Screw Theory Research Articles

Non-Inertial Dynamic Analysis of 3-SPS/U Parallel Platform by Screw Theory and Kane’s Method

This paper presents an improved method for the non-inertial dynamic analysis of the 3-SPS/U parallel platform (3-SPS/U PM), employing the screw theory and Kane’s method, where S, P, and U denote spherical, prismatic, and universal joints, respectively. The proposed method extends the traditional inertial dynamic analysis to non-inertial systems. First, the generalized screw method is introduced, followed by the derivation of a transformation formula that adapts the screw method to various co-ordinate systems. Subsequently, the velocities and accelerations of each rigid body within the platform under non-inertial conditions are examined by combining the extended screw method with the system’s inverse kinematics model. The extended screw method is not only conceptually simple, but also adaptable to other non-inertial systems. Finally, the standard non-inertial dynamic model of the 3-SPS/U PM is derived through the Kane’s method and validated by the co-simulations with RecurDyn (V9R5) and MATLAB/Simulation (2019b).

An Exploratory Study of a Choreographic Approach to Golf Swing Dynamics: Bridging Biomechanics and Laban Movement Analysis

This study introduces an innovative integration of Laban Movement Analysis (LMA) with biomechanical principles to examine the golf swing dynamics from an ecological perspective. Traditionally, LMA focuses on the qualitative aspects of movement, often isolated from external influences. This research bridges that gap by investigating how golfers manage and adapt to the inertial forces of the club throughout the swing. Using motion tracking sensors and screw theory, we analyzed the spatial movement pattern in the Kinesphere (mapped as an icosahedron) and related it to force dynamics in the Effort Cube through the inertia tensor. The results showed significant differences between skilled and novice golfers in terms of how efficiently they align their movements with the club’s inertia. Skilled golfers demonstrated smoother Instantaneous Screw Axes (ISAs) and better synchronization with inertia forces, while novice golfers exhibited more abrupt deviations. These findings suggest that integrating qualitative movement descriptors with biomechanical models provides deeper insights into swing efficiency, performance improvement, and injury prevention. This combined framework offers a novel method to enhance both qualitative and quantitative analysis of golf swings.

Design and analysis of a thick-panel origami-inspired soft crawling robot with multiple locomotion patterns

Abstract Due to the flexibility obtained through both materials and structures, soft robots have wide potential applications in complicated internal and external environments. This paper presents a new soft crawling robot with multiple locomotion patterns that integrate inchworm motion and various turning motions. First, the conceptual design of the proposed robot is presented by introducing thick-panel origami into the synthesis of a crawling robot, resulting in a Waterbomb-structure-inspired hybrid mechanism. Second, all locomotion patterns of the robot are precisely described and analyzed by screw theory in an algebraic manner, which include inchworm motion, restricted planar motion, quantitative turning motion, and marginal exploration motion. Then, the output motion parameter for each locomotion pattern is analytically modeled as a function of the robotic dimensional parameters, and the robot can thus be designed and controlled in a customized way for the expected output motion. Finally, the theoretical analysis and derivations are validated by simulation and physical prototype building, which lay the foundations for the design and manufacture of small-scale soft crawling robots with precise output motions in a complex planar environment.

Kinematics and dynamics characteristics of a double-ring truss deployable antenna mechanism based on triangular prism deployable unit

In order to effectively improve the single-ring truss deployable antenna mechanism due to the large aperture caused by the problem with low structural strength and low-profile accuracy, a series of double-ring truss deployable antenna mechanisms (DRTDAM) are proposed with constant height during folding and deployment process. First, a variety of DRTDAMs are proposed based on tetrahedral units and their topologies are analyzed. Secondly, degree-of-freedom (DOF) characteristics of DRTDAM proposed in this paper are analyzed based on the screw theory and screw-constrained topological graphs and based on this, the kinematic characteristics of DRTDAM is investigated. Thirdly, the dynamics of the whole DRTDAM is built with Newton-Euler equations of multi-rigid body system. Finally, the correctness of above analysis is verified through dynamics analysis software ADAMS and numerical analysis software MATLAB, and the principle prototype is produced to verify the correctness of DOF analysis. The mechanism proposed in this paper enriches the configuration of DRTDAM, and the process of kinematic characterization method is clear and simple, which is meaningful for the research in space complex mechanism.

Sensitivity analysis and compensation for tooth surface deviation of spiral bevel gear machine tool

To analyze the quantitative mapping relationship between the geometric errors of the five-axis CNC machine tool and the tooth surface deviation of spiral bevel gears, and identify the key geometric errors that affect the machining deviation of the spiral bevel gear tooth surface, a sensitivity analysis method for tooth surface machining deviation of spiral bevel gear based on screw theory and EFAST method is proposed. Firstly, the machining model of the spiral bevel gear tooth surface based on the five-axis CNC machine tool is established. Then, the geometric error transfer model of the machine tool is established based on the screw theory. Combined with the EFAST global sensitivity analysis method, the key geometric errors that affect tooth surface deviation are identified. Finally, the reliability and effectiveness tests are performed by comparing the results to the local sensitivity analysis method and simulating compensation for the key geometric errors. The result of compensation shows that the tooth surface deviation is reduced significantly according to global sensitivity analysis. The feasibility of applying sensitivity analysis to control the tooth surface deviation of spiral bevel gears has been demonstrated.

Design and parameter optimization of solid-surface antenna parallel mechanism constructed by multi-loop spatial coupling units

The optimization of design and structural parameters of solid-surface antennas is crucial for the development of aerospace satellites. In this paper, the study explores an innovative parallel solid-surface antenna mechanism, inspired by the daisy bloom pattern, which realizes the characteristics of Fewer input-More output (Fi-Mo). A single-DOF deployable/foldable spatial multi-loop coupled mechanism model of the bionic daisy solid-surface antenna is established based on the single-axis tilting hinge, RSSR mechanism, and Bennett mechanism. The motion characteristics of the antenna mechanism are analyzed using the topology, position and orientation characteristic (POC) and inverse screw theory. The error transfer law of multi-loop mechanism is derived by the low-layer-loop sequence. The optimal configuration parameter set of the antenna deployment mechanism is determined using the NSGA-II genetic algorithm. Finally, the optimized antenna mechanism is subjected to physical simulation analysis to verify its stability and the accuracy of its deployment path.

A Screw Theory Approach for Instantaneous Kinematic Analysis of Parallel–Serial Manipulators

Abstract The paper presents an approach to perform an instantaneous kinematic analysis of parallel–serial (hybrid) manipulators using screw theory. In this study, we focus on non-kinematically redundant manipulators that include a single parallel mechanism. The proposed systematic procedure allows deriving Jacobian matrices for such manipulators, which provide mathematical relations between the end-effector velocities and speeds in the actuated joints. A generalized structure of the obtained matrices also reflects the constrained motions of the end-effector and the parallel mechanism. To illustrate the developed techniques, we consider three examples where we analyze three well-known parallel–serial manipulators with six, five, and four degrees-of-freedom. Following the proposed method, we determine Jacobian matrices for each manipulator. Next, we apply the presented approach for velocity analysis of a novel parallel–serial manipulator with five degrees-of-freedom. Numerical simulations validate the proposed theoretical techniques. The suggested approach represents the basis for subsequent singularity and performance analysis, and it can be adapted to hybrid manipulators with other architectures.

Type synthesis of a new parallel mechanism with complete separation of constraints and drives

Abstract Currently, there is an increasing demand for parallel mechanisms with fewer inputs and more outputs in aerospace, antennas, and recreational facilities. Therefore, this paper proposes a new parallel mechanism (PM) with a separation of constraints and drives, facilitating centralized drive management. Based on screw theory, the type synthesis of new parallel mechanisms with 3T (T representing translation), 3R (R representing revolute), 2T1R, and 2R1T is proposed. Three-degree-of-freedom (3-DOF) parallel mechanisms with fewer inputs and multiple outputs are proposed. Taking the 3RPS-PPPS parallel mechanism as an example, the closed-loop vector method is employed to solve for the lengths of actuated branches. A complete Jacobi matrix is constructed. The motion/force transmission performance of the 3RRS/PPPS parallel mechanism is better than the 3RRS parallel mechanism. Centralized management of drive branches greatly reduces the number of drives, making maintenance and repair easier. It has many application scenarios in antennas, recreational facilities, and other occasions.

Kinematic and aerodynamic analysis of a Microraptor-inspired foldable wing mechanism

Bio-inspired mechanisms have opened new avenues of research to understand the flying capabilities of birds. While extensive studies have explored the aerodynamics and kinematics of bird flapping motions, limited attention has been given to the folding motion. This paper introduces a foldable wing mechanism inspired by avian anatomy, specifically drawing inspiration from Microraptor aerodynamics. Employing the screw theory approach, we analyze the kinematics of the mechanism and conduct parametric calculations. By segmenting the mechanism and integrating the solutions, we develop an algorithm that demonstrates favorable power transmission, enabling the wing to remain extended with minimal actuation forces. We further employ position analysis to investigate the system’s functionality analytically. To optimize the mechanism, we utilize the gradient descent method. We validate the achieved momentum and velocities through an illustrative example by solving individual four-bar segments and transmitting the outputs to adjacent segments. The study utilizes detailed 3D modeling techniques employing SolidWorks software to accurately represent the wing designs. The results obtained provide valuable insights into the aerodynamic behavior of Microraptor, by comparing the coefficients of lift and drag in graphical form and contribute to the advancement of micro-aerial vehicle design.

A Closed-Form Inverse Kinematic Analytical Method for Seven-DOF Space Manipulator with Aspheric Wrist Structure

The seven-degree-of-freedom space manipulator, characterized by its redundant and aspheric wrist structure, is extensively used in space missions due to its exceptional dexterity and multi-joint capabilities. However, the non-spherical wrist structure presents challenges in solving inverse kinematics, as it cannot decouple joints using the Pieper criterion, unlike spherical wrist structures. To address this issue, this paper presents a closed-form analytical method for solving the inverse kinematics of seven-degree-of-freedom aspheric wrist space manipulators. The method begins by identifying the redundant joint through comparing the volumes of the workspace with different joints fixed. The redundant joint angle is then treated as a parametric joint angle, enabling the derivation of closed-form expressions for the non-parametric joint angles using screw theory. The optimal solution branch is identified through a comparative analysis of various self-motion manifold branches. Additionally, a hybrid approach, combining analytical and numerical methods, is proposed to optimize the parametric joint angle for a trajectory tracking task. Simulation results confirm the effectiveness of the proposed method.

Serial metamorphic manipulator dynamics formulation implementing screw theory tools

Abstract In this work, a framework is proposed for the analytical formulation of dynamic equations for serial metamorphic manipulators using screw theory tools. The integration of structure reconfiguration is achieved in a compact and comprehensive manner. Based on the previously proposed Modular Structure Representation, additional statements are provided to strictly define the metamorphic structure assembly. To validate the precision of the extracted dynamics, two simulations are performed for paths defined in cartesian space. The generated trajectory is evaluated by comparing the dynamic matrices produced by the proposed method with those from an established dynamic modeling algorithm. Additionally, the trajectory is simulated in an open-source simulator, and the torques extracted from system dynamics are compared with the corresponding simulator torques under the same kinematic constraints.

Novel Design and Performance Analysis of 1R1T Remote Center-of-Motion Mechanisms With Partially Decoupled T- and R-Motions

Abstract Remote center-of-motion (RCM) mechanisms provide a way for surgical instruments to pass through a remote center (e.g., skin incision) under geometrical constraints, facilitating safer operations in minimally invasive surgery (MIS). One rotation and one translation (1R1T, pitch and insertion) are the basic requirements for RCM mechanisms. To make the structure simpler and control easier, a novel concept of 1R1T RCM mechanisms with partially decoupled motions, inspired by the double-parallelogram 1R RCM mechanisms, is proposed in this article, by investigating and proving its motion combination principle based on the screw theory. New evolution procedures based on the configuration evolution method have been derived to design 1R1T RCM mechanisms based on two approaches of inserting the T-motion in an original 1R RCM mechanism, resulting in two types of 1R1T RCM mechanisms with partially decoupled motions and base-locating actuators. The kinematic models of one typical proposed mechanism (including the forward and inverse kinematics) and its Jacobian matrix are derived. The performance analysis is presented, including RCM validation, velocity, singularity, and workspace analysis. Then, the dimensional optimization based on the discrete solution method is derived. Finally, a prototype of the proposed mechanism is presented with preliminary experiments performed to verify the feasibility of the synthesized RCM mechanisms. The results show that the RCM mechanism performs the 1R1T partially decoupled motion, and it can be used as the basic element of an active manipulator of an MIS robot.

Multi-Level Behavioral Mechanisms and Kinematic Modeling Research of Cellular Space Robot

The cellular space robot (CSR) is a new type of self-reconfigurable robot. It can adapt the variety of on-orbit service tasks with large space spans through multi-level reconfiguration mechanisms. As the CSR has a large configuration space, kinematic solving becomes a key problem affecting on-orbit operation capability, and kinematic automatic solving research must be conducted. In order to solve this problem, firstly, the cellular space robot system capable of realizing multi-level self-reconfiguration is proposed for the demand of space on-orbit service, and the kinematic equations of modules are constructed by considering a single module function using screw theory. Secondly, the kinematics of the cellular space robot are encapsulated and divided into multiple levels, and the multilevel-assembly relationship-description method for robotic systems is proposed based on graph theory. On this basis, the pathway-solving algorithm is proposed to express the robot organization reachability information. Finally, the module–organ–robot multilevel kinematics solving algorithm is proposed in combination with screw theory. In order to verify the effectiveness of the algorithm in this paper, numerical simulation is used to compare with the proposed algorithm. The results show that compared with the traditional algorithm, the method in this paper only needs to update part of the assembly relations after organ migration, which simplifies the kinematic modeling operation and improves the efficiency of kinematic computation.

GeoExplainer: Interpreting Graph Convolutional Networks with geometric masking

For Graph Convolutional Network (GCN), the inherent geometric topology and relationships within spatio-temporal graphs are critical to factors affect its predictive performance. Understanding the decision-making process of GCN remains a challenging task. Existing perturbation-based explanation methods are primarily tailored for Graph Neural Network (GNN) models and focus on how the information of nodes or subgraphs in static graphs impacts GNN predictions. Due to the geometric properties of spatio-temporal graphs, screw theory serves as crucial mathematical tools for describing the geometric relationships and patterns of motion within the geometric space of spatio-temporal graphs. Therefore,we propose GeoExplainer, which utilizes screw theory to geometric masking for spatio-temporal graphs with strong geometric correlations, generating explanations for GCN. Our method perturbs spatio-temporal graphs using geometric masking, and ultimately generating explanations in the form of geometric masks serve as importance mappings for model prediction results. Firstly, we design a screw motion vector model with geometric constraints to describe the spatio-temporal graph in screw system. Then, we design a geometric screw perturbation to generate smooth geometric masks. Finally, we propose a geometric masking approach to optimize and update the geometric mixture mask. We utilize pointwise mutual information (PMI) to maximize the correlation between the model predictions after geometric perturbation and the original predictions, obtaining the optimal geometric mask as an explanation for GCN. The interpretable experiments of ST-GCN, HD-GCN, GCN and GIN models on four datasets with geometric relationships demonstrate that GeoExplainer outperforms eight competitive interpretation methods in quantitative and visualization analysis.

Design, Analysis and Experiment of a Modular Deployable Continuum Robot

Continuum robots, possessing great flexibility, can accomplish tasks in complex work scenes, regarded as an important direction in robotics. However, the current continuum robots are not satisfying enough in terms of fabrication and maintenance, and their workspace is limited by structure and other aspects. In this paper, to address the above problems, a modular deployable robot, which adopts an origami structure instead of a flexible hinge, is proposed. A fabrication method is innovated, the Spherical Linkage Parallel Mechanism (SLPM) unit is optimized, and the installation and fabrication process of the robot is simplified through modularization. The forward kinematics and inverse kinematics of the robot and its workspace are analyzed by using the screw theory. The prototype of the robot is constructed, and its folding performance, bending performance, and motion accuracy are tested, and the error analysis and compensation optimization are carried out. After the optimization, the position error of the robot is reduced by about 65%, and the standard deviation is greatly lowered, which effectively improves the motion accuracy and stability of the robot.

Type synthesis of 3-DOF spherical hybrid mechanisms with fixed centers of rotation

To improve the load-bearing capacity and the rotation range about the normal of the moving platform in a spherical parallel mechanism (SPM), a type synthesis method for spherical hybrid mechanisms (SHMs) with fixed centers of rotation is proposed by coupling a serial transmission chain with the central passive limb chain of the SPM near its center area. Based on the analysis of the spherical mechanism configuration’s research status with a fixed rotation center, a method for systematically synthesizing SHMs is given, and four types of limb chains are developed. The possible limb constraint systems provided by each type of limb chain are analyzed via screw theory, and the type synthesis of each type of limb chain is carried out. Screening rules are proposed to obtain the preferred limb chains from the limb chain configuration results. By selecting and permuting preferred limb chains based on the mechanism’s center position of rotation and the constraint type, a series of SHMs that rotate unrestricted about the normal of the moving platform are produced. Selecting the RBR-2RRR SHM as an example, its workspace, singularity, dexterity, and stiffness are analyzed to verify the effectiveness of the research. This work enriches the configuration types of SHMs and provides theoretical support for the design and applications of SHMs in engineering.

Screw Motion Used in Semiconstrained Rotational Plate Systems for Anterior Cervical Discectomy and Fusion.

Retrospective observational study. To scrutinize screw motion used in semiconstrained rotational plate systems for anterior cervical discectomy and fusion (ACDF). Semiconstrained rotational plate systems are supposed to control graft subsidence and facilitate lordosis acquisition and maintenance by toggling the instrumented vertebrae via variable-angle screws. However, their benefits may be unrealized if the screws move within the vertebrae. We reviewed medical records of 119 patients who underwent 1-level, 2-level, 3-level, or 4-level ACDF, divided them into the short-segment (n=62, 1-level or 2-level ACDF) and long-segment (n=59, 3- level or 4-level ACDF) groups, and investigated their immediate and 1-year postoperative lateral radiographs. We measured the fused segmental angle, screw angles at the upper-instrumented vertebra (UIV) and lower-instrumented vertebra (LIV), distance from the screw base to the endplate of UIV/LIV (SBE), and distance from the screw tip to the endplate of UIV/LIV (STE) to analyze the screw motion used in these plate systems. The differences between the immediate and 1-year postoperative values were statistically analyzed. The nonunion level was also investigated. Screw angle and SBE at the LIV significantly decreased in the long-segment group (-14.5±9.8 degrees and -2.8±1.8mm, respectively) compared with those in the short-segment group (-4.6±6.0 degrees and -1.0±1.5mm, respectively). Thus, the long-segment group could not maintain the immediate-postoperative segmental angle. Overall, 27 patients developed nonunion, with 19 (70.4%) in the long-segment group and 21 (77.8%) at the lowest fused level. Semiconstrained rotational plate systems provide only vertical forces to the fused segment rather than toggling the instrumented vertebrae. Postoperatively in multilevel ACDF, LIV screws migrate caudally, suggesting that these plate systems are not always effective in maintaining lordosis. Moreover, LIV screws and the anterior wall of the LIV are subject to overloading, resulting in a high rate of nonunion at the lowest fused level. Level III.

Design and kinematics analysis of a parabolic cylinder deployment mechanism with modular over-constrained triangular pyramid

Space missions require novel mechanisms that can have compact form in complex space environments. This study proposes a modular triangular pyramid parabolic cylinder deployment mechanism. The modular deployable unit contains an over-constrained triangular pyramid deployable mechanism and a symmetrical trapezoidal Bricard linkage that drives the longitudinal and transverse motions of the mechanism. A cable net is added between two symmetrical linkages to form a parabolic cylindrical reflector and is analyzed by the force density method. The Denavit-Hartenberg (D-H) coordinate method is used to analyze the kinematic characteristics. Based on the analytical solution for the angular displacement, the degrees of freedom of the mechanism are derived from screw theory. Subsequently, the angular velocity and acceleration of the joint points are obtained. Finally, kinematic models of the modular triangular pyramid parabolic cylinder deployable mechanism are established, and the accuracy of the theoretical model is verified using a numerical method. This novel parabolic cylinder deployable mechanism will have a significant influence in aerospace domain. Crucially, the work has value to design deployment mechanism for parabolic cylinder antenna.

A family of folding single-loop metamorphic mechanisms for aerospace manipulators: Synthesis, network, and analysis

Guided by predetermined degrees of freedom for different desired tasks, the type synthesis of single-loop metamorphic mechanisms (SLMMs) has long posed a challenge. Owing to the complexity and coupling of their overconstraints and the variability of constraints arising from bifurcation motions, it is difficult to ensure geometric coordination and synchronous motion for a network of multiple SLMMs. Here, we propose an approach to type synthesize SLMMs using the atlas method. A novel family of SLMMs is further synthesized. The mobility analysis of a selected 7R SLMM is carried out via screw theory. The kinematics and bifurcation phenomena are analyzed and verified through numerical simulation using computer-aided design models. To evaluate the performance of the SLMMs, the mapping relationship between key design parameters and performance indicators, such as the grasping angle, folding angle, and mechanical advantage, is studied. A networking method is then proposed by considering the geometric coordination conditions and variation of the overconstraints of SLMMs. Prototypes of an SLMM and manipulator with optimal geometrical parameters are developed to verify the feasibility and correctness of the proposed method and kinematic analysis.

Design and performance analysis of the 4UPS-RRR parallel ankle rehabilitation mechanism

Abstract. Ankle sprains are among the most common musculoskeletal injuries. Patients often require systematic rehabilitation training to expedite tissue healing and facilitate joint recovery. However, such training places high demands on medical staff, involves a lengthy process, requires considerable labor, and suffers from a shortage of skilled rehabilitation personnel. To address the need for effective ankle joint dysfunction rehabilitation training, this study analyzes the bone structure and movement mechanism of the ankle. Drawing on the parallel mechanism configuration, we propose a 4UPS-RRR parallel ankle rehabilitation mechanism. The rotation center of the rehabilitation mechanism can be highly coincident with the rotation center of the human ankle joint. The structure and degrees of freedom of the mechanism were designed and analyzed using screw theory. Additionally, a kinematic model of the mechanism was established. The mechanism's workspace was mapped by constraining the linear actuator length and spherical joint rotation angle. Furthermore, the mechanism's dexterity was assessed through the establishment of its Jacobian matrix, with the correctness of the kinematic model verified through simulation. Finally, an experimental platform was utilized to test the maximum range of robot motion, confirming the practicality of the ankle rehabilitation mechanism.