Abstract This paper presents KC3 Tensegrity Sim, an open-source Python simulation framework for modeling class-k tensegrity structures with clustered cable routing and cylindrical 2.5D geometries. In this work, a 2.5D tensegrity structure refers to a planar tensegrity topology whose nodes are constrained to lie on a prescribed three-dimensional cylindrical surface while retaining the connectivity of the original planar pattern. Rather than proposing virtual work as a new theoretical method, this study applies a virtual-work equilibrium formulation to integrate three modeling capabilities that are not jointly supported in existing tensegrity software: class-k connectivity, clustered cables routed through multiple nodes, and cylindrical surface-wrapping constraints. The framework represents tensegrity systems through declarative configuration files, assembles the corresponding equilibrium residuals numerically, and solves for static equilibrium configurations in 2D, 3D, and cylindrical 2.5D settings. The framework is validated against a physical tensegrity structure and is intended to support early-stage design and configuration analysis of clustered and cylindrical surface-constrained tensegrity mechanisms, including wearable and morphing robotic structures.
Abstract Maintaining a precise remote center of motion is essential for safe and accurate tool manipulation in retinal microsurgery. However, existing numerical Jacobian identification methods for parallel manipulators often exhibit nonlinear, workspace-dependent inaccuracies and require frequent recalibration, limiting their reliability and clinical applicability. To address these challenges, this study presents an analytical kinematic framework for a hybrid parallel–serial robot designed for retinal surgery, known as the Steady-Hand Eye Robot (SHER 3.0). Closed-form solutions for forward and inverse kinematics, as well as analytical formulations of the direct and inverse Jacobians, are derived to ensure consistent motion estimation across the workspace. The kinematic performance of SHER 3.0 is analyzed to evaluate the manipulability and workspace efficiency. Building on these models, a model predictive control strategy is implemented on SHER 3.0, which maintains the remote center of motion constraint at the sclerotomy with sub-millimeter accuracy, with a root mean square error of 0.55 ± 0.12 mm, in a pilot study on a teleportation experiment. Experimental results demonstrate the effectiveness of the proposed analytical models and control framework in enhancing robot motion stability and robustness of the controller in maintaining the remote center of motion constraints, enabling safe robot-assisted retinal microsurgery.
Abstract This article focuses on experimental tests of three closed-loop control strategies: sliding mode control (SMC), model predictive control (MPC), and proportional-integral-derivative (PID) control with linearization applied to a tensegrity medical device, with the purpose of comparing them. The mechanism is designed to be part of a medical device for transcutaneous puncture applications where it is necessary to achieve a desired system orientation, adjust its stiffness, and ensure robustness against external disturbances such as natural human body movements. The performance of the three control strategies is compared for the tasks of trajectory tracking, stiffness adjustment, and robustness against external disturbances.
Abstract Powered two-degree-of-freedom (2-DOF) ankle-foot prostheses have distinct requirements for dorsiflexion/plantarflexion (DP) and inversion/eversion (IE) actuation. However, current designs rely on mechanically coupled DP and IE actuation with complex transmission stages. Thus, we present a proof-of-concept 2-DOF ankle-foot mechanism with unloaded kinematic validation using two simple and decoupled transmission stages. A ball-screw mechanism drives DP and a gear-and-chain mechanism drives IE, each constituting a single-transmission stage. A weighted mechanical complexity metric benchmarks this proof-of-concept architecture against five existing 2-DOF designs. Kinematic tracking is validated in Simscape Multibody simulation against gait data, and axis decoupling is experimentally confirmed using a 10-camera infrared motion capture system. The proposed design uses only two transmission stages instead of the four to six stages found in other alternatives. Experimental validation yields a DP-IE Pearson correlation coefficient of −0.018, confirming near-complete mechanical decoupling. The design achieves a DP range of −28.9 deg to 12.0 deg and an IE range of −22.5 deg to 22.5 deg, meeting daily-living motion requirements for level-ground walking. The unloaded kinematic decoupling validations provide a basis for further development of 2-DOF powered ankle-foot prostheses implementing our design with reduced transmission complexity.
Abstract Passive stiffness modulation is essential for compliant robotic systems in dynamic and uncertain environments, where rigid actuators or constant stiffness designs are often insufficient to ensure safety and adaptability. This article presents the design, modeling, optimization, and experimental validation of a load-dependent contact-aided compliant joint (LCCJ) that passively modulates stiffness in response to external torque. An integrated design pipeline is established, which bridges a high-fidelity analytical framework with a physically motivated optimization strategy. The framework combines a chained pseudo-rigid-body model (CPRBM) with Karush–Kuhn–Tucker (KKT) conditions to describe the complex beam-boundary interactions. Using the distinct deformation regimes of the mechanism, the pipeline employs a two-stage optimization strategy to precisely map the desired stiffness modulation back to the physical geometric parameters. Simulation results demonstrate that, across the benchmark and optimized-design validation cases, the model predictions agree closely with finite element analysis (FEA), with maximum relative errors in the torque-deformation response of 4.02% and 3.18% in the pre- and post-contact regions, respectively. Experimental validation confirms the effectiveness of the proposed design; compared to the FEA predictions, the experimental results exhibit relative errors below 2.6% in the precontact region and 5.22–6.21% in the post-contact region. The LCCJ offers a compact and monolithic solution for passive stiffness modulation in compliant joint applications.
Abstract Minimizing induced mechanical vibrations represents a challenging and critical issue in robotics, as they can degrade motion accuracy, reduce achievable performance, and accelerate mechanical wear. This article addresses the problem of minimum-jerk trajectory planning for redundant robotic manipulators by introducing an optimization approach that simultaneously exploits the structural redundancy of the robotic system and the functional redundancy of the assigned task. Unlike conventional redundancy-based approaches that typically rely on either kinematic redundancy alone or task redundancy properties, the proposed strategy leverages both types of redundancy to optimally plan the robot motion for the purpose of minimizing the end-effector jerk and, consequently, achieving smoother trajectories. In more detail, both the position of a selected redundant joint of the robot and one or more angles of the end-effector orientation are considered as optimization variables for each of the prescribed waypoints of the given path. The proposed strategy is verified on a robotic manipulator with seven degrees-of-freedom executing a pick-and-place operation. Extensive simulations and experimental tests demonstrate the effectiveness of the proposed strategy in reducing the end-effector jerk by more than 90% compared to a reference case.
Abstract Motion planning and control for robotic manipulation of deformable linear objects (DLO) necessitates computationally efficient and sufficiently accurate estimation of the DLO shape. Ideally, such an estimation should be able to reconstruct the deformation field from the pose of the terminal ends of the DLO only, which is particularly relevant for dual-arm manipulation. Numerical shooting and collocation methods accurately solve the associated boundary value problem, but are not applicable in time critical conditions. In this paper, a highly efficient algorithm is introduced for shape reconstruction of DLO undergoing large deformations. The method yields an explicit analytic representation of the displacement field. DLO are modeled as Kirchhoff rod since shear and compression can be neglected for the majority of relevant objects. The method is derived from a 3rd-order approximation of the exact solution. Assuming homogenous material and constant cross section, the shape estimation problem is reduced to a purely kinematic problem, which does not need material parameters. The solution method shows an excellent accuracy while being highly efficient at the same time. The result is equally relevant for continuum robots.
Abstract Conventional mechanisms (linkages) are typically characterized by the presence of a frame that remains fixed with respect to an inertial reference system. In contrast, mobile robotic systems, including articulated robots, consist of assemblies of rigid bodies that are free to undergo planar motion. The integration of these two paradigms leads to a class of mechanical systems in which a linkage structure is itself capable of moving on the plane. Such systems are hereafter referred to as mobile-linkage robotic systems (MLRSs). In an MLRS, the wheels not only provide locomotion but also actively participate in altering the kinematic configuration of the mechanism, resulting in a coupling between mobility and reconfiguration. This article provides a theoretical framework of general validity, applicable to a broad class of MLRSs, independently of their specific mechanical realization. In particular, both direct and inverse kinematic formulations are provided.
Abstract In multi-agent formation control, external flow fields introduce additional forces that affect the agents’ speed and heading angles, posing significant challenges to the formation stability. This article addresses the challenge of achieving multi-agent circular formation control in dynamic environments influenced by time-varying and spatially nonuniform flow fields. We consider the kinematics of the agents’ model as a second-order unicycle framework, where we control the linear acceleration and turn rate to facilitate smoother motion control. Moreover, while stabilizing the agents on the desired circle in different phase arrangements with limited communication topology, we impose the nonuniform motion constraint by considering the outer boundary nonconcentric. By leveraging the properties of Möbius transformation, we map the agents’ motion to a transformed plane where the motion constraints become uniform. In the transformed plane, we utilize the concept of the barrier Lyapunov function to stabilize the agents on the desired circular orbit without violating the constraints. Additionally, by utilizing the properties of Möbius transformation and its inverse mapping, we establish a connection between the control laws of the two planes and derive the actual plane control laws that depend solely on the parameters of the actual plane, ensuring applicability to real-world scenarios. Finally, we conduct numerical simulations to validate the effectiveness of the proposed approach.
Abstract To meet the requirements for defect inspection in spent nuclear fuel dry storage systems, this article proposes a leech-inspired wall-climbing robot. The robot employs a parallel mechanism composed of two suction cups, three flexible screws (corrugated tubes), and two fixed plates. This configuration enables peristaltic locomotion and large span transitions across intersecting wall surfaces. Based on the mechanical configuration and locomotion modes, a suction stability criterion is derived for different cases, and a dynamic model is further developed. Experiments are carried out in a simulated environment to validate the proposed approach. The results show that the robot can move stably in confined spaces and can negotiate transitions between different wall surfaces with a large span.
Abstract This study investigates the motion synchronization of serially connected, flexible multicable-driven systems, a configuration critical for compact robotic joints. A high-fidelity nonlinear dynamic model is established using a discrete element method, explicitly incorporating cable elasticity, damping, and nonlinear cable-sheave contact. The model effectively captures the coupled multibody dynamics essential for analyzing error propagation. Simulations reveal that under sufficient pretension and low load, the system maintains a stable bidirectional transmission state, with synchronization error accumulating along the drive chain. However, when the resistance torque exceeds a critical threshold, a qualitative transition to a unidirectional state occurs, characterized by cable slackness, a dramatic rise in error, and loss of kinematic constraint. This state transition defines a key performance boundary, directly impacting the joint's backdrivability and bidirectional impact resistance. The analysis provides quantitative insights into how pretension (enhancing effective stiffness) and resistance torque (perturbing tension distribution) govern synchronization. The proposed model serves as a design tool for determining crucial parameters, such as the minimum pretension and maximum allowable load, to ensure precise and robust synchronization in cable-driven robotic transmissions.
Abstract Conventional type synthesis of reconfigurable mechanisms mainly relies on case-specific geometric methods, which are mostly confined to single-loop mechanisms and structurally regular topologies. To overcome this limitation, this paper proposes an algebraic framework for the type synthesis of reconfigurable mechanisms, extending synthesis capabilities to multi-loop mechanisms. By combining redundant constraint detection, parameterized higher-order kinematic constraints, and Gröbner Cover theory, the framework formulates the synthesis process as a systematic algebraic decomposition of the parameter space. Applied to a planar four-bar linkage, the framework yields a reconfigurable mechanism that preserves its original planar and coaxial motion modes while introducing new spherical and 7R motion modes. Subsequently, the framework is applied to a 3-RPR parallel mechanism, with joints inserted to generate 3-UPU topologies. The resulting Gröbner Cover decomposition yields 12 distinct reconfigurable topologies, of which 3 are symmetric and 9 are asymmetric. Of these, 5 topologies contain an inserted joint numerically observed to remain passive across all sampled motion branches, suggesting its removability for structural simplification. This framework establishes a mathematical foundation for the systematic algebraic synthesis of multi-loop reconfigurable mechanisms.
Abstract This paper presents a post-design methodology for optimizing workpiece placement within the predefined workspace of a five-degree-of-freedom parallel kinematic machine tool (PKMT) with SPR–4SPRR architecture. The objective is to identify workpiece locations that improve force-transmission characteristics and reduce actuator effort during machining, without modifying machine geometry or control architecture. The approach combines analytical inverse kinematics, screw-theory-based Jacobian formulation, and force manipulability analysis to evaluate the force transmission capability of the machine across the workspace. The workspace is discretized into a dense three-dimensional grid and analysed for three representative tool tilt angles (0°, 15°, 45°). A data-driven threshold based on the empirical manipulability distribution is used to retain only well-conditioned configurations, and the optimal workpiece position is defined as the manipulability-weighted centroid of the resulting high-performance region. The method is assessed on an industrial-scale model of the METROM pentapod in MATLAB Simscape through simulated machining trajectories under representative quasi-static cutting loads. Results show that the optimized placement reduces mean peak actuator loads across additional simulated paths by 7.66% at 0°, 1.36% at 15°, and 21.22% at 45° tilt, with corresponding average force reductions of 1.66 N, 0.597 N, and 5.08 N. These findings demonstrate that workspace-aware workpiece placement can enhance the mechanical operating conditions of PKMTs and provide a practical post-deployment strategy for improving machining performance.
Abstract Tensegrity-based wearables offer a compact, effective, and simple solution to the absence of multi-stiffness braces. The Multi-Stiffness Expandable Tensegrity Structure (METS) introduces an arm-conforming sleeve that dynamically adjusts stiffness using a continuous cable system and tailored unit cell designs. Unlike powered or rigid exoskeletons, METS provides biomechanical support without external energy, enhancing joint stability, supporting rehabilitation, and mitigating muscle overuse injuries. This research demonstrates the feasibility of the METS concept through iterative design, experimental testing, and nodal displacement analysis. A custom benchtop tester and the Bending Arm axial and Twisting Apparatus (BABATA) were developed to measure force-displacement and angle-weight metrics. These testers showed an 184% increase in 2D axial stiffness and an 86% increase in radial stiffness across repeated trials. Three unit cell configurations—Herringbone, Walking Man, and Armadillo—were evaluated, with Herringbone delivering superior stiffness modulation. In its un-tensioned state, METS exhibited stiffness comparable to an off-the-shelf compression sleeve; when the continuous control cable was tensioned, stiffness increased substantially – a capability that passive sleeves cannot provide. These results establish METS as a mechanically viable, passive, and user-adjustable wearable platform with potential for application in orthotic systems, rehabilitation, and wearable robotics.
Neck pain is a common issue caused by prolonged static postures and cumulative fatigue, negatively impacting quality of life. While cervical collars support individuals with chronic neck injuries, there is a need for preventive solutions for healthy individuals, particularly office workers exposed to prolonged sitting and repetitive motions. The study introduces a novel ergonomic assistive device designed to reduce neck strain among office workers. Design objectives are based on the range of motion during daily activities for head motion as reported in the literature. Concept development was supported using a previously validated 20 degrees-of-freedom adams model of the cervical spine. Various design alternatives were evaluated using the model to identify the design that satisfied specific design criteria. The conceptual design was translated into a mechanical design, and a prototype was subsequently manufactured. Performance was evaluated on 20 healthy subjects using an inertial measurement unit and electromyography (EMG) sensors to compare two conditions: without device and with neck assistive cervical kit (NACK). Range of motion analysis revealed that the NACK condition reduced cervical mobility by 35.6%, 59.3%, and 53.4% in sagittal, lateral, and axial rotation directions compared to without device. Statistical analysis of EMG data using paired t-tests revealed significant reductions in muscle activation, with sternocleidomastoid activity decreasing by 23-29% maximum voluntary contraction (MVC) (p < 0.01) and upper trapezius activity decreasing by 10-15% MVC (p < 0.05). The results indicate that NACK provides support that limits excessive head movements while significantly reducing neuromuscular demand on the cervical musculature, thereby enhancing comfort and productivity in workplace environments.
Rescue and delivery missions in complex multidomain environments pose significant challenges for traditional robots, particularly regarding mobility limitations and the lack of precise interaction capabilities for final-stage delivery. To address this, we propose a triphibious robot equipped with a novel rolling-gripper, enabling versatile locomotion across air, ground, and water surfaces. The proposed rolling-gripper serves multifunctional purposes: it functions as a wheel for terrestrial mobility; acts as a gripper to perch and crawl on infrastructure or tree branches for the target area search and inspection; and operates as a manipulator to grasp supplies and deliver them directly into the victim's hand via an internal roller mechanism. This unique capability facilitates "last-meter" precise handover in water and ruin rescue scenarios, reducing failure risks where water waves drift supplies out of reach or where confined spaces block bulky robots from bringing essential aid to the victim. This article presents a mechanical analysis of the rolling-gripper mechanism, alongside kinematic and dynamic modeling of the robot's various motion modes. Experimental results validate the robot's triphibious mobility, its capability to perch and crawl on pole-like structures, and its specific efficacy in performing direct-to-hand delivery on water surfaces and within confined spaces, highlighting its significant potential for search-and-rescue in multidomain complex environments.
This article presents a successful design method of a novel planar linkage with a single degree-of-freedom, intended for advanced motion generation, which allows one to visit, in an exact manner, up to nine prescribed poses. The synthesis approach is based on formulating novel and explicit existence conditions, which are easy to understand and have a simple physical meaning, for the legs that make up the entire linkage. These conditions lead to a single closed-form design equation that must be valid for each prescribed pose. A challenging case study proposed in the literature is used to demonstrate the simplicity and potential of the proposed synthesis approach.
This paper presents a Multi-Index Collaborative Screening-based Optimization Method (MICSOM) for the geometric configuration optimization of 8-cable 6-DOF cable-driven parallel mechanisms (CDPMs). The method consists of two stages: the optimization of the cable connection method and the compactness optimization of frame geometric dimensions. In stage I, a global enumeration approach is used to identify the candidate cable connection method that satisfies static interference-avoidance and point set quantity constraints. A multi-objective evaluation coordinated function is constructed based on evaluation indices, including safe cable distance, cable tension quality, stiffness, wrench-feasible workspace, directional wrench output capability, and directional wrench output range, to select the optimal cable connection method. In the stage II, an improved PSO algorithm is applied to maximize the workspace occupancy ratio. A penalty function and dynamic inertia weight strategy are incorporated to optimize the spatial arrangement of frame anchor points and reduce the overall structural volume. Numerical experiments demonstrate that MICSOM effectively improves the kinematic performance, load-bearing capacity, and compactness of CDPMs, offering a valuable framework for the design of 8-cable 6-degree-of-freedom (DOF) CDPMs in complex task environments.
Gravity compensation is crucial for improving the energy efficiency of robotic systems, but achieving static balancing with variable payloads remains a design challenge. This article proposes a gravity compensation mechanism for variable payloads (GCVPs), designed for static balancing of variable payloads over a full range of motion. The GCVP integrates a slider, a pair of compression springs, and an adjustable pivot pin. Variable compensation is achieved by modulating the pivot radial position inside the slider to alter the stored energy in the springs without changing their stiffness parameters. The design methodology employs the potential energy conservation and virtual work principles to formulate the spring stiffness independent of the angular position of the payload. Numerical and experimental tests were used to show the performance of the GCVP. Numerical simulations demonstrate a torque reduction of up to 98.4%. Furthermore, experimental validation under variable loading (0.5-2 kg) shows a reduction in the peak torque from 1.29 N m to 0.16 N m (for 0.5 kg load) and from 4.61 N m to 0.51 N m (for 2 kg load). Similar reductions for intermediate loads were also observed, resulting in a maximum balancing efficiency of 90.05%.
This study investigates the design of magneto-active bistable compliant mechanisms for creating high-energy motion. Compared to traditional actuation methods, magneto-active actuation can enable remote and wireless control due to the ability of uniform magnetic fields to remotely induce torque on magnetic materials. In this study, we focus on bistable compliant mechanisms with slider-rocker geometries, where the input is a magnetic field-induced torque and the output is the linear motion of the slider. We investigate how the bistable design enables triggerable energy release during the rapid snap-through motion after the mechanism passes the unstable equilibrium. First, we introduce methods to determine the magnetic programming direction of the input link that enables reversible actuation between stable positions at the lowest possible magnetic field strength. Next, we investigate the design space to identify the geometries that maximize the energy stored in the mechanism's dominant spring and minimize the input magnetic field. Results from this study can guide the design of compliant mechanisms for creating high-energy motion when triggered by external uniform magnetic fields, such as remotely actuated rapid jumping or launching actuators for robotic applications.
