In this work, a vibration suppression trajectory planning method for parallel SCARA robots considering link flexibility is presented. A MATLAB-ADAMS-ANSYS co-simulation model is built to characterize the robot elasto-dynamics and is used in trajectory planning for vibration prediction. A multi-objective optimization problem is formulated to minimize the position errors due to the elastic deformation and energy consumption, wherein the dynamically parameterized quintic non-uniform B-spline curve is selected to design the trajectory, to find the optimal trajectory parameters. A set of optimal solutions is selected and compared to the trajectories with different parameters to show the effectiveness of the optimized trajectory. Compared to the traditional parameterized spline vibration suppression trajectory, the proposed approach can significantly reduce the process vibration and residual vibration of the robot end-effector with respect to the spatial motion.

A visual six-degree of freedom posture measurement system for evaluation of parallel manipulators using a pyramidal mirror and a phase-encoded binary scale

Non-iterative optimization algorithm for cable tension distribution of a class of n + 2 cable-driven redundant parallel robots based on computational geometry

Compound Cable-Driven Parallel Robots for improved wrench-feasible workspace and stiffness modulation

In this paper, the mechanical design and kinematic solution of a built-up prototype translational parallel manipulator (TPM) with position control of its limbs are presented. A SolidWorks-based design and simulation is used for additional analysis, and a MATLAB-based iterative algorithm is developed for inverse kinematics solutions of the limbs. Limb movements are provided via screw rails, which are driven and controlled by DC motors with encoders. After the general mechanical design of the prototype manipulator, all parts are drawn and modeled in SolidWorks, and a motion simulation in three-dimensional space is performed. For the kinematic analysis, relevant equations are derived from geometric vector relations and solved iteratively in MATLAB. The calculated kinematic solutions obtained using MATLAB iteration are then compared with those evaluated from the SolidWorks simulation model. Finally, the accuracy of position control is tested with the calculated values, and very satisfactory results are obtained.

Due to the fact that earthquakes cannot be predicted, earthquake simulation is of great importance. An earthquake simulator is a device that reproduces the seismic waves generated by an earthquake. The aim of this work is to present the design and prototyping of an earthquake simulator that simulates a real long-period ground motion earthquake with vertical displacement, according to the earthquake seismogram. A control interface was designed for a prototype earthquake simulator to reproduce a given earthquake seismogram. The mobile platform of the earthquake simulator prototype performs translational motions in the direction of the X and Y axes due to the use of a cable-driven parallel robot, and the vertical translational motion of the platform along the Z axis is performed by linear screw drives. A prototype earthquake simulator was manufactured and tested, confirming the feasibility of reproducing long-period ground motion during an earthquake. The earthquake simulator implements motions that make a person experience sensations similar to those that occur during real earthquakes.

The dynamic performance of parallel robots directly determines the machining accuracy in large optical mirror processing (LOMP). However, limitations in traditional dynamic modeling methods hinder their application in real-time control, constraining further improvements in robotic precision. This paper aims to establish a high-precision and practical dynamic model that considers joint friction for parallel robots used in LOMP, and to design an efficient real-time friction compensation control strategy to effectively enhance trajectory tracking and repetitive positioning accuracy. The novelty of this work lies in proposing a dynamic modeling approach that integrates the static mechanics-based “Disassembly Method” with a “Coulomb + Viscous” friction model. First, static analysis of the mechanism is conducted using the “Disassembly Method” to accurately compute the joint constraint reactions in any pose, providing critical input for friction calculation. Subsequently, a complete dynamic model incorporating friction in joints such as Hooke joints, composite spherical hinges, and ball screws is developed based on the Newton–Euler formulation. This method overcomes the shortcomings of traditional approaches in solving joint reactions and managing model complexity. Numerical simulations demonstrate that, compared to conventional friction-neglected models, the proposed model reveals a maximum increase of approximately 350 N in driving chain joint reaction forces and significant peaks in driving forces at motion reversal instants (e.g., 0.28 s, 0.45 s), quantitatively proving that neglecting friction severely underestimates the actual system loads. Experimental validation shows that the feedforward PD friction compensator designed based on this model reduces the rotational tracking errors of the moving platform around the X- and Y-axis from 0.295° and 0.286° to 0.134° and 0.128°, respectively, achieving an error reduction of about 55% and effectively improving motion control accuracy. This study provides a reliable dynamic modeling foundation and an effective real-time control compensation solution to address force output errors and trajectory deviations caused by joint friction in high-precision LOMP.

Abstract This paper focuses on six-degree-of-freedom (six-DOF) spatial cable-suspended parallel robots with eight cables (8-6 CSPRs) because the redundantly actuated CSPRs are relevant in many applications, such as large-scale assembly and handling tasks, and pick-and-place operations. One of the main concerns for the 8-6 CSPRs is the stability because employing cables with strong flexibility and unidirectional restraint operates the end-effector of the robot under external disturbances. As a consequence, this paper attempts to address two key issues related to the 8-6 CSPRs: the force-pose stability measure method and the stability sensitivity analysis method. First, a force-pose stability measure model taking into account the poses of the end-effector and the cable tensions of the 8-6 CSPR is presented, in which two cable tension influencing factors and two position influencing factors are developed, while an attitude influence function representing the influence of the attitudes of the end-effector on the stability of the robot is constructed. And furthermore, a new type of workspace related to the force-pose stability of the 8-6 CSPRs is defined and generated in this paper. Second, a force-pose stability sensitivity analysis method for the 8-6 CSPRs is developed with the gray relational analysis method, where the relationship between the force-pose stability of the robot and the 14 influencing factors (the end-effector’s poses and cable tensions) is investigated to reveal the sequence of the 14 influencing factors on the force-pose stability of the robot. Finally, the proposed force-pose stability measure method and stability sensitivity analysis method for the 8-6 CSPRs are verified through simulations.

Abstract. The design of parallel manipulators with 3 translational degrees of freedom to deliver short-duration reactive inertial forces on the base is discussed. The intended application is a device that can apply perturbing forces on human limbs. The device, called an anti-balance perturbator, has to be mounted around the limb in a non-obtrusive way, to be lightweight with most mass attached to the moving platform, to have a large workspace with respect to the available space and to have a large bandwidth. Three designs are compared: an exactly constrained manipulator with three RUU legs, an overconstrained overactuated manipulator with four RUU legs and a manipulator with three overconstrained RRPaR legs. The designs contrast to common ones, because most mass is placed on the movable platform and because the base and the platform are almost in the same plane. A kinematic analysis addresses singularities and the sensitivity of the platform motion for clearance in the joints. Moreover, the compliance at the platform due to leg flexibility is determined. For these analyses, aggregate properties of the legs are used, which simplifies the analysis. Since the results show that the overconstrained manipulators are much less sensitive to clearance and much stiffer than the exactly constrained 3RUU manipulator, the design specifications can be more easily met. This makes the overconstrained designs preferable.

This paper proposes a two-layer adaptive proportional–integral–derivative (PID) controller for precise pose control of a six-degree-of-freedom cable-driven parallel robot with eight cables, specifically designed to handle dynamic changes caused by the movement of attachment points. The positions of the attachment points on the base are adjusted to avoid collisions between humans and cables, where humans and robots are working in a shared workspace. The inherent nonlinearity of the robot system was addressed using model identification based on the recursive least squares (RLS) algorithm equipped with an adaptive forgetting factor. This method enables real-time updates to the dynamic model of the robot, thereby ensuring accurate parameter estimation as the attachment points move. The combination of the PID controller and RLS algorithm enhances the system’s ability to respond effectively to changing dynamics. Simulation results highlight the superior accuracy, robustness, and adaptability of the proposed approach, making it well suited for applications requiring a reliable performance in dynamic and unpredictable environments. The proposed method can guarantee human safety, while the end effector tracks the desired trajectory.

ABSTRACT To overcome the limitations of existing ankle rehabilitation algorithms that focus primarily on mechanical aspects while overlooking biological factors, this study proposes a joint torque feedback control (JTFC) algorithm based on a parallel ankle rehabilitation robot (3-SPS/RU*R configuration). The algorithm aims to prevent joint overload and secondary injuries caused by excessive driving forces. An inverse dynamics model integrating both mechanical and biological elements was developed using the virtual screw method. The JTFC system employs neural network prediction and a multi-objective genetic algorithm (MOGA) to optimize motion parameters, alongside particle swarm optimization (PSO) for weighted PID tuning, ensuring joint torque remains within safe thresholds. Experimental validation using a physical prototype demonstrated high tracking accuracy (NRMSE as low as 0.0002), robustness (R-values of 0.7495–0.7499), and energy efficiency (Ec: 17.6254–25.0527). The results confirm the algorithm’s precision, stability, and practical applicability, offering valuable theoretical and practical insights for biomechanically-integrated ankle rehabilitation.

This study presents a comprehensive simulation-based comparative analysis of four parallel robotic mechanisms, each developed to assist patient recovery through adaptive movement control and feedback, particularly for upper and lower limb therapy. Kinematic and dynamic models were developed and implemented in Matlab-Simulink, integrating force control via conventional regulators and real-time interaction with simulated patient-applied forces. The structural differences between spherical, rotational, and universal joints in each kinematic chain variant were evaluated. To systematically determine the most suitable design, a detailed Analytic Hierarchy Process was applied considering performance, precision, stability, and actuator effort. The study emphasizes the advantages of parallel robots in rehabilitation due to their precision, rigidity, and compact design, highlighting the potential of parallel robotic systems in customized and adaptive physical therapy interventions. These insights contribute to the optimal design selection of clinical motor therapy robots.

The emergence of surgical robots has revolutionized complex operations, improving precision, lowering operating risks, and shortening recovery periods. Given the merits, an eight degrees of freedom (DOF) hybrid surgical robot (HSR) has been proposed, which leverages the benefits of both serial and parallel manipulators. However, its performance is hindered by the constrained range of motion of its parallel platform. To address the issue, this research presents a systematic approach for designing and optimizing the proposed HSR. The first step is the design of the HSR, followed by a multi-stage design analysis of its parallel platform, concentrating on kinematic, geometrical, and singularity analysis. Higher values of the condition number indicate singular configurations in the platform’s workspace, highlighting the need for an optimized design. For optimization of the platform, performance parameters like global condition number (GCN), actuator forces, and stiffness are identified. Initially, the design is optimized by targeting GCN only through a genetic algorithm (GA). This approach compromised the other parameters and raised the need for simultaneous optimization employing a non-dominated sorting genetic algorithm (NSGA II). It offered a better trade-off between performance parameters. To further assess the working of the optimized parallel platform, workspace analysis and motion planning of a predefined trajectory have been performed.

Abstract Percutaneous interventions, including biopsies, thermal ablations, and regional anesthesia, involve the insertion of an instrument into the patient’s body to remove tissue or manage pain. In this context, the use of a robotic assistant is suitable to guide the medical gestures, leading to a more time-effective intervention and better patient care. For this purpose, this article introduces a novel URRR-URR parallel mechanism. The constraint and mobility analysis of the mechanism is performed using screw theory. A methodology for determining the solution to its direct and inverse geometric models is presented. The forward and inverse kinematic Jacobian matrices of the mechanism are then expressed. Some singularities of the mechanism are identified and illustrated. Additionally, the design problem of the parallel manipulator (PM) under study is formulated as a bi-objective optimization problem. The first objective function is expressed in terms of the condition number of the forward and inverse Jacobian matrices. The second objective function deals with the mechanism size. Lastly, the nondominated Pareto-optimal solutions are obtained and three Pareto-optimal solutions are detailed.

This study presents a hybrid calibration and model-free error compensation framework to enhance the positioning accuracy of a 5R1P (R: revolute, P: prismatic) spherical parallel manipulator. Calibrating such mechanisms is challenging due to the analytical intractability of their inverse kinematics. To address this, a forward-kinematics-only approach is developed that eliminates reliance on inverse models while preserving high precision. The method integrates geometric calibration based on Denavit–Hartenberg (D-H) modeling with a two-stage optimization combining Particle Swarm Optimization (PSO) and Levenberg–Marquardt (LM) refinement. To correct residual errors, a Positioning Error Compensation Method (PECM) is introduced, which iteratively updates joint commands using a numerically estimated Jacobian. The PECM operates in two modes: one utilizing direct end-effector measurements and another employing an Adaptive Neuro-Fuzzy Inference System (ANFIS) to predict positioning errors. Experimental validation on a 5R1P prototype demonstrates a 97% reduction in Cartesian error using measured feedback and a 73% reduction using ANFIS-based predictions. The proposed framework provides a generalizable, inverse-kinematics-free solution suitable for real-time implementation in robotic systems requiring compactness, accuracy, and reliability.

Design and Validation of an X-ray Compatible Remotely Actuated Rotational End-effector for Cable-Driven Parallel Robot

Abstract Polymer cables are increasingly employed in cable-driven parallel robots (CDPRs) for environmental monitoring and infrastructure inspection due to their low inertia and corrosion resistance. However, elastic and creep-induced elongation reduces positioning accuracy and limits outdoor deployment. This study proposes a passivity-theorem-based compensation method that ensures input–output stability while enabling efficient mapping between tensile force and elongation. An odd-polynomial force–elongation model was derived and calibrated through tensile tests on polyethylene cables under representative lengths and loading rates. The model was then integrated into the CDPR kinematic loop to compensate elongation. Experimental results, validated against simulations across a 0–500 N loading range, show close agreement and improved end-effector tracking. The proposed method is computationally lightweight, making it suitable for real-time control, and has potential applications in environmental surveying, green infrastructure inspection, and offshore robotics..

A digital twin-based smart assembly for cable-driven parallel robots

This paper introduces TETRArm, a four-legged parallel manipulator endowed with kinematic redundancy. The redundancy of the robot is leveraged by incorporating two internal degrees of freedom into the moving platform of a non-redundant spatial parallel manipulator. This contribution demonstrates how a generalized coordinate can function identically in both inverse and forward instantaneous kinematics. Due to the complexity of the resulting equations, the forward position analysis is solved numerically. The instantaneous kinematics of the robot is examined using screw theory. In that concern, the velocity and acceleration expressions for the eight-degree-of-freedom parallel manipulator are systematically derived through the cancellation of passive joint rates via the Klein form. Numerical applications complement the theoretical findings.

Abstract Underactuated Cable-Driven Parallel Robots ( UACDPRs ) typically rely on relative internal sensors to estimate the end-effector ( EE ) state. Therefore, at startup, the reference values of the quantities measured by these sensors are unknown, and so is the initial pose of the EE . The problem of determining the reference values of the internal sensors is called initial-pose self-calibration. The latter is often formulated as an overdetermined system of nonlinear equations and solved using nonlinear weighted least-squares methods, minimizing the error between modeled and measured variables, and its effectiveness is highly influenced by the choice of measurement configurations, as well as the motion planning and control strategy used to reach them. This work presents two practical data acquisition methods for initial-pose self-calibration of UACDPRs , aiming to reduce the overall time required by the procedure and enhance process automation. The first method is slower but richer in data, as it relies on equilibrium poses and, therefore, can leverage cable-tension data, whereas the second method is faster and is based on geometric constraints only. The performance of the methods is evaluated in terms of acquisition time, number of measurements, and calibration accuracy on a 4-cable UACDPR prototype. The results highlight the merits and shortcomings of both methods, namely, trade-offs between the velocity of data collection and the precision of pose estimation.