Planar Parallel Mechanism Research Articles

Multi-modal signal adaptive time-reassigned multisynchrosqueezing transform of mechanism

High-end mechanical equipment often operates under non-stationary conditions, such as varying loads, changing speeds, and transient impacts, which can lead to failures. Time-frequency analysis (TFA) integrates time and frequency parameters, allowing for detailed signal analysis and is widely used in this context. To improve the accuracy of assessing the operational status of mechanical equipment, this paper proposed a multi-modal signal adaptive time reassignment multiple synchrosqueezing transform (MSST) TFA method. This method enhances the MSST method by using a local maximum technique to address energy ambiguity in TFA. Additionally, the optimal window width for each function is determined through iterative processes to better concentrate energy in the TFA. Multi-modal signals are jointly analyzed using an impulse feature extraction method for signal reconstruction, enabling multi-dimensional fault analysis. The proposed method is validated with both simulation and experimental data from a planar parallel mechanism (PPM) and is compared against classical and advanced techniques. The results show that the method effectively captures shock features in multi-modal signals, offering a more consolidated time-frequency representation (TFR) than existing TFA algorithms.

A novel weighted-guided tensor completion missing data imputation method for health monitoring data of planar parallel mechanism

Abstract High-end mechanical equipment plays a crucial role in the manufacturing industry, making the monitoring of its operational status highly significant. Due to various factors such as environmental influences, the absence of monitoring signals in mechanical equipment status is a common issue, leading to a decline in data quality. To ensure data quality, this paper proposes an adaptive weighted low-rank tensor missing data imputation method. Firstly, based on the motion characteristics of a planar parallel mechanism (PPM), a new low-rank tensor model is established using periodicity, sliding windows, and time series. Secondly, the tensor truncation nuclear norm is defined, and a novel rate parameter is introduced to control the truncation degree of all tensor modes, thereby obtaining weights for each dimension. Finally, within the framework of the alternating direction method of multipliers (ADMM), adaptive weights for each dimension are obtained during each iteration, completing the filling of missing data. Two types of missing patterns are studied on a PPM experimental platform, and the results showed that as the missing rate increased, the mean absolute percentage error is less than 0.018, and root mean square error is less than 0.001, and the rate of change is less than 0.08, which was significantly better than other compared algorithms.

Design of a Three-Degree of Freedom Planar Parallel Mechanism for the Active Dynamic Balancing of Delta Robots

Delta robots are the most common parallel robots for manipulation tasks. In many industrial applications, they must be operated at reduced speed, or dwell times have to be included in the motion planning, to prevent frame vibrations. As a result, their full potential cannot be realized. Against this background, this publication is concerned with the mechanical design of an active dynamic balancing unit for the reduction of frame vibrations. In the first part of this publication, the main design requirements for an active dynamic balancing mechanism are discussed, followed by a presentation of possible mechanism designs. Subsequently, one the most promising mechanisms is described in detail and its kinematics and dynamics equations are derived. Finally, the dimensions of a prototype mechanism designed to experimentally validate the concept of active dynamic balancing are defined using the example of Suisui Bot, a low-cost Delta robot.

Performance evaluation and dimensional optimization design of planar 6R redundant actuation parallel mechanism

AbstractAiming at the problems of small good workspace, many singular configurations, and limited carrying capacity of non-redundant parallel mechanisms, a full-redundant drive parallel mechanism is designed and developed, and its performance evaluation, good workspace identification, and scale optimization design are studied. First, the kinematics analysis of the planar 6R parallel mechanism is completed. Then, the motion/force transmission performance evaluation index of the mechanism is established, and the singularity analysis of the mechanism is completed. Based on this, the fully redundant driving mode of the mechanism is determined, and the good transmission workspace of the mechanism in this mode is identified. Then, the mapping relationship between the performance and scale of the mechanism is established by using the space model theory, and the scale optimization of the mechanism is completed. Finally, the robot prototype is made according to the optimal scale, and the performance verification is carried out based on the research of dynamics and control strategy. The results show that the fully redundant actuation parallel mechanism obtained by design optimization has high precision and large bearing capacity. The position repeatability and position accuracy are 0.053 mm and 0.635 mm, respectively, and the load weight ratio can reach 15.83%. The research results of this paper complement and improve the performance evaluation and scale optimization system of redundantly actuated parallel mechanisms.

NEAR-ZERO PARASITIC SHIFT FLEXURE PIVOTS BASED ON COUPLED N-RRR PLANAR PARALLEL MECHANISMS

Abstract Flexure pivots, which are widely used for precision mechanisms, generally have the drawback of presenting parasitic shifts accompanying their rotation. The known solutions for canceling these undesirable parasitic translations usually induce a loss in radial stiffness, a reduction of the angular stroke, and nonlinear moment-angle characteristics. This article introduces a novel family of kinematic structures based on coupled n-RRR planar parallel mechanisms which presents exact zero parasitic shifts, while alleviating the drawbacks of some known pivoting structures. Based on this invention, three symmetrical architectures have been designed and implemented as flexure-based pivots. The performance of the newly introduced pivots has been compared with two known planar flexure pivots having theoretically zero parasitic shift via Finite Element models and experiments performed on plastic mockups. The results show that the newly introduced flexure pivots are an order of magnitude radially stiffer than the considered pivots from the state of the art, while having equivalent angular strokes. To experimentally evaluate the parasitic shift of the novel pivots, one of the architectures was manufactured in titanium alloy using wire-cut electrical discharge machining. This prototype exhibits a parasitic shift under 1.5 µm over a rotation stroke of ±15°, validating the near-zero parasitic shift properties of the presented designs. These advantages are key to applications such as mechanical time bases, surgical robotics, or optomechanical mechanisms.

A fast forward kinematics algorithm based on planar quaternion solution for a class of 3-DoF planar parallel mechanisms

A fast forward kinematics algorithm based on planar quaternion solution for a class of 3-DoF planar parallel mechanisms

Design and implementation of a 2-DOF 5R parallel mechanism with a coaxial-driven layout

In order to expand and improve the reachable workspace of planar parallel manipulators, a 2-DOF 5R parallel mechanism with a coaxial-driven layout is proposed. The configuration analysis and structural design are carried out, and the kinematic model is presented to conduct simulation analysis. The results indicate that the layout with the axes of the two driving devices overlapping has a larger workspace and a more compact structure. Meanwhile, a closed-loop PID control system is established to evaluate the accuracy of the proposed mechanism and analyse the kinematic error under different gain parameters. Simulation results indicate that the kinematic performance of the mechanism has improved. The control system is constructed based on using a motion control card as the primary control component and two servo motors as the drive device. Additionally, gain values are adjusted by the driver to reduce the deviation of the servo motors. Finally, the design of the prototype is deployed, and the experiment proved that the 2-DOF 5R planar parallel mechanism (PPM) with a coaxial-driven layout has the advantages of a large workspace, fast dynamic response, high stiffness, and easy control. The design of the 2-DOF 5R PPM solves the problem of single operation and high repeatability, which is increasingly utilized in the fields of electronics, food, daily chemicals, and pharmaceuticals.

Drive Layout Configuration Strategy and Scale Optimization Design of Multi-Drive Mode Parallel Mechanism

Abstract Aiming at the inherent defects of single-drive mode parallel mechanisms, such as small good workspace and many singular configurations, a new multi-drive mode parallel mechanism is proposed from the perspective of driving innovation. Taking the planar 6R parallel mechanism as an example, the driving layout configuration strategy and scale optimization design are studied. First, the potential driving layout of the mechanism is analyzed, and the inverse kinematics model of the mechanism is established. Then, based on the motion/force transmission index, the singular space and good transmission workspace of the mechanism are identified, and the mechanism-driven layout configuration strategy is formulated to complete the performance comparison analysis. Finally, based on the performance map method, the scale optimization design of the mechanism is carried out, the prototype is developed and manufactured, and the experimental verification is carried out. The research results show that the multi-drive mode parallel mechanism can improve its kinematic performance without changing the topological structure and scale parameters of the mechanism.

Kinematic Analysis of a Spatial Cable-Driven Mechanism and Its Equivalent Hybrid Mechanism for Elliptical Trajectory

In this paper, a spatial cable-driven parallel mechanism in a V-shaped cable arrangement is proposed. It is further simplified as a planar hybrid cable-driven parallel mechanism to analyze its kinematics, which consists of two identical active cable chains and a passive cross-slide mechanism. In order to investigate the degrees of freedom (DoFs) of the hybrid mechanism using screw theory, cable chains are represented as rotational–prismatic–rotational (RPR) chains. The motion pairs of all the chains are denoted according to screw theory. Firstly, the number and the types of DoFs of each chain are determined. Then, the number and the types of DoFs for the hybrid mechanism are calculated. Furthermore, the theoretical result is verified using the modified Grübler–Kutzbach (G-K) formula. It shows that the unique DoF of the equivalent mechanism is a rotation with a continuously changing axis, which is consistent with the V-type cable-driven mechanism with elliptical trajectories. Finally, the kinematics analysis of the cross-slider mechanism driven by two cables is carried out. The length, velocity and acceleration of the cables are obtained from numerical calculation in MATLAB, and the results are demonstrated using ADAMS simulation.

Control and determination of the kinematic model position of planar parallel mechanism

The mechanisms of parallel structure are the subject of many publications due to specific functional properties of these objects, such as load capacity and accuracy This paper offers a solution for the determination of the position and planar parallel two degrees mechanism control. Two problems are solved: the problem of the position of the mechanism and the problem of transition by the executive link of the mechanism through a special position and calculated the motor forces to pass through a special position. There was a proposed and tested control algorithm that offered an example of controlling. The solution for the accuracy position determination for a planar parallel mechanism with two degrees of freedom was offered.

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.

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.

Accuracy modeling, analysis and radical error distribution of 3-RPR planar parallel mechanism

Accuracy modeling, analysis and radical error distribution of 3-RPR planar parallel mechanism

Optimal Design for Vibration Mitigation of a Planar Parallel Mechanism for a Fast Automatic Machine

This work studies a planar parallel mechanism installed on a fast-operating automatic machine. In particular, the mechanism design is optimized to mitigate experimentally-observed vibrations. The latter are a frequent issue in mechanisms operating at high speeds, since they may lead to low-quality products and, ultimately, to permanent damage to the goods that are processed. In order to identify the vibration cause, several possible factors are explored, such as resonance phenomena, elastic deformations of the components, and joint deformations under operation loads. Then, two design optimization are performed, which result in a significant improvement in the vibrational behaviour, with oscillations being strongly reduced in comparison to the initial design.

Design Approaches of an Exoskeleton for Human Neuromotor Rehabilitation

This paper addresses a design for an exoskeleton used for human locomotion purposes in cases of people with neuromotor disorders. The reason for starting this research was given by the development of some intelligent systems for walking recovery involved in a new therapy called stationary walking therapy. This therapy type will be used in this research case, through a robotic system specially designed for functional walking recovery. Thus, the designed robotic system structure will have a patient lifting/positioning mechanism, a special exoskeleton equipped with sensors and actuators, a treadmill for walking, and a command and control unit. The exoskeleton’s lower limbs will have six orthotic devices. Thus, the exoskeleton’s lower limbs’ motions and orthoses angle variations will be generated by healthy human subjects on the treadmill with the possibility of memorizing these specific motions for obtaining one complete gait cycle. After this, the memorized motions will be performed to a patient with neuromotor disorders for walking recovery programs. The design core is focused on two planar-parallel mechanisms implemented at the knee and ankle joints of each leg’s exoskeleton. Thus, numerical simulations for the design process were carried out to validate the engineering feasibility of the proposed leg exoskeleton.

Razvoj sistema za programiranje i simulaciju 4-osnog robota sa hibridnom kinematikom

This paper presents an approach for developing the programming and offline simulation systems for low-cost industrial robots in the MatLab/Simulink environment. The approach is presented in the example of a virtual model of a 4-axis robot with hybrid kinematics intended for manipulation tasks. The industrial robot with hybrid kinematics consists of the well-known 5R planar parallel mechanism to which two serial axes have been added. The programming system developed in a MatLab environment involves generating G-code programs based on given pick and place points. The virtual model included in the simulation system is configured in the Simulink environment based on the CAD model of the robot and its kinematic structure. The kinematic model and the inverse kinematic problem have to be included in the virtual model to realize the motion of the virtual robot. The system of programming and simulation has been verified through several examples that include object manipulation to perform various tasks.

Prescribed flexible orientation workspace and performance comparison of non-redundant 3-DOF planar parallel mechanisms

The functionality of a workspace is one of the most important considerations in planar parallel manipulators (PPMs) design. Dexterous workspace (DW) is the subset of the reachable workspace (RW) and it means that full rotational dexterity is preserved in every translational position in space. However, DW is impractical as PPMs cannot rotate a full 360° because of interference. This paper proposes a workspace called prescribed flexible orientation workspace (PFOW) that characterizes the orientation capability of PPMs. To optimize and compare 3 degree-of-freedom (3-DOF) PPMs, a normalized and unified performance characteristic index is built based on indices including PFOW, condition number, velocity, payload, stiffness, and transmission indices which plays a guiding role in the optimization process. The best configuration is obtained through graphical performance comparison. In general, this work presents the analysis of rotational dexterity of PPMs and provides a guidance for optimization and selection.

CGA-based novel modeling method for solving the forward displacement analysis of 3-RPR planar parallel mechanism

This paper put forward a new geometric modeling method for forward displacement analysis of 3-RPR planar parallel mechanisms (PPMs) under the conformal geometric algebra (CGA) framework. A geometric constraint relationship of four lines intersecting at a point is first given. Then, a new coordinate-invariant geometric constraint equation of 3-RPR PPMs is elaborated via CGA operation. Next, an univariate polynomial equation without algebraic elimination is published. At last, the coordinates of three points on the mobile platform are figured out. The best part of this research is that a complete geometric modeling method by geometric constraint relationship of four lines intersecting at a point is formulated under the CGA framework, which has good intuition and offers a novel idea for solving the other complex mechanisms. Three numerical examples are utilized to confirm the effectiveness of the proposed method.

Optimized design of 5R planar parallel mechanism aimed at gait-cycle of quadruped robots

In quadruped robot locomotion using parallel mechanisms, researchers have used equal link lengths as legs for walking. However, force requirements are not the same in the forward and return strokes. An unsymmetrical parallel mechanism can be considered to accommodate such requirements. This work presents optimized dimensions of a 5R planar parallel mechanism (5R-PPM) with two degrees of freedom (DoF). Optimized dimensions are determined by formulating an optimization problem using kinematics and dynamics equations for the 5R-PPM. Genetic algorithm is considered to obtain solutions for the optimization problem formulated in this study. The constraint condition expressed here for optimization will attempt to minimize the peak torque essential to displace the links in the mechanism for the given height of the robot body and the path to be traced by the end-effector. After analysing all the four possible working modes for the same end-effector movement, the best working mode is selected for the quadruped legs. The equations are formulated and solved in MATLAB, and validated in the MATLAB Simscape Multibody toolbox.

Development of a novel 6-DOF hybrid serial-parallel mechanism for pose adjustment of large-volume components

In this paper, a novel 6-degrees-of-freedom (DOF) hybrid mechanism is proposed to realize position and posture adjusting for large-volume equipment. The designed hybrid manipulator is composed of the lower and upper modules, namely, a 3-DOF redundant spatial parallel mechanism (SPM) and a 3-DOF planar parallel mechanism (PPM), which has three rotational and three translational DOFs. According to the step-by-step pose adjusting strategy, the kinematics analyses of the lower and upper modules have been carried out systematically. For the whole hybrid mechanism, a complete kinematic model has been established; and visualized workspace of the kinematic model with regular shape and large volume demonstrates profound application prospects in engineering. In order to evaluate the performance of the proposed mechanism, experimental tests have been conducted in an automated docking system for pose adjustment of large and heavy components. The analysis results demonstrate the effectiveness and practicability of the new mechanism.