6-DOF Parallel Research Articles

A 3-DOF multi-mode parallel positioning platform utilizing piezoelectric–electromagnetic hybrid actuation

Abstract To improve the overall performance of 3-DOF parallel position platforms such as resolution, travel range, and linearity, this study proposes a novel compact piezoelectric-electromagnetic platform (PEP). The platform supports motion in XYθZ directions and operates in three working types: high-speed mode (HSM), low-speed stepping mode (LSM), and high-precision positioning mode (HPM). The PEP utilizes signal control to switch modes, enabling tasks such as rapid movement, precise positioning, and fine position adjustments. It also supports object rotation for orientation adjustments. Theoretical model was established to analyze the working principle of the actuator. A prototype was fabricated, assembled, and tested in a series of experiments to evaluate its performance across the three modes. The experimental results demonstrate the following: the PEP achieves a resolution of 20 nm in HPM, continuous and stable minimum rotary step movement of 0.37 μrad, and a linear coupling of less than 3.5%. The maximum forward and backward speeds reach 2681 μm/s and 2697.5 μm/s, respectively, under 100 VPP and 300 Hz. The piezoelectric-electromagnetic hybrid structure proposed in this study not only simplifies structural design but also delivers excellent output performance.

Kinematic and dynamic analysis of a 2DOF parallel robot arm for wind turbine blade fatigue testing

In response to the issues of low efficiency and significant impact on blade intrinsic frequency posed by the current biaxial resonance blade fatigue testing method, an innovative dynamic characterization method based on a 2-DOF (two-degree-of-freedom) planar parallel testing device is proposed in this paper. Firstly, the kinematic forward and inverse solution equations of the mechanism are established by scrutinizing the inherent positional relationships that govern its operation. The velocity Jacobian matrix is derived, and three types of singularities prevalent in the mechanism are analyzed. Secondly, based on the kinematics of the mechanism, an analysis of its workspace is undertaken to subsequently determine the range of its motion. Thirdly, by applying the Lagrange equations, the kinetic model of the mechanism is established, which can capture the dynamic interplay of forces and accurately calculate the changes in angular displacement, angular velocity, and angular acceleration of the active joint. Finally, a virtual prototype model and kinematics simulation are conducted based on the mechanism dimensions and assembly mode. The results show that the angular velocity, angular acceleration, and torque of the active joint all demonstrate smooth and uninterrupted curves that align with the actual testing trajectories, confirming the accuracy and effectiveness of our approach.

Design and control of a novel 3-DOF parallel MFC micromanipulation platform

Design and control of a novel 3-DOF parallel MFC micromanipulation platform

Development of 3-USR Type Spatial 6-DOF Parallel Mechanism with Large Workspace—Proposal of 3-USR Mechanism and Design of Spherical 5-Link Mechanism to Replace Active Universal Pairs (U)—

In this paper, we present a 3-USR-type 6-degree-of-freedom (6-DOF) parallel mechanism characterized by an expansive workspace. This mechanism consists of three coupling chains, each comprising a universal pair (U), a spherical pair (S), and a rotational pair (R), in sequence from the stationary base. To achieve a large workspace, the three stationary universal pairs are designated as active pairs, with their rotational axes intersecting at a single point, thereby creating a hemispherical workspace akin to that of a serial mechanism. To implement the active universal pair within a parallel mechanism, we replaced the spherical 5-link mechanism, which originally featured two stationary active rotational pairs, with stationary active universal pairs, and conducted an inverse kinematics analysis. Subsequently, we assessed the expansive workspace of the spherical 5-link mechanism, a key factor influencing the working area of the 3-USR-type 6-DOF parallel mechanism, by examining its motion transmissibility. Based on this evaluation, we designed two compact mechanisms that provide a large workspace and allow for the configuration of all three rotational axes to intersect at a single point. We experimentally investigated the relationship between motion transmissibility and rigidity for these two types of spherical 5-link mechanisms, demonstrating that motion transmissibility can serve as an indicator of rigidity. Finally, a prototype of the 3-USR mechanism was fabricated.

A novel real-time tension distribution method for cable-driven parallel robots

Abstract The tension distribution problem of cable-driven parallel robots is inevitable in real-time control. Currently, iterative algorithms or geometric algorithms are commonly used to solve this problem. Iterative algorithms are difficult to improve in real-time performance, and the tension obtained by geometric algorithms may not be continuous. In this paper, a novel tension distribution method for four-cable, 3-DOF cable-driven parallel robots is proposed based on the wave equation. The tension calculated by this method is continuous and differentiable, without the need for iterative computation or geometric centroid calculations, thus exhibiting good real-time performance. Furthermore, the feasibility and rationality of this algorithm are theoretically proven. Finally, the real-time performance and continuity of cable tension are analyzed through a specific numerical example.

The optimization of the hinge point position with a 2-DOF planar parallel heavy-duty hoisting mechanism

The optimization of the hinge point position with a 2-DOF planar parallel heavy-duty hoisting mechanism

Research on the Control Method of a 2DOF Parallel Platform Based on Electromagnetic Drive

In this paper, a spatial two-degree-of-freedom (2DOF) parallel platform based on electromagnetic redundant drive and its control method are investigated. The platform is redundantly driven by three electromagnetic-spring conforming branched chains, and the design provides better flexibility and responsiveness than conventional parallel structures. The introduction of the electromagnetic drive alleviates the stresses within the conventional rigid redundant drive structure and reduces the detrimental effects associated with rigid redundancy. In this paper, the structure and equivalent SPU model of the platform are first introduced, with S referring to the kinematic sub, P to the spherical sub, and U to the universal joint. The degrees of freedom of the platform are analyzed, and the inverse kinematic model and velocity Jacobi matrix are derived, so as to derive the relationship between the pitch, roll angles, and length of the gimbal chain, and the relational equation between the angle and the current is further established to realize the electromagnetic control of the parallel redundant platform. The control part is realized as follows. Firstly, the angle information of the platform is obtained from the gyroscope to the microcontroller, the filtered angle is derived through the Untraceable Kalman Filter (UKF), and the angle value can be fused with data by both the mathematical model and PID algorithm to introduce the current value required to achieve the balance and realize the balance. In the simulation part, this paper uses Simulink and Simscape in MATLAB for joint simulation, and by giving the simulated trajectory and the desired trajectory of the joints, the driving force diagrams of the three branched chains based on the Least-Second Paradigm method are derived, and the trajectory error and driving force error are given to validate the reliability of the method of this paper.

Design, Analysis and Optimization of Four Degrees of Freedom of Parallel Gripper Mechanism for Industrial Automation

Objectives: To obtain the positions, velocities, and acceleration of actuators of the 4-DOF of the parallel gripper, and optimization of the mechanism is carried out to find the optimal dimensions of the mechanism. Methods: Kinematic analysis is carried out to find the positions and velocities of the gripper of the mechanism. The method used to solve the position of the mechanism is inverse kinematics. A source code is written in MATLAB software to find the positions and velocities of the gripper. This software is a computing platform which can solve large size matrices easily which is most suitable for robots. A model of the mechanism is created in CATIA with constraints. The developed CATIA model is used in ANSYS software for structural analysis. The method used for finding optimal dimensions is Genetic algorithms. Optimization is carried out using Genetic Algorithms (GA’s) using the Energy Manipulation Index as an objective for obtaining the optimal dimensions of the parallel gripper mechanism. Finally, ADAMs software is used to simulate the mechanism. Findings: using inverse kinematic equations the results of displacements, velocities, and accelerations obtained for in-plane horizontal motion, and in-plane vertical motion s plotted. After checking the gripper performance, It is observed that the in-plane vertical transmission is better than the in-plane horizontal transmission. Based on the Energy Manipulation Index (EMI), the performance-to-effort ratio of the gripper object is calculated. It tells about the physical significance of energy transfer efficiency. If the energy occupied by the end-effector is higher than the 4-DOF Parallel Gripper achieves higher efficiency and possesses better manipulability performance. Maximum EMI is taken as an objective for optimization using GA. Simulation is carried out using ADAMS software to determine the driving forces or torques. Novelty/improvement: In this paper the performance index EMI is taken as objective to find the optimal dimensions of the 4-DOF of parallel gripper. Keywords: ­ DOF parallel gripper, In­hand manipulation, In­hand twisting, Driving force, Energy Manipulation Index (EMI)

Design and Control of a Pneumatic Muscle Servo Drive Applied to a 6-DoF Parallel Manipulator

Design and Control of a Pneumatic Muscle Servo Drive Applied to a 6-DoF Parallel Manipulator

Analysis of energy harvesting on 3-DOF mobile tetrahedron-based sun tracker

Abstract The use of solar panels to be placed on mobile platforms is still not able to absorb maximum solar energy. Therefore, we need a sun tracker system that is able to respond to disturbances from above, such as the movement of clouds, and also disturbances from below, such as movements from mobile platforms. The proposed mobile tetrahedron-based sun tracker is capable of fast and continuous response to movement and movement from various directions, with an effective control algorithm that will be able to keep the solar panels always perpendicular to the sun’s rays. This mobile tetrahedron-based sun tracker is a 3-DOF parallel construction with a stepper motor as the actuator. This sun tracker is installed on a moving platform and is capable of tracking the sun in a 3-DOF parallel manner. Test results with PV polycrystalline silicon with normal operating specifications of 5V/2W, show an average voltage measurement of around 2.62V and an average current of around 190.613mA. The average power produced is around 0.798W, with peak power reached around 11:40-12:00, while the lowest power was recorded at 07:00-08:00 and 17:00-18:00. The research results also obtained that the total electrical energy collected for one full day using a sun tracker was 9.571Wh (higher 7.166% than fixed PV).

Unified dynamics analysis of parallel manipulators: A joint-based approach and generalized inertia constraint matrix for parallel manipulators (GICM-P) framework

Parallel manipulators, a distinctive subset of closed-loop multi-body systems, are in high demand due to their precision-centric applications. This research introduces a unified approach to tackle both inverse and forward dynamic analyses of parallel manipulators, rooted in joint-based principles. The methodology dissects a given parallel manipulator into symmetric open-loop subsystems and a mobile body within either a planar or spatial context, depending on the manipulator’s nature. Conventional practices, involving the introduction of joint cuts at relevant locations, are employed to partition the system into multiple open-loop subsystems. Subsequently, the joint coordinate-based approach, typically applied to open-loop systems such as industrial manipulators, is utilized to derive solutions. In particular, this approach focuses on forward dynamics by introducing the generalized inertia constraint matrix for parallel manipulators (GICM-P), a concept built upon the authors’ prior work, originally addressing the GICM for general closed-loop systems. Notably, GICM-P aligns conceptually with the operational space inertia matrix (OSIM) designed for closed-loop systems elsewhere. However, unlike OSIM, which requires mapping joint-space inertia to operational-space inertia, GICM-P leverages acceleration-level constraints between subsystems and the moving platform through straightforward matrix operations. GICM-P offers a deeper understanding of the physics of the problem compared to OSIM, primarily due to its ability to explicitly express subsystem-level interactions via various block matrices – an aspect not previously documented. The paper provides explicit numerical values for GICM-P in the context of a spatial six degrees of freedom (6-DOF) Stewart platform and a planar 3-DOF parallel manipulator along with interpretations.

A Numerical Approximation Approach for Deriving Computational Efficient Inverse Dynamics of 6-DOF Parallel Robots Based on Principle of Virtual Work

A Numerical Approximation Approach for Deriving Computational Efficient Inverse Dynamics of 6-DOF Parallel Robots Based on Principle of Virtual Work

Dynamic modelling and energy-efficiency optimization in a 3-DOF parallel robot

AbstractEnergy efficiency is a challenging and relevant research field in modern manufacturing industries, where robotic systems play an essential role in the automation of several industrial operations. In this paper, we present an approach for the energy-efficiency optimization of a 3-DOF parallel robot. The proposed strategy leverages the task placement, the execution time, and the length of the robot lower arms to minimize the energy consumption for the execution of a predefined high-speed pick-and-place operation. To evaluate the actuators energy consumption, the kinematic, dynamic and electro-mechanic mathematical models, as well as an equivalent multibody model, of the parallel robot are implemented. The results of extensive numerical simulations show that the proposed strategy provides notable improvements in the energy efficiency of the parallel robot, with respect to alternative approaches. Starting from a pick-and-place task with optimal task placement with a consumption of 38.2 J (with a cycle time of 0.4 s), the energy expenditure can be reduced to 3.75 J (with a cycle time of 1.86 s), with a reduction percentage of 90.2%, by additionally optimizing the execution time, and the length of the robot lower arms. These results lead to a reduction from 5733 J/min (for 150 cycles/min) to 121 J/min (for 32 cycles/min), allowing to choose the best trade-off between robot productivity and consumed energy.

Structure design and kinematic performance of the deployable translational parallel tape-spring manipulator

AbstractA deployable manipulator has the characteristics of a small installation space and a large workspace, which has great application prospects in small unmanned platforms. Most existing deployable manipulators are designed based on rigid links, whose complexity and mass inevitably increase sharply with increasing numbers of rigid links and joints. Inspired by the remarkable properties of tape springs, this paper proposes novel deployable parallel tape-spring manipulators with low mass, simple mechanics, and a high deployed-to-folded ratio. First, a double C-shaped tape spring is presented to improve the stability of the structure. The combined fixed drive component (CFDC) and combined mobile drive component (CMDC) are designed. Then, novel 2-DOF and 3-DOF deployable translational parallel manipulators are proposed based on the CFDC and CMDC, and their degrees-of-freedom (DOFs), kinematics, and stability are analyzed. The coiled tape spring is regarded as an Archimedean spiral, which can significantly improve the accuracy of kinematic analysis. The correction coefficient of the Euler formula is obtained by comparison with simulation results and experimental results. Furthermore, the stability spaces of the 2-DOF and 3-DOF deployable parallel manipulators are given. Finally, a prototype is fabricated, and experiments are conducted to validate the proposed design and analysis.

Sensorless admittance control of 6-DoF parallel robot in human-robot collaborative assembly

This paper presents an adaptive admittance control to achieve human-robot collaborative (HRC) assembling of large, heavy components without using external sensors. This sensorless adaptive admittance control is constructed by the dynamic model of a six degree-of-freedom (DoF) parallel robot based on finite and instantaneous screw (FIS) theory. The dynamic model is intuitive and easy to be programmed. After getting stable actuation force by Kalman filter and identifying friction by LuGre model, accurate force estimator is built. Admittance controller is adopted to convert the change of estimated force to the change in position, velocity and acceleration. As a result, the 6-DoF parallel robot is capable of following the guidance of operator. Particularly, adaptive admittance control is design by using robot velocity as reference. A fast motion before contacting and a fine motion during contacting are allowed. Experiments are conducted to verify force estimator, admittance control and adaptive admittance control for HRC assembly. Results show that external force is accurately estimated. Robot complaint control in response to operator's force is achieved. The adaptive admittance control enhances execution time, accuracy of the HRC assembly.

Kinematically redundant (6＋2)-dof HEXA robot for singularity avoidance and workspace augmentation

This paper introduces a novel (6＋2)-degree-of-freedom (dof) kinematically redundant parallel robot. The proposed architecture is based on the 6-dof HEXA parallel robot. The paper applies methodologies for avoiding type II singularities using kinematic redundancy that were originally proposed for robots with prismatic actuators to a new architecture with revolute actuators. The singularities of the HEXA robot are first examined based on previous work, and new instances of singularities are discovered. The singularity locus in the orientational workspace is identified using the Power Inspired Measure. Then, a novel kinematically redundant leg architecture is proposed to allow for the avoidance of these type II singularities. It is shown that the singularities present within the orientational workspace can successfully be avoided if two kinematically redundant legs are included in the robot architecture. The performance of the new architecture is then examined in various trajectories within the orientational workspace. Results show that the attainable orientational workspace is significantly increased with the proposed architecture.

Hexad robot: A 6-dof parallel PnP robot to accommodate antagonistic rotational capability and structural complexity

This paper proposed a new structure of full-mobility parallel robot, which combined the advantages of high-rotational capabilities and structural simplification, for high-speed operations of material handling. The proposed robot structure integrates lightweight and simple linkages with a relatively complex (i.e., compared to the single platform with limited rotational capability) articulated mechanism or gear train as wrist mechanism to amplify the end-effector rotations, but without significantly increased structural complexity of gearbox, compared to the existing designs. Parametric modeling are carried out for position analysis, workspace evaluation, singularity identification and dynamic characterization to qualify the proposed robot. Moreover, the structure of the proximal links are designed with topology optimization to ensure design requirements of stiffness and low inertia. The performance evaluation shows that the proposed robot can be of high potential application in the industrial production line.

Mechatronic 5-DOF Parallel External Fixator With Correction-Assisted Software for Correcting Foot–Ankle Deformities

Mechatronic 5-DOF Parallel External Fixator With Correction-Assisted Software for Correcting Foot–Ankle Deformities

Kinematic Analysis of a New 3-DOF Parallel Wrist-Gripper Assembly with a Large Singularity-Free Workspace

This paper introduces a novel dexterous 3-DOF parallel wrist-gripper assembly with a large singularity-free range of motion. It consists of a zero-torsion 2-DOF parallel wrist and a 1-DOF parallel gripper. The wrist produces a 2-DOF sphere-on-sphere pure rolling motion. This large singularity-free 2-DOF sphere-on-sphere pure rolling motion of the wrist allows for smooth and precise manipulation of objects in various orientations, making it suitable for applications such as assembly, pick-and-place, and inspection tasks. Using a geometrical approach, analytical solutions for the inverse and forward kinematics problems of the wrist and gripper are derived. From the inverse kinematic equations, the Jacobian matrices are derived and it is shown that the whole workspace is free of type I and type II singularities. It is shown that with a proper choice of design variables, a large singularity-free range of motion can be obtained. The absence of singularities in the whole workspace of the wrist-gripper assembly is an important feature that enhances its reliability. Finally, the correctness of the derived equations for the wrist inverse and forward kinematics are verified using MSC Adams. These results confirm the feasibility and effectiveness of the proposed parallel wrist-gripper assembly. Overall, the novel parallel wrist-gripper assembly presented in this paper demonstrates great potential for improving the efficiency and flexibility of robotic manipulators in a variety of industrial and research applications.

A Comparative Study on Kinematic Calibration for a 3-DOF Parallel Manipulator Using the Complete-Minimal, Inverse-Kinematic and Geometric-Constraint Error Models

Kinematic calibration is a reliable way to improve the accuracy of parallel manipulators, while the error model dramatically affects the accuracy, reliability, and stability of identification results. In this paper, a comparison study on kinematic calibration for a 3-DOF parallel manipulator with three error models is presented to investigate the relative merits of different error modeling methods. The study takes into consideration the inverse-kinematic error model, which ignores all passive joint errors, the geometric-constraint error model, which is derived by special geometric constraints of the studied RPR-equivalent parallel manipulator, and the complete-minimal error model, which meets the complete, minimal, and continuous criteria. This comparison focuses on aspects such as modeling complexity, identification accuracy, the impact of noise uncertainty, and parameter identifiability. To facilitate a more intuitive comparison, simulations are conducted to draw conclusions in certain aspects, including accuracy, the influence of the S joint, identification with noises, and sensitivity indices. The simulations indicate that the complete-minimal error model exhibits the lowest residual values, and all error models demonstrate stability considering noises. Hereafter, an experiment is conducted on a prototype using a laser tracker, providing further insights into the differences among the three error models. The results show that the residual errors of this machine tool are significantly improved according to the identified parameters, and the complete-minimal error model can approach the measurements by nearly 90% compared to the inverse-kinematic error model. The findings pertaining to the model process, complexity, and limitations are also instructive for other parallel manipulators.