic model reflecting the mapping relationship between input force/displacement and output displacement is further derived. The finite element analysis (FEA) is used to verify the kinetostatic model, and the results show that under the predefined spiral trajectory, the maximum absolute error between the theoretical calculation and the simulation result is less than 6 × 10⁻⁷ m, which proves the high accuracy of the established model. Moreover, a comprehensive performance analysis of the 4-PSS mechanism is carried out from the perspectives of output stiffness and parasitic motion, with the traditional 3-PSS compliant parallel mechanism as the reference. The comparative results indicate that within the specified 50 μm cubic workspace, the 4-PSS mechanism achieves a 33.3% improvement in output stiffness and a 28.15% reduction in the maximum parasitic displacement compared with the 3-PSS mechanism, while maintaining excellent global stiffness isotropy (GSI). Sensitivity analysis confirms the robustness of these advantages against manufacturing variations, and the workspace-to-footprint ratio remains unchanged. This research verifies that the introduction of symmetric redundant actuation branch chains can effectively enhance the comprehensive performance of compliant parallel micro-motion mechanisms and provide engineering references for the redundant design and performance optimization of high-precision compliant parallel mechanisms in the field of micro-nano manipulation. Full article

SSRMS refers to a Space Station Remote Manipulator System. The robotic arm of the Wentian module can complete tasks such as supporting astronauts’ extravehicular activities, installing and maintaining payloads, and inspecting the space station. The seven-joint SSRMS manipulator is critical for space missions. This study aims to build its kinematic model via screw theory. It simplifies SSRMS to right-angle rods, defines joint screw axes, twist coordinates, and initial pose matrix. Using the PoE (Product of Exponentials) formula, the 7-DOF forward kinematics equation is derived. In addition, it derives fixed joint angle for inverse kinematics, including analytical solutions and numerical solutions. It elaborates analytical solutions for fixing joints 1/7 and 2/6 and numerical solutions for fixing joints 3/4/5, solves all joint angles via kinematic decoupling, and addresses special cases. Experiments with China’s space station small arm parameters show the probability of meeting the accuracy threshold ${10}^{-4}$ is 99.79%, verifying model effectiveness, while noting singularity-related weak solving areas. This provides a reliable basis for subsequent inverse kinematics optimization. Full article

Limited workspace and singularities are major challenges for parallel mechanisms. This article addresses these issues for a 4-DOF 1-SPS/3-RRRRR parallel mechanism with a circular rail, proposed in our prior work. The mechanism has a 3R1T motion type with a movable center of spherical motion. The paper begins with a detailed description of the mechanism design. A closed-form solution of the inverse kinematics follows next, which computes the active joint coordinates and determines the spatial positions of all joints and links. Based on this solution, an iterative approach is applied to analyze the workspace for three different heights of the spherical motion center. The analysis reveals the regions of a full twist about the platform symmetry axis, bounded by maximum tilt angles of 51°, 38°, and 23°, respectively. Introducing joint constraints significantly reduces the workspace, limiting the tilt angles to 21°, 26°, and 0° at the same heights. Subsequently, screw theory is applied to identify serial, parallel, and constraint singularities, and an iterative approach is used to find the boundary of the singularity-free workspace. The analysis shows that the full-twist tilt angles are limited to 33°, a value determined solely on the platform geometry and independent of the spherical motion center height. These results establish a foundation for the design optimization and prototyping of the mechanism. Full article

Current analytical theories of recirculating flow in single-screw extruders consider only cross-channel flow in channels of infinite width with only one exception. Proper analysis of recirculating flow requires inclusion of normal velocities and the effect of finite channel width. More broadly, this paper presents an analytical description of lid-driven cavity flow—one of the most frequently studied flows in fluid dynamics. Expressions for velocities and flow rates for Newtonian fluids are obtained that satisfy the balance equations. These expressions have been compared to results of numerical analyses with good agreement. Flow rates and velocities are displayed with 3D surface plots and contour plots. These plots provide better insight into the flow behavior than 2D graphs. We have analyzed flow in slit channels with width much greater than the height ($W>>H$) and flow in a square channel ($W=H$). The vortex center (stagnation point) in a slit channel is located at normal coordinate $\psi =2/3$. The vortex center in a square channel is located at $\psi =0.76$. These analytical results allow for the development of better analytical models for melt temperature distribution, mixing, and devolatilization in single-screw extruders. Full article

In winter, ice is prone to forming on the surface of stay cables in cable-stayed bridges, posing a threat to their structural safety. As temperatures rise, the risk of ice shedding increases, posing a potential hazard to pedestrians and vehicular traffic. At present, de-icing relies mainly on manual operations, which are associated with high safety risks and low efficiency. As a result, the application of robotic systems for stay cable de-icing has become an emerging research focus. A key challenge in robotic de-icing operations lies in the complex and variable surface conditions of ice-covered stay cables, which frequently hinder stable climbing performance. To address this issue, a climbing mechanism was designed, integrating a grooved-track drive and a spring-assisted lead screw clamping system. A fuzzy PID control strategy was implemented to achieve adaptive coordination between the clamping force and climbing speed. Simulink simulations and indoor climbing experiments were performed to verify its effectiveness. The results show that compared with traditional PID control, the fuzzy PID controller reduces the response time by approximately 50%, exhibits better adaptability in icy environments, maintains a climbing speed error within ±1.5%, and improves overall climbing performance. Full article

The powder-laying arm of a metal 3D printer is heavy, which can easily cause long-term damage to the powder-laying servomotor or belt, so it is necessary to design a lightweight powder-laying arm. To this end, we first use 3D modeling Rhino software to rebuild the powder-laying arm, and then, we carry out topology optimization design on the rebuilt powder-laying arm in Altair Inspire software. Finally, we use the Aurora Elva 3D printer to complete manufacturing and assembly to verify compatibility. The results show that the maximum displacement of the original powder-spreading arm is concentrated in the lower right corner at 4.319 × 10⁻⁵ mm; the maximum stress is concentrated in the middle transition part, decreasing toward the ends; the maximum stress is 3.843 × 10⁻² MPa; the stress concentration and deformation of the powder-spreading arm when spreading powder is small, which provides a large optimization space. The topology-optimized powder-spreading arm, with a 25% quality objective, maintains the integrity of the connection with the fixing hole while having a large mass reduction. The surface of the parts of the completed 3D-printed powder arm is bright, with low roughness, and there is no obvious warping and deformation or other defects; the completed 3D-printed powder-spreading arm and the assembly of the wall are closely coordinated with each other, and the location of the screw holes is appropriate, having no obvious assembly conflicts between the parts, which lays the foundation for the mass production of the powder-spreading arm of high-performance metal 3D printers. Full article

Background/Objectives: The combined effect of femoral neck–shaft angle and lag screw position on unstable intertrochanteric fracture fixation has not been well established. This biomechanical study evaluated the effects of two caput–collum–diaphyseal (CCD) angles and two lag screw positions on construct stability. Methods: Twenty-four synthetic femurs with identical AO/OTA 31-A2.2 fracture gaps (2 mm) were fixed using cephalomedullary nails with CCD angles of either 125° or 130°, each with a central or inferior (calcar) lag screw (n = 6/group). Constructs were tested in a single-leg stance under preloading, cyclic loading (75–750 N, 10,000 cycles, and 2 Hz), and axial loading to failure. Lag screw migration was measured radiographically, and femoral head rotation was recorded using a three-dimensional coordinate-measuring device. Stiffness, failure load, and rotations were compared using the Kruskal–Wallis and Bonferroni post hoc tests. Results: The 125° inferior configuration showed the highest stiffness (188 ± 15 N/mm, p = 0.038) and failure load (1350 ± 97 N, p = 0.047), with the least screw migration (0.54 ± 0.11 mm, p = 0.003), significantly outperforming the 125° central and 130° central constructs. However, it exhibited greater varus collapse (2.25 ± 0.27°, p = 0.013) and axial rotation (~20–30% higher than others, p = 0.025). Screw position had a stronger effect on stability than the CCD angle, although the 130° inferior construct showed slightly less varus deformation. Conclusions: An inferior calcar-guided lag screw improves fixation strength and stiffness in unstable intertrochanteric fractures, particularly in those with a 125° nail. However, this configuration increases varus and rotational displacement, warranting adjunct measures to enhance rotational control in clinical applications. Full article

We develop a rigorous algebraic–analytic framework for multidual complex numbers ${\mathbb{DC}}_n$ within the setting of Clifford analysis and establish a comprehensive theory of hyperholomorphic multidual complex-valued functions. Our main contributions are (i) a fully coupled multidual Cauchy–Riemann system derived from the Dirac operator, yielding precise differentiability criteria; (ii) generalized conjugation laws and the associated norms that clarify metric and geometric structure; and (iii) explicit operator and kernel constructions—including generalized Cauchy kernels and Borel–Pompeiu-type formulas—that produce new representation theorems and regularity results. We further provide matrix–exponential and functional calculus representations tailored to ${\mathbb{DC}}_n$, which unify algebraic and analytic viewpoints and facilitate computation. The theory is illustrated through a portfolio of examples (polynomials, rational maps on invertible sets, exponentials, and compositions) and a solvable multidual boundary value problem. Connections to applications are made explicit via higher-order automatic differentiation (using nilpotent infinitesimals) and links to kinematics and screw theory, highlighting how multidual analysis expands classical holomorphic paradigms to richer, nilpotent-augmented coordinate systems. Our results refine and extend prior work on dual/multidual numbers and situate multidual hyperholomorphicity within modern Clifford analysis. We close with a concise summary of notation and a set of concrete open problems to guide further development. Full article

The clinical case presented demonstrates how a person living with type 2 diabetes and treated with insulin reuses the same pen needle several times to save money and performs an incorrect maneuver while screwing the needle, which breaks, remains stuck at the end of the pen, and causes loss of insulin during subsequent use. The findings in this case study are observed in many others in clinical practice but have only been sporadically published. Who is responsible for incorrect injections? Indeed, health workers, diabetic patients, and all the other actors involved in diabetes care and insulin utilization share responsibility. Recommendations and guidelines are not enough to fill this gap. Moreover, not all healthcare providers (HCPs) know or adhere to them. It is observed daily that more than half of insulin users make mistakes that affect glycemic control, increase the risk of complications, and reduce the quality of life of people living with diabetes, who, by a rough estimate, make up a population of over 100 million in the world. This case study offers us the opportunity to briefly review the literature on the most common errors made during insulin injection technique and, therefore, consider how necessary it is to promote structured and coordinated actions among various actors to promote the culture of therapeutic education. Full article

Background: Skilled human movement, such as the golf swing, emerges from coordinated rotational and translational dynamics. This study investigates pitch—a screw-theoretic invariant defined as the ratio of linear to angular velocity along the instantaneous screw axis (ISA)—as a compact metric for quantifying motor coordination. Methods: We reanalyzed a validated motion capture dataset involving a proficient and a novice female golfer. ISA trajectories and pitch values were computed from 3D marker data, and synchronized with vertical ground reaction force (GRF) signals collected via force plate. Results: The proficient golfer exhibited tightly bounded pitch oscillations (approximately ±0.0025 cm/rad) that were temporally aligned with a single, well-defined GRF peak. In contrast, the novice showed irregular pitch fluctuations (−0.025 to +0.01 cm/rad) and asynchronous GRF patterns with multiple peaks. Conclusions: These findings demonstrate that pitch can serve as a biomechanical indicator of skilled performance, reflecting the degree of intersegmental coordination and force timing. Screw theory thus offers a rigorous framework for evaluating movement efficiency in sport and rehabilitation contexts. Full article

The shallow, soft subsea formations, characterized by low strength and poor stability, lead to complex interactions between the screw motor drilling tool and the wellbore wall during directional drilling, complicating the accurate evaluation of the tool’s deflection capability. To address this issue, this paper proposes an integrated mechanical analysis method combining three-dimensional finite element analysis and transient dynamic analysis. By establishing a finite element model using 12-DOF (degree-of-freedom) spatial rigid-frame Euler–Bernoulli beam elements, coupled with well trajectory coordinate transformation and Rayleigh damping matrix, a precise description of drill string dynamic behavior is achieved. Furthermore, the introduction of pipe–soil dynamics and the p-y curve method improves the calculation of contact reaction forces between drilling tools and formation. Case studies demonstrate that increasing the tool face rotation angle intensifies lateral forces at the bit and stabilizer, with the predicted maximum dogleg severity within the first 10 m ahead of the bit progressively increasing. When the tool face rotation angle exceeds 2.5°, the maximum dogleg severity reaches 17.938°/30 m. With a gradual increase in the drilling pressure, the maximum bending stress on the drilling tool, maximum lateral cutting force, and stabilizer lateral forces progressively decrease, while vertical cutting forces and bit lateral forces gradually increase. However, the predicted maximum dogleg severity increases within the first 10 m ahead of the bit remain relatively moderate, suggesting the necessity for the multi-objective optimization of drilling pressure and related parameters prior to actual operations. Full article