3-DOF Parallel Mechanism Research Articles

Design and experiment of a 3-DoF master device with a 2-DoF parallel mechanism for flexible ureteroscopy.

Traditional commercial master devices and specialied serial master devices meet insufficient workspace, low intuitiveness, low stiffness, and poor accuracy during master-slave mapping for robot-assisted flexible ureteroscopy (FURS). This paper presents a 3-DoF master device for FURS. A 2-DoF parallel mechanism was designed and utilised in the master device for higher stiffness based on requirements analysis. A Back Propagation Neural Network was built for the forward kinematics of the parallel mechanism during master-slave mapping. Analysis of mechanical characteristics was carried out for the usability of the master device. A contrast experiment on the phantom was conducted to evaluate the performance between the proposed master device and a previous one. The completion time for each trial of the proposed master devices is shorter than that of the previous master serial device. Meanwhile, the proposed device provides a more comfortable operating style than the previous one. The proposed 3-DoF configuration for the master device is with more intuitive performance. A better comfort level indicates its usability in clinical applications.

Design of a 2T1R-Type Parallel Mechanism: Performance Analysis and Size Optimization

The planar three-degree-of-freedom (DoF) parallel mechanism plays a significant role in the fields of automobiles and electronics due to its advantages such as high stiffness, large carrying capability, and stable operation. In this paper, a planar 3-DoF (2T1R) parallel mechanism is derived by structural evolution from the parallelogram by means of Grassmann line geometry and the Atlas method. First, the position equation of the mechanism is established and the inverse kinematics and Jacobian matrix are investigated. The maximum deviation between the theory and simulation results of the inverse kinematics and Jacobian matrix is 0.48%, which verifies the accuracy of the theoretical model. Then, the constraint conditions of the mechanism are defined. Based on the inverse position solution, the numerical method is used to solve the workspace of the mechanism. It is concluded that the ratio of the workspace to the entire triangular space is about 15% higher than that of the 3-PRR parallel mechanism. Next, based on the Jacobian matrix, the performance indexes are established to evaluate stiffness and dexterity. Finally, the size of the mechanism is optimized by means of the genetic algorithm to improve the comprehensive performance.

Inverse Dynamics of A 3-DOF Parallel Mechanism Based on Analytical Forward Kinematics

For the development of a parallel mechanism (PM), it is necessary to establish a dynamic model which can accurately meet the requirements of real-time control. Compared with the general dynamic analysis model based on the inverse kinematics, the dynamic analysis model based on the forward kinematics has the advantage of low-complexity. In this paper, a new type of 3-DOF PM with analytical forward displacement analysis is proposed. Different from the general dynamic analysis based on the inverse kinematics, the displacement, velocity and acceleration equations of the PM are established and solved by forward kinematics. The inverse dynamic equation of the PM is constructed and solved by analyzing the forces on each link and based on Newton-Euler method. Then the theoretical results of an example are compared with the simulation results, which shows that the simulation results are basically consistent with the theoretical results. And the maximum error of the driving force of each pair is 1.32%, 5.8% and 5.2%, respectively, which verifies the correctness of the dynamic model. The PM has a potential application prospect in the grasping, spraying and picking of workpieces. The research results of this paper provide a theoretical basis for the design, manufacture and application of the PM.

Stiffness analysis of a 3-DOF parallel mechanism for engineering special machining

Abstract. There are considerably rigorous requirements for accuracy and stability of the mechanism to accomplish large-scale and complex surface machining tasks in the aerospace field. In order to improve the stiffness performance of the parallel mechanism, this paper proposes a novel three degrees of freedom (DOF) redundantly actuated 2RPU-2SPR (where R, P, U and S stand for revolute, prismatic, universal and spherical joints, respectively) parallel mechanism. Firstly, the kinematics position inverse solution is derived and a dimensionless generalized Jacobian matrix is established through the driving Jacobian matrix and constraint Jacobian matrix. Secondly, the stiffness model of the parallel mechanism is deduced and the accuracy of the stiffness model is verified through finite-element analysis. Using eigenscrew decomposition to illustrate the physical interpretation of the stiffness matrix, the stiffness matrix is equivalent to six simple screw springs. Finally, the simulation experiment results demonstrate that redundantly actuated parallel mechanism has better stiffness performance compared to the traditional 2RPU-SPR parallel mechanism.

Posture Evaluation Based on Forward Kinematics and Inverse Kinematics of Parallel Link Type Machine Tool

Parallel mechanisms with multiple links have been expected to be used in machining because they are higher in rigidity, accuracy, and output power than series mechanisms, such as industrial robots. However, unlike conventional machine tools, which consist of linear and rotary axes, parallel mechanisms have a large number of error factors. In the parallel link mechanism, there is no guide surface that physically guarantees linearity, and all accuracy is determined by the operating performance of the composite axes. This makes it difficult to identify any error factors. Therefore, a kinematics model is devised, and the behavior of the tool tip is checked by inputting the encoder information during the actual operation of a specific axis. Based on the results, we evaluate the machining characteristics of the target machine tool. The target machine tool in this study is a 5-axis machine tool that combines a 3-DOF parallel mechanism consisting of three linear motion axes and a 2-DOF serial mechanism consisting of two rotary axes. In our previous research, we tried to build a forward kinematics model. Although its prediction accuracy was insufficient, it was possible to actually identify the cause of the defect in the quality of the machined surface using the servo position information of the kinematics machine. However, we have not been able to construct an inverse kinematics model that is suitable for calculating the correction position command value to improve the quality of the machined surface. In this study, based on the shape creation theory, we devise and evaluate the kinematics model of a robotic machine tool that has a parallel mechanism. As a result of comparing the kinematics model with the 3D-CAD model in order to evaluate the accuracy of the former, it was confirmed that the proposed method has high simulation accuracy. Then, machining tests were carried out to evaluate the machining accuracy by measuring, based on proposed kinematics model, the machined surfaces in order to identify the mechanism that affects the texture of the machined surface. In addition, we performed a circle interpolation to confirm the effects of reversing the motion of each drive axis on the behavior of the tool tip. As a result, it is considered that the linear motion axis has a large effect on the behavior of the tool tip on the quadrant glitch of each drive axis. It was also found that the effects of the 1st- and 3rd-axes on the behavior of the tool tip are different from those of the 2nd-axis.

Cross coupling effects of modal space decoupling control for six degree of freedom 6-DOF parallel mechanism (6 DOF PM)

This study presented the performance of an alternative and effective control strategy through a decoupled controller by an input and an output transformation matrix, such that each Degrees of Freedom can be tuned independently with their bandwidth raised near to the eigenfrequencies. The simulation results of the Modal Space Decoupled Controller were analyzed in Matlab/Simulink environment and comparison made between the conventional PID controllers based on cross coupling effects. The results indicate that the conventional joint space conforms to the theoretical analysis when the compensation for the coupling effects was not considered. The results further showed that the Modal Space Decoupled Controller modified the dynamics characteristics, which can be attributed to reduction in the coupling effects between degrees of freedom motions.

Kinematics of a 5-axis hybrid robot near singular configurations

• A method based on kinematics modification for singularity avoidance is proposed. • A criterion for choosing the appropriate inverse kinematic solution is presented. • A semi-analytical algorithm for forward kinematic analysis is developed. • An algorithm is developed by modifying C -axis instructions. • Both simulations and experiments are carried out to verify the proposed approach. This paper proposes a method for non-singular tool path generation based on inverse kinematics modification in joint space to deal with the singularity problem of a 5-axis hybrid robot in machining process. Firstly, a criterion for choosing the appropriate solution of inverse displacement analysis is presented, that enables the avoidance of mechanical interference and enlargement of the task workspace. As a counterpart of inverse displacement analysis, a semi-analytical algorithm for forward displacement analysis is developed with high computational efficiency. These works lay a comprehensive and solid foundation for motion control and tool path simulation of the hybrid robot. Then, it reveals that at a singular configuration that varies with the system configurations, sudden changes occur in both rotation of the C -axis of the 2-DOF wrist and lengths of three telescopic legs within the 3-DOF parallel mechanism. This finding leads to an effective method for non-singular tool path planning by directly modifying the C -axis commands in the joint space using linear interpolation technique. Finally, both simulation and experimental results on a prototype machine show that in the neighborhood of singularity, continuous and smooth joint motions and acceptable tracking accuracy can be ensured after the modification.

Design, development, and clinical validation of a two degrees of freedom compliant ankle-foot prosthesis based on a 4-4r parallel mechanism

Compared with active prostheses, passive compliant ankle prostheses offer the advantages of reduced energy consumption, a lighter weight, a simple structure, and lower costs. However, although various commercial products are available, these designs do not provide adequate degrees of freedom (DOFs) for movement. This paper presents a compliant passive ankle–foot prosthesis (CPAF) capable of 2-DOF rotation during locomotion. The CPAF uses a 2-DOF parallel mechanism to support the bodyweight and offer limited rotation during movement, and it incorporates a compliant component to facilitate and generate torque to conform to uneven terrains. The kinematics of the parallel mechanism, including the workspace and singularities, were investigated. Then, a prototype was developed, and the performance evaluations showed that sufficient torque could be generated with an appropriate range of motion for the ankle. Concequently, clinical validations were conducted: the dynamic analysis indicated that the CPAF provided good gait movement and generated sufficient ankle torque during level-ground walking, and the metabolic tests demonstrated that the configuration-4 of the compliant component could achieve the best efficiency during walking.

4自由度球面パラレルリンク機構を有する脚部の機構解析

We have designed and built a leg named “MELEW-2LR” with a 4-DoF spherical parallel link mechanism, in order to develop a highly maneuverable 4-legged wheeled robot with active wheels mounted on the tip of the leg-type robot. This paper describes the mechanical analysis of the 4-DoF parallel link mechanism of the MELEW-2LR. In this paper, the leg mechanism of MELEW-2LR is examined and the features and DoF analysis of the designed parallel link mechanism are reported. The derivation of analytical solutions for the forward and inverse kinematics of MELEW-2LR and the range of motion of MELEW-2LR are also presented. Finally, the validity of inverse kinematics of MELEW-2LR is confirmed by conducting motion experiments in which the translational motion of the tip of its leg in the forward-backward, left-right, and vertical directions and the rotational motion of its yaw angle are controlled by inverse kinematics.

Dynamic Modeling and Solution of 6-DOF Parallel Mechanism

When a parallel robot used in a scene that requires force control, rapid attitude adjustment, or precise positioning, we need to know the dynamic characteristics of the moving platform and the motion branch, so it is necessary to do the dynamic analysis of the parallel robot. In this study, for the six-degree-of-freedom parallel mechanism, the Newton-Eulerian method is used to model the dynamics, and then the inverse dynamics simulation is performed through the ADAMS simulation software to verify the correctness of the established dynamic equations. Finally, the Euler integration method is used to solve the dynamic equations numerically. When establishing dynamic equations, it is more convenient to use spiral coordinates to express the angular motion of the motion platform of the parallel mechanism. However, it is difficult to solve the equation numerically. When solving the equations in this study, Euler angles are used to express angular motion. The Euler angle is used as an iterative variable representing the angular motion in the solving process. Then the Euler angle is converted into a rotation matrix, and the parameters of the spiral coordinates are obtained through the rotation matrix, and the dynamic equation is finally solved. The simulation and calculation results show that the established dynamic equation is correct, and the solution to the dynamic equation is also correct.

Kinematic Analysis and Verification of a New 5-DOF Parallel Mechanism

This paper first designs a new 5-DOF parallel mechanism with 5PUS-UPU, and then analyses its DOF by traditional Grubler–Kutzbach and motion spiral theory. It theoretically shows that the mechanism meets the requirement of five dimensions of freedoms including three-dimensional movement and two-dimensional rotation. Based on this, the real mechanism is built, but unfortunately it is found unstable in some positions. Grassmann line geometry method is applied to analyze its unstable problem caused by singular posture, and then an improving method is put forward to solve it. With the improved mechanism, closed loop vector method is employed to establish the inverse position equation of the parallel mechanism, and kinematics analysis is carried out to get the mapping relationships between position, speed, and acceleration of moving and fixed platform. Monte Carlo method is used to analyze the workspace of the mechanism, to explore the influencing factors of workspace, and then to get the better workspace. Finally, an experiment is designed to verify the mechanism working performance.

Parametric Vibration Analysis of a Six-Degree-of-Freedom Electro-Hydraulic Stewart Platform

Electro-hydraulic Stewart 6-DOF platform is a 6-DOF parallel mechanism combined with the electro-hydraulic servo control system, which is widely used in the field of construction machinery. In actual working conditions, the flow and pressure pulsation of the hydraulic oil output from the hydraulic leg of the electro-hydraulic Stewart platform are inevitable, so the equivalent stiffness of the platform leg will change, and the stiffness parameters of the transmission system will change, resulting in vibration, which will affect the accuracy of the platform. This paper considering the fluid unit equivalent stiffness cyclical fluctuations and leg, on the basis of the relationship between hydraulic stiffness, constructs the electric hydraulic Stewart platform machine vibration dynamics equation, fluid coupling parameters of vibration parameters using the method of the multiscale approximate analytic formula of the main resonance and combination resonance are derived, and the system parameters vibration time-domain response and frequency response under two different poses are discussed. Results show that the system first to six order natural frequency and the first to the sixth order natural frequency and frequency of hydraulic oil equivalent stiffness of the combination of frequency will have an effect on the parameters of the system vibration. In the main resonance, the dominant frequency is mainly the first to sixth order natural frequency of the system; in the combined resonance, the dominant frequency is the combined frequency. Through the parameter vibration analysis of two different positions of the platform, it is concluded that when the platform is in an asymmetric position, each leg of the system is more involved in vibration. This study can provide the reference for the subsequent dynamic optimization and reliability analysis of the electro-hydraulic Stewart platform.

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.

Design, Dynamic Analysis, and Experimental Evaluation of a Hybrid Parallel–Serial Polishing Machine With Decoupled Motions

Abstract In this paper, a novel six degrees-of-freedom (DOF) hybrid kinematic machine (HKM) is designed, analyzed, and evaluated for precision polishing. The design adopts a 3-DOF tripod-based parallel mechanism (PM) to locate the workpiece, a 2-DOF serial mechanism (SM) to orient the polishing tool, and a functional extension limb to provide a redundant DOF when polishing the workpieces with axially symmetrical shapes. Compared with the existing HKMs, the most distinctive feature is that the position and orientation adjustments of the tool with respect to the workpiece are decoupled during the synchronous machining, thus allowing the rotational tool center point (RTCP) function to be conveniently realized. For the developed HKM, the kinematics are studied systematically, including position, velocity, acceleration, and workspace. The dynamic model of the PM is derived by employing the principle of virtual work. For a pre-defined trajectory, the required driving forces are obtained through dynamic simulation. Based on these analyses, a laboratory prototype of the HKM is designed and developed. A preliminary accuracy assessment of the HKM is implemented with a double ball-bar, and a series of polishing experiments are conducted to show the capacity and feasibility of the developed HKM.

Development of 6 DOF Displacement Sensor Using RUS Parallel Mechanism.

Nowadays, many types of manipulators have been developed and used in lots of production processes. Force-based control methods or additional mechanical devices called Remote Center Compliance (RCC) have increased the system’s compliance and accuracy. However, the force-based control method’s operating speed is low, and the RCC cannot measure deflection. Thus it cannot calculate the position of the end-effector accurately. For accurate force and position control, it is necessary to measure the deflection of the RCC and to perform this, a different type of device than the existing RCC is required. This paper presents the necessity and possibility of developing an RCC capable of measuring the displacement of the end-effector and showing the displacement sensor’s feasibility using a 6 DOF parallel mechanism. In particular, we suggest that it is possible to make devices cheaper and more compact by using angular displacement sensors. Finally, we show the possibility of use in actual industrial sites through peg-in-hole simulation using the device.

Kinematic and dynamic analysis of a 3-DOF parallel mechanism

Kinematic and dynamic analysis of a 3-DOF parallel mechanism

Design and Analysis of an Intelligent Toilet Wheelchair Based on Planar 2DOF Parallel Mechanism with Coupling Branch Chains.

Due to the fixed size of the structure or the possibility of only simple manual adjustment, the traditional toilet wheelchair cannot easily be adapted to the size of the user or the toilet. In this paper, a planar two-degree-of-freedom parallel mechanism with coupling branch chains is proposed to enable both seat height adjustment and body posture adjustment of a toilet chair, solving the problems of posture adaptability between the user and the machine, and height matching in the process of using the wheelchair-assisted toilet. The model of the parallel mechanism was designed after analyzing the general rules of posture transformation in the human body before and after the toilet process, and the dimensions of each linkage were then determined according to the constraint conditions. By analyzing the degree of freedom, kinematics, workspace, singularity and position of the center of gravity, the rationality of the design was ensured. The weighted average function was used to find the optimal fixed point of the horizontal moving slider, and the actual trajectory at the end of the single driving mode was close to the ideal trajectory. The experimental results show that the adjustable seat height range is 290~550 mm and the adjustable angle range is 0~90°, which can enable disabled people to use the toilet independently.

Type synthesis of plane-symmetric deployable grasping parallel mechanisms using constraint force parallelogram law

Type synthesis methods of parallel mechanisms or metamorphic mechanisms have drawn rising interest for mechanism designers. However, existing synthesis approaches cannot synthesize both parallel mechanisms and metamorphic mechanisms. This paper develops a synthesis method of metamorphic mechanisms, which enables it to construct a family of 2-degree-of-freedom (DOF) deployable grasping parallel mechanisms. Namely, the originality of this paper is that it explores a common synthesis method for both parallel mechanisms and metamorphic mechanisms. First, a new type of grasping sub-mechanisms is designed. Then, a kinematic sub-chain is constructed after assembly of a base, a platform, and the grasping sub-mechanism, whose constraint-screw system is obtained using reciprocal screw theory. This constraint-screw system is further applied to derive the desired constraints of auxiliary sub-mechanisms using the constraint force parallelogram law. Subsequently, auxiliary sub-mechanisms are type synthesized based on such desired constraints. Finally, a class of parallel mechanisms is constructed by assembling the auxiliary and the kinematic sub-chain. Thus, this paper and related work generate fresh insight into synthesizing both single-DOF metamorphic mechanisms and 2-DOF parallel mechanisms.

Rigid-Flexible Modal Analysis of the Hydraulic 6-DOF Parallel Mechanism

In view of the problems encountered in previous hydraulic 6-DOF parallel mechanism projects, flexible modes appear that the actual natural frequencies of x and y degrees of freedom of the parallel mechanism are lower than those obtained through calculation. The phenomenon above not only decreases the dynamic response characteristics of the mechanism, but also leads to doubts about the actual performance of the mechanism. The real reason for the phenomenon above is solved in this paper. First the flexible structure of the hydraulic cylinder is analyzed and simplified, and then the dynamic model of the rigid-flexible 6-DOF parallel mechanism is established with the extended Hamilton’s principle. Finally the rigid-flexible modes are calculated with the dynamic model obtained, further analysis and verification with a simulation model and an experimental platform are also conducted. Results show that the phenomenon of the flexible modes is mainly caused by the O-rings of the step-seals of the guide sleeve and those with less elasticity should be adopted to keep the dynamic characteristics of the parallel mechanism.

Re-Design and cost reduction in fabrication of a novel 3 DoF active ankle joint

The mechanism of active ankle is a novel 3 DoF parallel mechanism that operates in an almost spherical manner. It is a project by DFKI Germany and currently it is being used in medical rehabilitation. The project was re-engineered with techniques like CAD and Rapid-Prototyping to reduce the cost of fabrication. In the present paper, a comprehensive study of the design, and fabrication of the active ankle is provided. Various motions of human ankle joint such as adduction-abduction, inversion-eversion, and plantarflexion-dorsiilexion, was achieved by the prototype. This project was modeled in CAD software like SolidWorks, accordingly mounting were prepared for the available motors. Various parts of Active Ankle prototype was printed using Olivetti 3D printer by feeding the .gcode file created by slicing software Cura. The paper also discuss about the integration of Dynamixel motors with MATLAB for control. Finally, the paper talks about various application of parallel manipulator in the area of medical rehabilitation.