Flexible Parallel Mechanism Research Articles

A New Theoretical Method for Solving Forward Kinematics of the Parallel Mechanisms Based on Transfer Matrix

The flexible parallel mechanism is widely utilized in precision instruments, thanks to its numerous advantages, such as high precision, frictionless operation, and seamless movements. The establishment of the motion equations for this mechanism is crucial for designing, analyzing, controlling, and simulating parallel mechanisms. While the existing inverse kinematics solution theory is comprehensive, developing a forward solution model is challenging due to the nonlinear nature of the attitude equation. To address this issue, a new method based on the transfer matrix approach is proposed in this research to calculate the forward kinematics of parallel mechanisms. The proposed method is applied to analyze the forward kinematics and workspace of both planar and spatial flexible mechanisms. Simulation calculations and experiments are conducted to verify the method’s effectiveness. The results demonstrate that the error is approximately 2%, indicating the feasibility and accuracy of the calculation method.

A Flexible Transoral Robot Towards COVID-19 Swab Sampling.

There are high risks of infection for surgeons during the face-to-face COVID-19 swab sampling due to the novel coronavirus’s infectivity. To address this issue, we propose a flexible transoral robot with a teleoperated configuration for swab sampling. The robot comprises a flexible manipulator, an endoscope with a monitor, and a master device. A 3-prismatic-universal (3-PU) flexible parallel mechanism with 3 degrees of freedom (DOF) is used to realize the manipulator’s movements. The flexibility of the manipulator improves the safety of testees. Besides, the master device is similar to the manipulator in structure. It is easy to use for operators. Under the guidance of the vision from the endoscope, the surgeon can operate the master device to control the swab’s motion attached to the manipulator for sampling. In this paper, the robotic system, the workspace, and the operation procedure are described in detail. The tongue depressor, which is used to prevent the tongue’s interference during the sampling, is also tested. The accuracy of the manipulator under visual guidance is validated intuitively. Finally, the experiment on a human phantom is conducted to demonstrate the feasibility of the robot preliminarily.

A New Extensible Continuum Manipulator Using Flexible Parallel Mechanism and Rigid Motion Transmission

Abstract An extensible continuum manipulator (ECM) has specific advantages over its nonextensible counterparts. For instance, in certain applications, such as minimally invasive surgery or pipe inspection, the base motion might be limited or disallowed. The additional extensibility provides the robot with more dexterous manipulation and a larger workspace. Existing continuum robot designs achieve extensibility mainly through artificial muscle/pneumatic, extensible backbone, concentric tube, and base extension, etc. This article proposes a new way to achieve this additional motion degree-of-freedom by taking advantage of the rigid coupling hybrid mechanism concept and a flexible parallel mechanism. More specifically, a rack and pinion set is used to transmit the motion of the i-th subsegment to drive the (i+1)-th subsegment. A six-chain flexible parallel mechanism is used to generate the desired spatial bending and one extension mobility for each subsegment. This way, the new manipulator can achieve tail-like spatial bending and worm-like extension at the same time. Simplified kinematic analyses are conducted to estimate the workspace and the motion nonuniformity. A proof-of-concept prototype was integrated to verify the mechanism’s mobility and to evaluate the kinematic model accuracy. The results show that the proposed mechanism achieved the desired mobilities with a maximum extension ratio of 32.2% and a maximum bending angle of 80 deg.

Actuation Spaces Synthesis of Lower-Mobility Parallel Mechanisms Based on Screw Theory

The lower-mobility parallel mechanism has been widely used in the engineering field due to its numerous excellent characteristics. However, little work has been devoted to the actuator selection and placement that best satisfy the system’s functional requirements during concept design. In this study, a unified approach for synthesizing the actuation spaces of both rigid and flexure parallel mechanisms has been presented, and all possible combinations of inputs could be obtained, laying a theoretical foundation for the subsequent optimization of inputs. According to the linear independence of actuation space and constraint space of the lower-mobility parallel mechanism, a general expression of actuation spaces in the format of screw systems is deduced, a unified synthesis process for the lower-mobility parallel mechanism is derived, and the efficiency of the method is validated with two selective examples based on screw theory. This study presents a theoretical framework for the input selection problems of parallel mechanisms, aiming to help designers select and place actuators in a correct and even optimal way after the configuration design.

一种新型刚柔混合并联机构的动力学研究

一种新型刚柔混合并联机构的动力学研究

A Compliant Transoral Surgical Robotic System Based on a Parallel Flexible Mechanism.

Transoral robotic surgery (TORS) allows for access to oropharyngeal regions in an effective and minimally invasive manner. However, safe TORS access to deep pharyngeal (such as hypopharynx) sites remains a great challenge for current surgical robotic systems. In this work, we introduce a novel continuum robot with an optimized flexible parallel mechanism, to meet stringent requirements imposed by TORS on size, workspace, flexibility, and compliance. The system is comprised of two parts, a guidance part and an execution part, and achieves 11 controllable degrees of freedom. The execution part of the robot, based on the optimized flexible parallel mechanism, is able to reach deep sites in the oropharynx and larynx with the assistance of the continuum guidance part. In addition to the mechanical design, extensive analysis and experiments were carried out. Kinematic models were derived and the reachable workspace of the robot was verified to cover the entire target surgical area. Experimental results indicate that the robot achieves significantly enhanced compliance. Additionally, the designed robot can withstand a load of 1.5N within the allowable range of the deflection. The positioning errors caused by the interference between different mechanisms can be effectively eliminated using the proposed compensation method. The maximum displacement error of this system under various conditions is less than 2mm and the maximum bending error is less than 7.5°, which are satisfied for TORS. Cadaver trials were conducted to further demonstrate the feasibility. The reduced setup time and the reduced time to access the target site indicate that the developed surgical robotic system can achieve better operative efficiency in TORS when compared with current systems.

Fabrication, Experiments, and Analysis of an LBM Additive-Manufactured Flexure Parallel Mechanism.

Additive manufacturing technology has advantages for realizing complex monolithic structures, providing huge potential for developing advanced flexure mechanisms for precision manipulation. However, the characteristics of flexure hinges fabricated by laser beam melting (LBM) additive manufacturing (AM) are currently little known. In this paper, the fabrication and characterization of a flexure parallel mechanism through the LBM process are reported for the first time to demonstrate the development of this technique. The geometrical accuracy of the additive-manufactured flexure mechanism was evaluated by three-dimensional scanning. The stiffness characteristics of the flexure mechanism were investigated through finite element analysis and experimental tests. The effective hinge thickness was determined based on the parameters study of the flexure parallel mechanism. The presented results highlight the promising outlook of LBM flexure parts for developing novel nanomanipulation platforms, while additional attention is required for material properties and manufacturing errors.

Design and analysis of symmetric and compact 2R1T (in-plane 3-DOC) flexure parallel mechanisms

Abstract. Symmetry is very necessary in flexure mechanisms, which can eliminate parasitic motions, avoid buckling, and minimize thermal and manufacturing sensitivity. This paper proposes two symmetric and compact flexure designs, in-plane 3-DOC (degree of constraint) mechanisms, which are composed of 4 and 6 identical wire beams, respectively. Compared to traditional leaf-beam-based designs, the two present designs have lower stiffness in the primary motion directions, and have smaller stiffness reduction in the parasitic directions. Analytical modelling is conducted to derive the symbolic compliance equations, enabling quick analysis and comparisons of compliances of the two mechanisms. A prototype has been tested statically to compare with analytical models.

Dynamic response analysis and chaos identification of 4-UPS-UPU flexible spatial parallel mechanism

In order to realize the dynamic response analysis and the chaos identification of flexible spatial parallel mechanism, the nonlinear elastic dynamics model of 4-UPS-UPU flexible parallel mechanism is established under the ideal situation, and the dynamic response, phase diagrams, Poincare map and largest Lyapunov exponent of the spatial parallel mechanism are investigated. Based on the finite element method, the driving limbs of spatial parallel mechanism are divided into elements. The kinetic energy equation and potential energy equation of units are built. Then the nonlinear elastic dynamics model of 4-UPS-UPU parallel mechanism is acquired by Lagrange equation. The dynamic response of kinematic error for 4-UPS-UPU flexible parallel mechanism is analyzed. In addition, the chaos phenomenon contained in the mechanism is identified by phase diagrams, Poincare map and largest Lyapunov exponent, respectively. Subsequently, the relationship between the basic parameters of parallel mechanism and largest Lyapunov exponent is discussed. The results indicate that there exists chaotic phenomena in the 4-UPS-UPU flexible parallel mechanism, and the basic parameters, including the material of driving limbs, diameter of driving limbs, mass of moving platform and the distribution radius of hinges of moving platform all have great effect on chaotic motion of 4-UPS-UPU flexible parallel mechanism. The researches can provide important theoretical for the further nonlinear dynamics behaviors research and optimal design of 4-UPS-UPU flexible spatial parallel mechanism.

基于3-RRR结构的光学元件柔顺微动调整机构的位姿正解

基于3-RRR结构的光学元件柔顺微动调整机构的位姿正解

Dynamic Analysis on Flexible Cable-Driven Parallel Mechanism

The interference between cables and surface of acutator limits the movement in the cable-driven parallel mechanism. The mechanism with fixed hinge can’t absolutely avoid the interference point of the track when using linear programming method. One new method, named as distant interference, was proposed to pick out all the interferential points of the track. Based on the principle of symmetrical force, the alteration to position of the six fixed hinges and two extensive hinges eliminated the interference. Through the simulation of combined spiral movement, the workspace of the flexible cable-driven parallel mechanism is larger than that of the mechanism with fixed hinge and reduce the interferece of long and big track. Compared with the original mechanism, the value of cables force in the flexible cable-driven parallel mechanism is smooth, continous and no sudden change.

The initial value problem for the mathematical model of a multiple-input multiple-output flexible parallel mechanism

The cable-net support structure of the Five-hundred-meter Aperture Spherical Telescope (FAST) is a multiple-input multiple-output (MIMO) flexible parallel mechanism. The mathematical model of the cable-net structure is set up with the catenary equation, which produces a large number of non-linear equations. Finding the initial value plays an important role in the working state of the FAST. In this paper, a novel method is proposed to solve the equations of the model. This method uses the solution of the (n−1)-th layer cable-net as the initial value of the n-th layer cable-net. The n-layer cable-net equations are then solved simultaneously and the tension of each cable and the coordinate of each node in the cable-net can be obtained. With the introduction of the symmetry of cable-net, the number of unknown parameters in the equations is reduced to about one-tenth of the whole cable-net. The initial value of the cable-net support structure of the FAST is provided to show the validity of the method. The results of this study are of practical value for the FAST's new type of flexible cable driving mechanism design and control method.

An Analytical Approach for Synthesizing Line Actuation Spaces of Parallel Flexure Mechanisms.

In this study, we present an analytical approach for synthesizing line actuation spaces of a parallel flexure mechanism (PFM) that can help designers to arrange linear actuators within the PFM in a correct and optimal way. On the basis of screw theory and upon an assumption of small deformations, an important synthesis criterion stated as "any actuation space of a flexure mechanism is always linearly independent of its constraint space" has been derived and disclosed for the first time. Guided by this criterion, a general synthesis process for the line actuation spaces of PFMs is introduced and demonstrated with several selective examples. The proposed synthesis criterion and process will enable designers to (i) systematically formulate line actuation spaces in the format of screw systems; (ii) likely yield a multiple solution to actuation spaces; and (iii) potentially determine an optimal result from those alternatives for actuator placement.

Kinematics modeling of a 6-PSS parallel mechanism with wide-range flexure hinges

A novel 6-PSS flexible parallel mechanism was presented, which employed wide-range flexure hinges as passive joints. The proposed mechanism features micron level positioning accuracy over cubic centimeter scale workspace. A three-layer back-propagation (BP) neural network was utilized to the kinematics analysis, in which learning samples containing 1 280 groups of data based on stiffness-matrix method were used to train the BP model. The kinematics performance was accurately calculated by using the constructed BP model with 19 hidden nodes. Compared with the stiffness model, the simulation and numerical results validate that BP model can achieve millisecond level computation time and micron level calculation accuracy. The concept and approach outlined can be extended to a variety of applications.

Flexure Parallel Mechanism: Configuration and Performance Improvement of a Compact Acceleration Sensor

This research presents a tridimensional acceleration sensor based on flexure parallel mechanism (FPM). Three perpendicular compliant limbs with compact monolithic structure are developed to serve as the elastic component for acquiring the inertial signals in each direction. With integrated flexure hinges, each chain containing multiple revolute joints and cantilever beams are designed to carry compressive and tensile loads. First, the structure evolution and kinematics modeling are introduced, followed by the multispring modeling of the directional compliance for the flexure limb. Then, the comprehensive finite-element analysis (FEA) including the strain of the sensitive limbs, modal analysis for total deformation under different frequency is conducted. The compliances calculated by FEA and multispring model are compared. Finally, the dimensional optimization is implemented based on multipopulation genetic algorithm to obtain the optimal flexure parameters. The proposed methods and algorithms are also useful for the analysis and development of other flexure parallel mechanisms.

Development of a Three-Degree-of-Freedom Parallel Workpiece Table for Ceramic Grinding

The grinding precision and the surface characteristics of the engineering ceramic are hard to control because of the hardness and brittleness. In order to grind the engineering ceramic under ductile mode, it is necessary to reduce the displacement of the grinding machine for the limitation of its stiffness to keep the grinding parameters in micro scale. A three-degree-of-freedom parallel workpiece table for ceramic grinding is developed to compensate the deformation of grinding machine caused by grinding force during grinding process. Based on the principle of negative stiffness, the workpiece table can generate a displacement which is reverse to the loading direction to compensate the deformation of the grinding machine. The developed precise workpiece table is a three degree of freedom negative stiffness controllable parallel mechanism composed of three piezoelectric actuators and a flexible parallel mechanism. Then the characteristics, such as kinematics and workspace, of the workpiece table are studied.

A unified approach to type synthesis of both rigid and flexure parallel mechanisms

Type synthesis of both rigid and compliant parallel mechanisms has become a hot issue in the field of mechanisms and robotics research in recent years. A unified approach to type synthesis of the two classes of mechanisms, however, has not been referred and investigated up to date. Based on the state-of-art analysis for several major type synthesis approaches related to rigid and compliant mechanisms, respectively, it proves feasible to establish a unified methodology for type synthesis of these two classes of mechanisms. That is a synthesis philosophy in terms of the hierarchy mapping between mathematic, physical, and mechanical building blocks in the framework of screw theory, as addressed in this paper. The key point of the proposed method lies in establishing the mapping among three different building blocks (i.e. geometric building block, kinematic or constraint building block, and mechanical building block). As a result, it makes the whole type synthesis process simple and visible. By using the proposed method, two examples are taken to verify the effectiveness for the type synthesis of both rigid and flexure mechanisms. The content of this paper may provide a theoretical frame for constructing a visualized algorithm or software about the unified type synthesis (or conceptual design) of both rigid and flexure parallel mechanisms.

Type Synthesis and Principal Freedom Analysis of Parallel Flexure Mechanisms Based on Screw Theory

With the development of precision engineering,flexure mechanisms are more and more applied in many fields.The increasing of application requirements call for development of a variety of flexure mechanisms,especially high performance ones.Under the direction of screw theory,a graphic configuration synthesis method based on the complementary rule of freedom and constraint is proposed to synthesize parallel flexure mechanisms.This method is visual and has a definite physical meaning.The synthesis chart of 2R1T and 3R parallel flexure mechanisms is presented as an illustration.In order to verify the characteristic of freedom,a principal freedom analysis method aiming at the practical flexible constraint is also proposed.The analysis of a 2R1T parallel flexure mechanism is implemented,and the influence of structure parameters on the mechanism characteristic compliance is given through the analysis.

A New Design of a Submicropositioner Utilizing Electromagnetic Actuators and Flexure Mechanism

In this paper, a novel <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">XY</i> -dimensional submicropositioner, including mechanism, control, and analysis, is successfully presented. The design of the submicropositioner utilizes a monolithic parallel flexure mechanism with built-in electromagnetic actuators and optical sensors to achieve the object of 3-DOF precise motion. From the provided experimental results, there are several main goals that have been achieved in this paper: (1) to integrate the electromagnetic actuator and the parallel flexure mechanism for planar positioning system; (2) to establish the mathematical modeling; (3) to develop an advanced adaptive sliding-mode controller; and (4) to perform extensive experiments to test the realistic performance.

Implementation of a novel large moving range submicrometer positioner

A novel, compact and two degree-of-freedoms (DOF) submicrometer positioner with a large moving range is presented in this paper. The design of the positioner utilizes a monolithic parallel flexure mechanism with built-in electromagnetic actuators and eddy current sensors to achieve the precision 2-DOF motion. The travel range of the positioner is 1000 μm/5 mrad and which depend on the eddy current sensor’s range of measurement (ROM) and electromagnetic actuator’s effective length. The analytical model and its dynamics were analyzed and derived. The whole control architecture takes the measured configuration parameters and endeavors to control the positioner motion by regulating the currents in the electromagnetic actuators. To increase the compactness and stability of the positioner, a self-tuning adaptive (STA) controller was analyzed and proposed. From the experimental results, satisfactory performances of the system, including stiffness and precision, have been successfully demonstrated.