Degrees Of Freedom Parallel Mechanism Research Articles

Kinematics and Dynamics Analysis of a 3UPS-UPU-S Parallel Mechanism

In this paper, a two-rotational degrees of freedom parallel mechanism with five kinematic subchains (3UPS-UPU-S) (U, P, and S stand for universal joints, prismatic joints, and spherical joints) for an aerospace product is introduced, and its kinematic and dynamic characteristics are subsequently analyzed. The kinematic and dynamic analyses of this mechanism are carried out in screw coordinates. Firstly, the inverse kinematics is performed through the kinematic equations established by the velocity screws of each joint to obtain the position, posture, and velocity of each joint within the mechanism. Then, a dynamic modeling method with screw theory for multi-body systems is proposed. In this method, the momentum screws are established by the momentum and moment of momentum according to the fundamentals of screws. By using the kinematic parameters of joints, the dynamic analysis can be carried out through the dynamic equations formed by momentum screws and force screws. This method unifies the kinematic and dynamic analyses by expressing all parameters in screw form. The approach can be employed in the development of computational dynamics because of its simplified and straightforward analysis procedure and its high adaptability for different kinds of multi-body systems.

Dynamic modeling and vibration characteristics analysis of parallel antenna

Abstract. Research on the vibration characteristics of the mechanical systems is a necessary step for the stable and reliable operation of high-end equipment. The 6 degrees of freedom parallel mechanism is proposed for the supporting mechanism of the antenna. First, the dynamic equations of the moving platform and branch of the mechanism are established. The closed-form dynamics of the mechanism are derived based on the Newton–Euler method. In addition, the vibration equation of the parallel antenna is established based on the vibration theory, and the relationship between the natural frequency, displacement response, and vibration frequency is obtained. Afterward, the pitch and roll poses of a 1.8 m aperture antenna are developed based on a MATLAB software simulation. The actuation forces of parallel antenna under no-load and load conditions are simulated. Finally, the natural frequencies and vibration modes of the initial position and roll (20∘) are simulated based on the Adams software vibration analysis module. Furthermore, the relationship between the displacement response of the moving platform and the resonant frequency is studied based on the harmonic response analysis. The control strategy based on the dynamic model improves the control accuracy of parallel antenna. This research work provides a guarantee for the dynamic characteristics analysis and engineering application of parallel antenna.

Singularity analysis of a kinematically redundant (6+2)-DOF parallel mechanism for general configurations

Parallel mechanisms suffer from type II singularities which reduce their useful orientational workspace. Adding kinematic redundancy in parallel mechanisms enhances their orientational workspace by providing singularity avoidance capabilities. However, an increasing number of kinematically redundant degrees of freedom (DOFs) requires additional actuators and makes the redundancy resolution more complex. Moreover, examples in the literature exist where a minimal number of kinematically redundant DOFs was used to produce a singularity-free orientational workspace for planar mechanisms. In this work, the architecture of a kinematically redundant (6+2)-DOF parallel mechanism akin to the well-known Gough–Stewart platform is studied, and its singularity locus is derived. The results show that, while some singularities still remain in the useful workspace of the mechanism, they can be accurately localized with simple closed-form analytical expressions for trajectory planning purposes. Furthermore, the redundancy resolution may find itself easy to handle, since the avoidable singularities and mechanical interference can be mapped into the 2-D space of the redundant parameters. Finally, the proposed architecture is considered as a compromise between obtaining a singularity-free workspace and handling easily the redundancy resolution for the trajectory planning.

Trajectory tracking performance of modal space decoupled controller for six Degree of Freedom parallel mechanism (6 DOF pm)

Trajectory tracking performance of modal space decoupled controller for six Degree of Freedom parallel mechanism (6 DOF pm)

Trajectory tracking performance of modal space decoupled controller for six Degree of Freedom parallel mechanism (6 DOF pm)

The paper presented the trajectory performance of the Modal Space Decoupled Controller (MSDC) and the conventional joint space controller. Phase retarding and amplitude fading were chosen to evaluate how well the modal space decoupling controller can follow a trajectory. The responses of sinusoidal inputs along six directions surge, sway, heave, roll, pitch, and yaw were given. The result indicates that the modal space decoupling controller has better tracking performance when compared to conventional PID controller. For the conventional joint space controller (CJS), the phase retarding for the linear and angular motions motion attains maximum value at 40.90º and 23.98º respectively. The maximum phase retarding is at 22.84º in linear motions and 0.975º in angular motions for the modal space decoupling controller. The amplitude of the conventional controller fades at 0.54dB in linear motions and 0.47dB in angular motions, while for the modal space decoupling controller, the amplitude fades at 0.1696dB in linear motions and 0.082dB in angular motions. Subjecting the two controllers to the tracking of a desired circular combined motion of surge and sway, the predefined circular trajectory was well tracked much more by the proposed MSDC than the CJS.

Optimal design and trajectory tracking experiment of a novel 3-DOF parallel antenna mechanism

The tracking range and pointing performance of the antenna are important indices to measure the antenna system. First, the 3 degree of freedom parallel mechanism is proposed for the supporting mechanism of the antenna. The trajectory tracking principle of the antenna mechanism is analyzed based on the inverse position solution model. Meanwhile, the kinematic model of the antenna mechanism with a specific motion trajectory is derived. In addition, the structural optimization design is demonstrated based on the actuation torques and motion range index. In addition, the trajectory planning research is carried out according to the trajectory tracking requirements. The trajectory planning simulation is carried out in the joint space. Afterward, the antenna motion range is obtained through simulation. The specific trajectory tracking simulation of the antenna is completed. Furthermore, the pitch and azimuth motion performance experiments are carried out based on the developed antenna mechanism prototype. Finally, the pentagram trajectory tracking performance is verified via experiments. This research serves as a reference for designing and engineering application of the antenna.

Singularity analysis of a kinematically redundant (6+2)-DOF parallel mechanism for zero-torsion configurations

The orientational workspace of parallel mechanisms is known to be restricted due to singular configurations of type II. Recently, a (6+3)-degree-of-freedom (DOF) kinematically redundant parallel mechanism was proposed based on the well-known Gough–Stewart platform. It was shown that, for the specific architecture proposed, a minimum of three redundant DOFs is necessary to guarantee the existence of a non-singular configuration for any pose of the platform. This work presents a different architecture with two redundant DOFs instead of three, and has for primary objective to derive the singularity locus for zero-torsion configurations. The results indicate that the mathematically possible singularities are outside of the reachable workspace, suggesting that for zero-torsion trajectories, two kinematically redundant DOFs are sufficient to greatly enhance the orientational workspace of the proposed architecture. An example path with large tilting angle is presented in a multimedia extension of the article in order to demonstrate the capability of the mechanism to reach such orientations without encountering inevitable singularities.

Optimal 5R parallel leg design for quadruped robot gait cycle

This paper presents the design of optimal dimensions for a two degrees of freedom parallel mechanism used in quadruped for walking application. Serial linkages or open link mechanisms have less stiffness and poor dynamic performance, thus parallel mechanisms were developed. Many researchers have used symmetrical parallel leg for quadruped walking but force requirements are different in forward and return stroke, thus unsymmetrical parallel leg may be optimal. Using genetic algorithm, optimum link length values are obtained and the corresponding peak torque is also found.

Enumeration and optimum design of a class of translational parallel mechanisms with prismatic and parallelogram joints

Spatial joints (Hooke and spherical joint) generally limit parallel manipulator's motion range and performance, while higher performance will be achieved when applying more planar pairs (prismatic and revolute joint), which can promise small movement constraints and high stiffness. In this paper, a novel design method for three translational degrees of freedom parallel mechanisms containing prismatic joints and parallelogram units ((R-R)2 linkage) is proposed by mapping relationship with augmented matrices of upper triangular matrix. All these mechanisms can be assembled quickly with modular parts and most of which are partially decoupled. In this study, one of these proposed structures is taken as an example for developing a redundant manipulator. Based on vector-loop equations, its position model is derived and the singular configurations are investigated. Kinematic and static performance of this architecture are conducted, as well as the multi-objective optimization is implemented using Genetic Algorithm.

An Underwater Vector Propulsion Device Based on the RS+2PRS Parallel Mechanism and Its Attitude Control Algorithm

In order to overcome the disadvantages of some existing autonomous underwater vehicles (AUVs), such as actuator extraposition and degree-of-freedom (DOF) redundancy, a 2-DOF vector propeller propulsion system with built-in actuator based on the deficient DOF parallel mechanism is proposed. The RS+2PRS (Revolute-Spherical+ Prismatic-Revolute-Spherical) parallel mechanism is used as the main structure, and the driving parts are placed in the interior of the AUV cabin, which is beneficial to the sealing and protection of the propulsion system. In addition, the motion parameters decoupling shows that the two independent parameters are the precession angle and the nutation angle of the propeller installation platform. Therefore, the attitude control algorithm uses two prismatic joints as driving units to establish the nonlinear mapping model with the two Euler attitude angles. In the end, the simulation analysis and the real device are used to verify the feasibility of the attitude control algorithm and the in situ adjustment function of the propeller, which lays the theoretical foundation for engineering applications in the future.

Body-mounted robotic assistant for MRI-guided low back pain injection.

This paper presents the development of a body-mounted robotic assistant for magnetic resonance imaging (MRI)-guided low back pain injection. Our goal was to eliminate the radiation exposure of traditional X-ray guided procedures while enabling the exquisite image quality available under MRI. The robot is designed with a compact and lightweight profile that can be mounted directly on the patient's lower back via straps, thus minimizing the effect of patient motion by moving along with the patient. The robot was built with MR-conditional materials and actuated with piezoelectric motors so it can operate inside the MRI scanner bore during imaging and therefore streamline the clinical workflow by utilizing intraoperative MR images. The robot is designed with a four degrees of freedom parallel mechanism, stacking two identical Cartesian stages, to align the needle under intraoperative MRI-guidance. The system targeting accuracy was first evaluated in free space with an optical tracking system, and further assessed with a phantom study under live MRI-guidance. Qualitative imaging quality evaluation was performed on a human volunteer to assess the image quality degradation caused by the robotic assistant. Free space positioning accuracy study demonstrated that the mean error of the tip position to be [Formula: see text] mm and needle angle to be [Formula: see text]. MRI-guided phantom study indicated the mean errors of the target to be [Formula: see text] mm, entry point to be [Formula: see text] mm, and needle angle to be [Formula: see text]. Qualitative imaging quality evaluation validated that the image degradation caused by the robotic assistant in the lumbar spine anatomy is negligible. The study demonstrates that the proposed body-mounted robotic system is able to perform MRI-guided low back injection in a phantom study with sufficient accuracy and with minimal visible image degradation that should not affect the procedure.

Input Rationality Analysis of Three Degree of freedom Parallel Mechanism with Limbs of Embedding Structures

Abstract. Three degrees of freedom (3-DoF) parallel mechanism (PM) with limbs of embedding structures is a kind of PM with a coupling relationship between limbs. In order to obtain a more desirable motion, the analysis of its actuated pairs shall be conducted. However, the fact that the existence of limbs coupling results in non-unique limb group, this mechanism has multiple limb groups. In this regard, the traditional input selection theory is not suitable for direct application in the input rationality analysis. Aiming to avoid this, a general extended input selection theory and limb group selection rule are proposed. The former tackles the traditional input selection theory which is not suitable for analyzing the input of PM with limbs of embedding structures since it does not take the influence of group into consideration, whereas the latter makes the calculation of the former easier. Based on the extended input selection theory and the limb group selection rule, the input and configuration of the 3-DoF PM with limbs of embedding structures are improved.

Contouring control of a 3-[P2(US)] parallel manipulator

Graphical

A novel decoupled parallel mechanism with two translational and one rotational degree of freedom and its performance indices analysis

Less degrees of freedom parallel mechanism is widely used in many fields with its unique advantages. A decoupled parallel mechanism with 2 degree-of-freedom translation and 1 degree-of-freedom rotation is presented, and its performance evaluation indices analysis is performed. By the constraint screw method, the motion feature of the mechanism and its number of degree of freedom are analyzed. The constrained equations of the mechanism are established according to the constrained conditions of the pole length. The analytical expression of the forward and inverse position for the mechanism is deduced, and the expression of the Jacobian matrix is derived, which validated the decoupling feature of the mechanism. The singularity of the mechanism is also carried out. The performance evaluation indices for the decoupled parallel mechanism are discussed and the corresponding performance indices analysis of the proposed decoupled parallel mechanism is executed. The novel decoupled parallel mechanism presented herein enriches the parallel mechanism structure, and the definition and analysis of the performance evaluation indices should be meaningful for the further design and optimization of the decoupled parallel mechanism.

Kinematic Analysis of 4-UPU Parallel Mechanism Based on Influence Coefficient

Mechanism kinematic influence coefficient deeply reflects the essence of the kinematics and dynamics mechanism, analysis of the problems of many institutions can use the influence coefficient of clear and clearly expressed. In this paper, with less degree of freedom parallel mechanism as the research object, through the virtual mechanism method to derive one or two order influence coefficient matrix, based on the analysis of the mechanism and influence of speed and acceleration coefficient matrix. Finally, the precision of the method for solving the kinematics is proved by examples of numerical analysis.

A serial of novel four degrees of freedom parallel mechanisms with large rotational workspace

SUMMARYIn this paper, a class of novel four Degrees of Freedom (DOF) non-overconstrained parallel mechanisms with large rotational workspace is presented based on screw theory. First, the conflict between the number of independent constraints applied on the moving platform and the number of kinematic limbs for 4-DOF non-overconstrained parallel mechanism is identified. To solve this conflict, the platform partition method is introduced, and two secondary platforms are employed in each of the parallel mechanisms. Then, the motion requirements of the secondary platforms are analyzed and all the possible kinematic chains are enumerated. The geometrical assembly conditions of all possible secondary limbs are analyzed and some typical non-overconstrained parallel mechanisms are generated. In each of the parallel mechanisms, a planetary gear train is used to connect both of the secondary platforms. The large rotational workspace of the moving platform is obtained due to the relative motion of the two secondary platforms. Finally, the kinematics analysis of a typical parallel mechanism is conducted.

Force/Motion Transmissibility Analysis of Six Degree of Freedom Parallel Mechanisms

Drawing mainly on the concepts of dual space and dual basis in linear algebra and on existing screw theory, this paper presents a novel and systematic approach for the force/motion transmissibility analysis of 6DOF parallel mechanisms. By taking the reciprocal product of a wrench on a twist as a linear functional, the property exhibited by the dual basis allows the formulation of the force/motion transmissibility between the joint space and operation space in an accurate and concise manner. The consistency between the force/motion transmissibility and the minimum singular value of the Jacobian for singularity identification is rigorously proved. This leads to the development of a set of homogeneously dimensionless local and global transmission indices for measuring the closeness to singular configurations as well as for kinematic performance evaluation over a given workspace. A Stewart platform is employed an exemplar to illustrate the effectiveness of the approach.

Design and kinematic analysis of redundantly actuated parallel mechanisms for ankle rehabilitation

SUMMARYIn this paper, we present the design of two serial spherical mechanisms to substitute for a single spherical joint that is usually used to connect the platform with the base in three degrees of freedom parallel mechanisms. According to the principle derived from the conceptual design, through using the two serial spherical mechanisms as the constraint limb, several redundantly actuated parallel mechanisms are proposed for ankle rehabilitation. The proposed parallel mechanisms all can perform the rotational movements of the ankle in three directions while at the same time the mechanism center of rotations can match the ankle axes of rotations compared with other multi-degree-of-freedom devices, due to the structural characteristics of the special constraint limb and platform. Two special parallel mechanisms are selected to analyze their kinematical performances, such as workspace, dexterity, singularity, and stiffness, based on the computed Jacobian. The results show that the proposed scheme of actuator redundancy can guarantee that the redundantly actuated parallel mechanisms have no singularity, better dexterity, and stiffness within the prescribed workspace in comparison with the corresponding non-redundant parallel mechanisms. In addition, the proposed mechanisms possess certain reconfigurable capacity based on control strategies or rehabilitation modes to obtain sound performance for completing ankle rehabilitation exercise.

Location Analysis and Simulation of one Kind 4D Stereoscopic Gaming Platform

The Institutions of 4D interactive three-dimensional game is essentially a three degree of freedom parallel mechanism. This papers start from introducing 3D of parallel structure, then analyzes a two-rotation a translation of the three degrees of freedom motion simulation platform, by changing the length of the three scalable support this platform achieves the specific position and orientation of the simulation platform. By the institutional characteristics, it deduces the inverse solution of the agency's position, then according to the anti-solution of their mathematical formulas, using MATLAB to simulate and analysis its trajectory, verifying the correctness and practicality of the agency model.

Dexterity Analysis of a 4-UPS-RPS Parallel Mechanism

A novel 4-UPS-RPS spatial 5 degrees of freedom parallel mechanism is introduced and its dexterity measures are analysed. The stationary platform of the parallel mechanism is connected with the moving platform by the same four UPS (universal joints-prismatic pairs-spherical joints) driving links and a RPS (revolute joints-prismatic pairs-spherical joints) link. The velocity Jacobian matrix and the force Jacobian matrix of the parallel mechanism are derived, and the dimensionless velocity Jacobian matrix is established. On this basis, the three dexterity measures, including average conditional number, the smallest singular value and operation, are obtained. According to these, the square mean dexterity coefficient, which is used to comprehensively evaluate the dexterity of various configurations, is proposed. In addition, the distribution of different dexterity measures above in the workspace is analysed respectively. This research can provide an important theoretical base for the dimensional synthesis and trajectory planning for a parallel mechanism.