3-DOF Parallel Mechanism Research Articles

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.

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.

Symbolic position analysis for three 6-DOF parallel mechanisms and new insight

AbstractThe authors‘ previous research has demonstrated that parallel mechanisms (PMs) with hybrid branch chains (i.e., branch chains containing planar or spatial loops) can possess symbolic forward position (SFP) solutions and motion decoupling (MD). In order to further study the conditions of a three-chain six degrees of freedom (DOF) parallel mechanism with SFP and MD, this paper proposes one 6-DOF branch chain A and two 5-DOF branch chains B and C. Based on these, a class of four 6-DOF PMs with three branch chains is devised. The symbolic position analysis of three of four such PMs is performed consequently, featuring partial MD and SFPs, which reveals that if the position or orientation of a point on the moving platform can be determined by the position of the hybrid branch chain, the PM exhibits partial MD and SFP. Finally, the accuracy of the symbolized forward and inverse solution algorithms is verified through numerical examples. This research brings a new insight into the design and position analysis of 6-DOF PMs, particularly those with SFP and partial MD.

A Novel Cooperative Control Strategy for Three-Degree-of-Freedom Pneumatic Parallel Mechanism

The three-degree-of-freedom (3-DoF) parallel mechanism (PM) is widely used due to its simple structure and ability to avoid coupling problems commonly found in high-DoF PMs. The conventional control approach is usually independent control for each branch of the mechanism using a PID controller, without considering the consistency among branches. This paper proposes a novel cooperative control strategy for the 3-DoF PM to achieve both synchronized and differential motion. A pneumatic actuated test rig was constructed to validate the effectiveness of the cooperative controller. The results demonstrate our control approach outperforms the PID controller. Our self-designed platform is functional and intuitive, which can be regarded as a control scheme test bench for a 3-DoF PM.

High-Speed Cell Assembly with Piezo-Driven Two-Finger Microhand

In the past few decades, researchers have conducted extensive studies on cell micromanipulation methods. However, there has consistently been a lack of a micromanipulation system that excels in both precision and speed. Additionally, many of these methods rely on manual control, thus significantly reducing efficiency. In this paper, a robotized micromanipulation system employing a two-finger microhand is proposed. The microhand has a 3-DoF parallel mechanism driven by three piezoelectric actuators, enabling high-precision micromanipulation. Replacing the needle-tip end-effector with a hemispherical end-effector makes cell grasping easier and more stable. In addition, a vibration-based release method combined with gel coating is proposed to reduce the release difficulty caused by adhesion forces. Through multiple sets of experiments, we have determined the optimal grasping and releasing conditions while balancing precision, stability, and damage degree to cells. An automated cell assembly strategy based on microscopic visual feedback and pick-and-place path planning is proposed to achieve the robotized high-speed cell array. Hela cells were chosen as the operation objects, achieving a 95% success rate in grasping and a 97% success rate in releasing. A “T” letter array formed by cells was successfully assembled with an average grasp and release time of less than 0.8 s and an assembly accuracy of 4.5 μm for a single cell. This study holds significant implications for the fields of biology and medicine, presenting potential applications in tissue engineering.

Elastodynamic modeling and structural error compensation for a 5-DOF parallel mechanism with subclosed loops

In order to reduce the adverse effects of structural errors on a novel 5-degrees of freedom (DOF) parallel kinematic mechanism (PKM) with subclosed loops, studies on the elastodynamic modeling and structural error compensation are conducted in this paper. First, considering that introduction of subclosed loops significantly increased the complexity and difficulty of elastodynamic modeling, an equivalent unit modeling method for the branch chain with subclosed loop is proposed based on force analysis and deformation compatibility condition. Then, elastodynamic model of the whole 5-DOF PKM is established with the matrix structural analysis based method. Second, by defining a six-dimensional error (three translational errors and three rotational errors) for each node, structural error model of the PKM is constructed based on closed-loop vector method. To consider the coupling effects of static and dynamic structural errors, the dynamic structural errors derived by above elastodynamic model would be substituted into the structural error model along with given static structural errors. Finally, structural error compensation optimization model is established and structural errors are compensated by adjusting the driven parameters based on the improved particle swarm optimization (PSO) algorithm. Numerical simulations are conducted to verify the proposed elastodynamic modeling and structural error compensation methods. After compensation, the position errors along x, y, and z directions are respectively decreased by 68.036%, 81.409%, and 90.625%, and the angle errors around x and y directions are respectively decreased by 91.426% and 62.042%.

Configuration Design and Kinematic Performance Analysis of a Novel 4-DOF Parallel Ankle Rehabilitation Mechanism with Two Virtual Motion Centers

Aiming at the problem that the existing ankle rehabilitation robot is difficult to fully fit the complex motion of human ankle joint and has poor human-machine motion compatibility, an equivalent series mechanism model that is highly matched with the actual bone structure of the human ankle joint is proposed and mapped into a parallel rehabilitation mechanism. The parallel rehabilitation mechanism has two virtual motion centers (VMCs), which can simulate the complex motion of the ankle joint, adapt to the individual differences of various patients, and can meet the rehabilitation needs of both left and right feet of patients. Firstly, based on the motion properties and physiological structure of the human ankle joint, the mapping relationship between the rehabilitation mechanism and ankle joint is determined, and the series equivalent model of the ankle joint is established. According to the kinematic and constraint properties of the ankle equivalent model, the configuration design of the parallel ankle rehabilitation robot is carried out. Secondly, according to the intersecting motion planes theory, the full-cycle mobility of the mechanism is proved, and the continuous axis of the mechanism is judged based on the constraint power and its derivative. Then, the kinematics of the parallel ankle rehabilitation robot is analyzed. Finally, based on the OpenSim biomechanical software, a human-machine coupling rehabilitation simulation model is established to evaluate the rehabilitation effect, which lays the foundation for the formulation of a rehabilitation strategy for the later prototype.

Design and analysis of a novel underwater vector propulsion system based on 2SPS+SP/SPR parallel propelling mechanism

Due to the dual function of propulsion and manipulation, vector propulsion systems (VPSs) have recently become an emerging research hotspot. The 3-DOF parallel mechanism (PM) has been proven to be significant advantageous in underwater VPSs. However, the current design is mostly dominated by a three-limb propelling mechanism, and its stiffness remains to be improved. In the present research, a novel VPS based on a three-actuated limb and one-passive limb parallel propelling mechanism is proposed. Firstly, a kinematic model is studied, taking into account the terminal coupling relationships overlooked in previous studies; the independent parameters in the kinematic model correspond to the yaw and pitch angles of an underwater robot propelled by the VPS. Secondly, a mechanism inversion method for obtaining all singularity configurations is proposed to solve the singularity problem of the parallel propelling mechanism proposed herein. Finally, motion simulations are performed to verify the feasibility, effectiveness, and accuracy of the proposal. These simulations provide some pitch/yaw adjustment references for improving the VPS propulsion efficiency.

Design of a Redundant 6-DOF Parallel Platform for Mirror Precision Pose Adjustment

The pose control of 6-DOF parallel mechanism depends on the measurement accuracy of the position of the active driving strut, which affects the pose control accuracy of 6-DOF parallel mechanism. In order to overcome the influence of heavy load large impact force on the measurement accuracy of the active drive strut, a redundant 6-DOF parallel mechanism that separates the measurement struts from the active drive struts was proposed. The fixed platform and the moving platform are connected by six identical active drive struts and six redundant measurement struts. The active driving strut is an active motion unit used to achieve various pose movements of the parallel mechanism, and the follower redundant measurement strut is a precision measurement unit, and does not constrain any DOF of the platform. Only the follower accurately measures the distance between the upper and lower hinge points of the redundant hinges. The accurate position and pose of the 6-DOF parallel mechanism are obtained by using the forward kinematics solution. The controller is used to implement the pose closed-loop control algorithm to achieve precise pose control. The design of this redundant 6-DOF parallel mechanism improves the movement accuracy of the parallel mechanism under heavy load. It can be applied to the precision adjustment of the primary mirror or secondary mirror under heavy load in large aperture optics, and has strong engineering application value.

Modeling and structural optimization design of switched reluctance motor based on fusing attention mechanism and CNN-BiLSTM

Six-degrees of freedom (6-DOF) parallel mechanisms driven by switched reluctance motors (SRMs) can realize flexible control with high precision. Efficiency is an important indicator to measure the speed control system of SRMs. There are many characteristic factors affecting efficiency and strong nonlinear relationships between different characteristic parameters, which makes it difficult for analytical models and traditional neural network models to express their spatial correlation. For this reason, a convolutional neural network (CNN)-bidirectional long short-term memory network (BiLSTM) efficiency regression prediction model (CNN-BiLSTM-SENet) that integrates the attention mechanism (SENet) is proposed. Firstly, customize a formula for sensitivity analysis to screen characteristic parameters of efficiency. Secondly, build the CNN-BiLSTM-SENet model and use sparrow search algorithm (SSA) for hyperparameter optimization, input data to CNN to extract high-dimensional feature vectors that reflect complex changing relationships between features and efficiency while establishing feature channels. Embed the SENet to adaptively perceive and assign different weights to the feature channels, enhancing the influence of key features. Input the feature vectors outputted by the front-end network to BiLSTM to bidirectionally learn coupling relationships between sequences and complete regression prediction. Finally, propose improved northern goshawk optimization (MNGO) to solve the regression model to obtain the maximum efficiency and corresponding characteristic parameters. The results proved that the SSA-optimized CNN-BiLSTM-SENet model has higher fitting exactness and better prediction effect for efficiency regression prediction, and the MNGO also has stronger search ability and faster convergence.

Type Synthesis of 5-DOF Hybrid (Parallel-Serial) Manipulators Designed from Open Kinematic Chains

The article proposes an approach for synthesizing hybrid (parallel-serial) manipulators with five degrees of freedom (5-DOF) using open kinematic chains. The method idea consists in taking an open kinematic chain, selecting a subchain within it, and replacing the subchain with a parallel mechanism. The article considers 5-DOF open chains and 3-DOF subchains, substituted for 3-DOF parallel mechanisms with the same motion pattern as the subchain. Thus, synthesized hybrid manipulators have a 3-DOF parallel part and a 2-DOF serial part. First, we grouped 26 structures of open chains with revolute and prismatic joints into five types and 78 subtypes. Next, for each type, we selected one subtype and presented several hybrid mechanisms that can correspond to it. We considered hybrid manipulators that included 3-DOF parallel mechanisms with planar, spherical, and other commonly used motion types. The suggested synthesis method is intuitive for a designer, and it does not need any mathematical formulations like screw theory or group theory approaches.

Design and multi-objective optimization of a novel 5-DOF parallel mechanism with two double-driven chains

AbstractThis paper focuses on the design, analysis, and multi-objective optimization of a novel 5-degrees of freedom (DOF) double-driven parallel mechanism. A novel 5-DOF parallel mechanism with two double-driven branch chains is proposed, which can serve as a machine tool. By installing two actuators on one branch chain, the proposed parallel mechanism can achieve 5-DOF of the moving platform with only three branch chains. Afterwards, analytical solution for inverse kinematics is derived. The 5 $\times$ 5 homogeneous Jacobian matrix is obtained by transforming actuator velocities into linear velocities at three points on the moving platform. Meanwhile, the workspace, dexterity, and volume are analyzed based on the kinematic model. Ultimately, a stage-by-stage Pareto optimization method is proposed to solve the multi-objective optimization problem of this parallel mechanism. The optimization results show that the workspace, compactness, and dexterity of this mechanism can be improved efficiently.

Comprehensive Compensation Method for Motion Trajectory Error of End-Effector of Cable-Driven Parallel Mechanism

The accuracy of the end-effector motion trajectory is a critical performance indicator for cable-driven parallel mechanisms. This study aims to address the problem of trajectory error during the end-effector motion in a cable-driven parallel mechanism. It proposes a comprehensive compensation method based on the simultaneous application of the improved sparrow search algorithm and the cable length space error compensation algorithm, leveraging kinematic analysis. To compensate for the motion trajectory error of the end-effector caused by the geometric parameter error, the study establishes the kinematic model of the cable-driven parallel mechanism using the vector method. It creates the end-effector position error model and motion trajectory error model using the differential kinematic theory, analyzes the impact of the geometric parameter error on the motion trajectory error, constructs the kinematic parameter identification matrix, and uses an improved sparrow search algorithm to compensate for the position error of the motion trajectory interpolation point. For the motion trajectory error of the end-effector caused by non-geometric parameter error, the study analyzes the intrinsic correlation between the adjacent position error of the end-effector and the variation of the cable length using the error similarity theory. It then compensates for the position error of the interpolation point of the trajectory using a cable length space interpolation compensation method to enhance the motion trajectory accuracy of the end-effector. The study experimentally verifies the proposed comprehensive compensation method for end-effector motion trajectory error on a 4-cable-driven 2-DOF parallel mechanism, which reduces the motion trajectory error of the end-effector by 75%.

A highly efficient computational strategy to model the inverse dynamics of a novel 4-DOF parallel mechanism with direct constraints from the base at two point-contact higher kinematic pairs

A highly efficient computational strategy to model the inverse dynamics of a novel 4-DOF parallel mechanism with direct constraints from the base at two point-contact higher kinematic pairs

Stiffness modeling of a 2-DoF over-constrained planar parallel mechanism

Stiffness model acquisition of over-constrained parallel mechanisms is relatively difficult since they have more than necessary kinematic loops. In this study, a stiffness modeling solution for over-constrained parallel mechanisms is proposed while considering the computational cost efficiency. Three contributions of the paper are: (1) Presenting the stiffness modeling procedure for serially connected closed-loop structures by using the Virtual Joint Method (2) Considering the effect of dynamic auxiliary forces and dynamic external forces on the mobile platform’s deflection and achieving a direct solution by using superposition principle (3) A model fitting procedure for modifying the stiffness coefficients to comply with the experimental data. A 2 degrees-of-freedom over-constrained parallel mechanism is investigated as a case study. However, the proposed stiffness model is 6-DoF since compliant deflections occur in any direction. A finite element analysis and an experimental study verify the model’s results.

Congratulations! Journal of Robotics and Mechatronics Best Paper Award 2022

300-N Class Convex-Based Telescopic Manipulator and Trial for 3-DOF Parallel Mechanism Robot We are pleased to announce that the 15th Journal of Robotics and Mechatronics Best Paper Award (JRM Best Paper Award 2022) has been decided by the JRM editorial committee. The following paper won the JRM Best Paper Award 2022, severely selected from among all 123 papers published in Vol.33 (2021). The Best Paper Award ceremony was held on December 23, 2022 in hybrid style (both on-site and online; venue: Gakushi-Kaikan, Tokyo, Japan), attended by the authors and JRM editorial committee members who took part in the selection process. The award winners were given certificates and a nearly US$1,000 honorarium. Editorial committee members who participated online also congratulated them through Zoom. We congratulate the winners and sincerely wish them success in the future. Takashi Kei Saito, Kento Onodera, Riku Seino, Takashi Okawa, and Yasushi Saito Journal of Robotics and Mechatronics, Vol.33, No.1, pp. 141-150, February 2021 doi: 10.20965/jrm.2021.p0141

Dynamic Analysis and Design of an SMCNN of a 6-DOF Parallel Mechanisms using Translation Driver Motor

—Recently, many technological improvement apply in the discovery of various designs of haptic devices. Several mechanism structures including serial, parallel, and hybrid-kinematic manipulators can be considered for making a haptics device. The most successful haptic mechanisms are parallel-type, because of low moving inertia, large force reflection, and high stiffness. This research shows the 6-DOF parallel haptics device based on the parallel mechanism using a translation driver motor mounted on each leg. Firstly, we introduce a 6-DOF parallel mechanism using a translation driver motor haptics device model. Due to the unsure parameters, we focus on solving the mathematics model with the nonlinear parameters of the 6-DOF parallel mechanism. Secondly, to fix the kinematics and dynamics nonlinear uncertainties parameters, the SMCNN controller for 6-DOF parallel mechanism application using a translation driver motor is designed. The Sliding model control base on artificial intelligence neural network is used to calculate the unsure factors. In this technique, to prove the stability of the system the Lyapunop theory is used. Finally, the authors the simulation results of two control algorithms with different uncertain components are presented and comparing them to demonstrate the effectiveness of the new control method. The control method is demonstrated by way of implementing the set of rules in artificial surroundings with realistic parameters, in which the received consequences are fairly promising. The obtained from SMCNN algorithm results are highly promising and accurate.

An Approach to Improve the Resolution of DLP 3D Printing by Parallel Mechanism

For 3D printing based on Digital Light Processing (DLP) technology, the tradeoff of size and resolution remains challenging due to the limitations of the existing techniques. Therefore, we propose an approach to improve the feature resolution without sacrificing the part size. It is achieved by changing the projection distance and then adjusting the projection resolution and format, which is different from the previous printing principle of fixed resolution. To achieve this process, the tripteron 3-Degree-of-Freedom (3-DoF) parallel mechanism is innovatively applied to the DLP 3D printing structure, which simplifies the control process. Since the projection is fixed on the motion platform, the projection distance changes as the platform moves in space. Then the PLC-based program is developed according to the motion process, which successfully runs on the established prototype. Finally, the experiments are designed through the orthogonal method to optimize the molding process parameters. The effectiveness of the approach is verified by the feature forming comparison experiment. The results show that it can reduce the size of features by about 1.3 times through adjusting the projection resolution under the same size parts. Our method provides a new way for solving the contradiction, but more research needs to be done.

Optimal Design of a Kinematically Redundant Planar Parallel Mechanism Based on Error Sensitivity and Workspace

Abstract In this paper, the dimensional optimization of a (2PRR)-R + 2RRR (P and R represent the prismatic and revolute joint, respectively, and the underline indicates that the joint is the actuator) kinematically redundant parallel mechanism is performed by taking the integrated error sensitivity index and workspace as the objectives. Based on the matrix method, a generalized method for error modeling of the planar three-degree-of-freedom (3-DOF) parallel mechanism is proposed. The process of the generalized error modeling method is explained, and the error model of the planar (2PRR)-R + 2RRR kinematically redundant parallel mechanism is established. Based on the proposed error model, the error sensitivity indices of different dimension types are calculated. In order to reduce the error sensitivity and expand the workspace, the elitist non-dominated sorting genetic algorithm (NSGA-II) is used for multi-objective optimization of the mechanism. The comparative analysis between the optimized and the non-optimized mechanism is carried out from three aspects: error sensitivity, distribution of low-error sensitivity area, and area of the workspace. The results show that the optimization algorithm not only expands the workspace of the mechanism but also effectively reduces the error sensitivity in the workspace.

Influence of deformation zone length on bending radius of SS304 tubes with small diameters manufactured via free bending-based active motion

In three and six-axis free-bending equipment, the deformation zone length (A) is a fixed mechanical structure parameter modified when the relevant structure is redesigned and manufactured. In this study, a six degree of freedom (6-DOF) parallel mechanism was used as the control mechanism of the bending die, and a new method of changing the deformation zone length (A) was proposed. Firstly, an idealized geometric model of free bending-based active motion was established. Then, the influence of the deformation zone length (A) on the bending moment and the bending radius of the tube was analyzed. In addition, the finite element simulation and a kinematic model of free bending-based active motion controlled by the 6-DOF parallel mechanism were established, and bending processes of the SS304 tube with different deformation zone lengths were investigated. Afterwards, the impact of the deformation zone length (A) on the bending radius, bending moment, wall thickness, and motion of the parallel mechanism were analyzed. Finally, experiments were carried out on the free-bending equipment based on the 6-DOF parallel mechanism. Experiments verified the rules in the theoretical analysis, finite element simulation, and kinematic simulation.