3-PRS Parallel Mechanism Research Articles

Experimental investigations and error analysis on 3-PRS parallel kinematic machine

Industrial robots play a predominant role in factory automation particularly in the area of machining like grinding, cutting, milling, drilling, polishing etc. In these applications serial manipulators could not provide rigidity and accuracy. This research focuses on the need for precise angular drilling applications. Generally, special fixtures are used to make angular hole in drilling machines. In this research, the 3-PRS (Prismatic – Revolute – Spherical) parallel mechanism is redesigned to execute angular drilling operations. The moving/mobile platform (MP) of the proposed manipulator is utilized as worktable. The experimental model is fabricated with lead screw and nut pair to obtain precise position of drill tool and to maintain high stiffness. By varying the geometric parameters, the positions of parallel kinematic machine (PKM) are analysed. Moreover, the orientation error and parallelism of the developed PKM are studied in detail using laser torch and height gauge. Further, the PKM positions are simulated through ADAMS software package and the same is compared with the real-time accelerometer values. From the experimental study, the deviations in orientation, parallelism and position of the PKM are found to be minimal and satisfactory.

Development of Integrated Innovation Experiment Platform Based on 3- PRS Parallel Mechanism

Background: The parallel mechanism plays an important role in various fields. The multifunctional integrated innovation experiment platform can improve the utilization rate of the mechanism and be applied in many fields. Objective: The main objective of the study is to establish an integrated innovation experiment platform based on the 3-PRS parallel mechanism, which can be used in typical application and related technology development. Methods: The integrated innovation experiment platform is established and analyzed based on the 3-PRS parallel mechanism. According to the 3D model of the experiment platform, the kinematics and dynamics are analyzed. The force/position control strategy of the system is adopted. According to the function of the experiment platform, two kinds of application and the position and pose measurement technology are developed. The experiment platform is developed by the following methods: (1) The XY table is set up on the fixing platform of the 3-PRS parallel mechanism, so that the mechanism has five degrees of freedom, and the many kinds of workpiece can be easily processed. (2) By selecting the impedance parameter, the experiment platform can realize the compliant control of plantar flexion/dorsiflexion and varus/eversion simultaneously. (3) The binocular vision position and pose measurement method is used to obtain the marked images of the experiment platform through dual cameras, and the position and pose is obtained through image processing, 3D reconstruction and stereo matching, etc. (4) The position and pose detection based on deep learning is divided into two parts: one is to detect the slider height using the regression Convolutional Neural Network (CNN); the other is to compute the position and pose using the Back Propagation Neural Network (BPNN). Results: The experiment results show that the function of the 3-PRS parallel mechanism integrated innovation experiment platform can be effectively realized. The position and pose can be accurately measured in real time using the proposed two measurement methods. The impedance parameters are selected to achieve the rehabilitation training function of the 3-PRS ankle rehabilitation robot and the characters are processed to verify the function of the 3-PRS-XY series-parallel machine tool. Conclusion: The integrated innovation experiment platform based on the 3-PRS parallel mechanism can achieve the function of mechanical processing and rehabilitation training, and can also measure the state of motion in real time through machine vision and deep learning.

Error analysis and kinematic calibration of a new 3-PRS parallel mechanism

Taking a new 3-PRS parallel mechanism as the research object, error analysis and kinematics calibration are carried out. Combining with inverse kinematics, the parameter error of the mechanism is analyzed comprehensively. a calibration method of inverse kinematics based on structural parameters and genetic algorithm is proposed, and the error calibration model of 3-PRS parallel mechanism is deduced. The calculation by MATLAB shows that the reverse motion error calculated by nominal machine tool structural parameters is larger than that obtained by calibrated structural parameters. The position of the three cylindrical and spherical hinges after calibration is closer to the nominal position. It shows that the error calibration can correct the machine tool structure and guide the subsequent installation and debugging of the machine tool.

An iterative method for the inverse kinematics of lower-mobility parallel mechanism with three RS or SR chains based on kinematically equivalent mechanism

This paper presents an iterative method for solving the inverse kinematics (IK) of lower-mobility parallel mechanisms (LMPMs) with three RS or SR chains based on the kinematically equivalent mechanism (KEM). KEM is a virtual parallel mechanism with 6 DOF having the same motion as the original LMPM under the actuated joint motion constraints. The method enables us to solve the IK of such parallel mechanisms considering various structural parameters and different sets of output degrees of freedom (DOF) in a unified way, yet without formulating conventional constraint equations. As a demonstration, an iterative procedure for solving the IK of a 3-PRS parallel mechanism based on its KEMs is presented. Numerical examples show the process in solving the IK of the LMPMs considering different sets of output DOFs and various structural parameters using the proposed method.

Hardware-in-the-loop simulation for the contact dynamic process of flying objects in space

In the one-gravity environment on the ground, the simulation of the contact process of two flying objects in the zero-gravity environment of space has been a challenging issue since humans first explored space by flying objects. Hardware-in-the-loop (HIL) simulation is an important and effective method to test the usability, reliability, and safety of real docking mechanisms in space. There are four main issues for HIL simulation systems: Design of simulators capable of high frequency response, high motion precision, high velocity, and rapid acceleration; compensation for simulation distortion; design of a control model for the HIL simulation process; and experimental verification. Here, we propose a novel HIL simulator system with a 6-DOF 3-3 perpendicular parallel mechanism and a 3-DOF 3-PRS parallel mechanism; discover the principle of simulation distortion; present distortion compensation models for the force measurement system, dynamic response, and structural dynamics of the simulator; and provide a control model for the HIL simulation process. Two kinds of experiments were performed on the passive-undamped elastic rod and the docking mechanisms to test their performances and to verify the effectiveness and usability of the HIL simulator. The HIL simulation system proposed in this paper is useful for developing space docking, berthing, refueling, repairing, upgrading, transporting, and rescuing technologies.

Design and workspace analysis of a 3-degree-of-freedom parallel swivel head with large tilting capacity

Traditional parallel mechanisms are usually characterized by small tilting capability. To overcome this problem, a 3-degree-of-freedom parallel swivel head with large tilting capacity is proposed in this article. The proposed parallel swivel head, which is structurally developed from a conventional 3-PRS parallel mechanism, can achieve a large tilting capability by means of structural improvements. First, a modified spherical joint with a maximum tilting angle of ±120° is devised to diminish the physical restrictions on the orientation workspace. Second, a UPS typed leg is introduced for the sake of singularity elimination. The superiority of the proposed parallel swivel head is theoretically proved by investigations of singularity-free orientation workspace and then is experimentally validated using a prototype fabricated. The theoretical and experimental results illustrate that the proposed parallel swivel head has a large tilting capacity and thus can be used as swivel head for a hybrid machine tool which is designed to be capable of realizing both horizontal and vertical machining.

Dimensional Synthesis of 3PRS Parallel Mechanism Based on a Dimensionally Homogeneous Analytical Jacobian

Jacobian matrix plays a crucial role of kinematic synthesis of a parallel mechanism, however, can not directly be used for its nonhomogeneous physical units. This paper proposes the detailed formulation of the dimensionally homogeneous analytical Jacobian of 3PRS parallel mechanism. After defining a kinematic index and the design variables, the sensitivity that the index varies with dimension parameters is performed. Based on the two chosen case, it is also conducted that the index distributes in the prescribed workspace. Then, the kinematic characteristics of the system are discussed. These results provide the informative insight for choosing the optimal solution of the dimension parameters of 3PRS.

Design and Experimental Study of a 3-DOF Parallel Swivel Head

Traditional parallel mechanisms (PMs) are usually characterized by small tilting capability. To overcome this problem, a 3-DOF parallel swivel head (PSH) with large tilting capacity is proposed in this paper. The proposed PSH, which is structurally developed from a conventional 3-PRS parallel mechanism (PM), can achieve a large tilting capability by means of structural improvements. Firstly, a modified spherical joint with a maximum tilting angle of ±120o is devised to diminish the physical restrictions on the orientation workspace. Secondly, a UPS typed leg is introduced for the sake of singularity elimination. The superiority of the proposed PSH is theoretically proved by investigations of singularity-free orientation workspace and then is experimentally validated using a prototype fabricated. The theoretical and experimental results illustrate that the proposed PSH has a large tilting capacity and thus can be used as swivel head for a hybrid machine tool which is designed to be capable of realizing both horizontal and vertical machining.

Optimal design of 3-DOF PKM module for friction stir welding

Friction stir welding (FSW) has recently emerged as a solid-joining technology for high-strength aluminum alloys and light metal welding. The large axial force to be maintained between the welding tool and workpiece is the primary requirement of FSW process, which has also been a great obstacle to the design and application of FSW in manufacturing. Further complicating the issue is the need to perform FSW over three-dimensional contours, which requires a mechanism dexterous enough to set the stir pin used in welding to track a predefined trajectory with prescribed poses. Apart from the position specification, the design of a dexterous mechanism to pose the orientation of stir pin is a great challenge. This paper proposed the application of 3-PRS (P, R, and S standing for prismatic, revolute, and spherical joint, respectively) parallel mechanism as a welding tool head and employed it to form a five-axis welding machine tool for FSW. In order to accommodate the orientation capability requirements, the kinematic feature has been analyzed. With the dimensionless treatment of the Jacobian matrix of 3-PRS manipulator, a global condition index is proposed to estimate the kinematic dexterity in the whole orientation workspace. Finally, by means of an optimal design method and performance atlas, optimal designs of the 3-PRS parallel mechanism is carried out. A preferable set of optimized geometric parameters are obtained to achieve a compact and dexterous design, and the optimization results are used in development of a prototype machine for FSW.

一类平转耦合并联机构运动学性能的评价方法

The parallel mechanisms having mixed degrees-of-freedom (DoFs) of one translation and two rotations have been used in manufacturing the extra large structural aircraft components with complex geometries. This statement can be demonstrated practically by very successful applications of the Sprint Z3 head to aircraft industry. However, to evaluate the kinematic performance of these parallel mechanisms is a challenging issue because serious problems may occur due to dimensional inconsistencies of the Jacobian matrix. By taking a 3-PRS parallel mechanism as an example, this paper presents an approach to formulate a set of local dimensionless kinematic performance indices on the basis of the overall Jacobian developed by screw theory. The merits of these indices are that they can be represented by the instantaneous virtual power transmission ratios within one limb and amongst limbs, leading to the global ones represented by their mean values and standard deviations throughout the entire workspace. In-depth discussion is made via the example to illustrate the validity of these brand new indices. The outcome may provide with the designers a powerful tool for the kinematic performance evaluation and optimal design of the parallel mechanisms having combined DoFs in terms of translations and rotations.

A Fast Forward Kinematics Algorithm for 3-PRS Parallel Mechanism

Parasitic motion of 3-PRS (prismatic-revolute–spherical) parallel mechanism is discussed, inverse kinematics model of this mechanism is established. Based on the structure feature of 3-PRS parallel mechanism, a new forward kinematics algorithm for this mechanism is presented. The algorithm consists of approximate calculation and iterative calculation. The mathematical model of the proposed algorithm is clear simple, no derivative operation or Jacobi matrix inverse operation is needed, so computation is less. The experiment shows that in the same computing environment, the calculation speed of the proposed algorithm is about 2 times of the existing algorithms to achieve the same accuracy, so it can be applied to real-time control. Complexity and workload of programming is less than half of before. The algorithm is based on 3-PRS parallel mechanism, but it is also applicable for other parallel mechanism.

Dynamic Modeling and Decentralized Control of a 3 PRS Parallel Mechanism Based on Constrained Robotic Analysis

In this paper, a novel dynamic model is developed for analysis and control of a 3-PRS (Prismatic, Revolute, Spherical) parallel mechanism. The dynamic model is formulated in the joint space and three holonomic constraint equations are derived to specify the coupling relationships between the actuated legs and the moving platform. The associated constraint forces are determined to be internal forces and it leads to a novel model where the dynamics of the moving platform can be separated from that of the actuated legs. By utilizing the developed model, the constraint forces can be computed more efficiently as compared to the conventional approach. After compensation of the coupling dynamics, each actuated legs could be considered as a decoupled system. The coupling behavior of the parallel mechanism can then be easily illustrated by the proposed model. To facilitate real-time control implementation, the derived model can be further simplified and a decentralized control scheme integrated with a disturbance observer is proposed. The computational efficiency and tracking performances for the proposed control method are then validated by computer simulations.

Research on Accuracy Analysis and Simulation for Typical Parts with PRS-XY NC Hybrid PMT

The paper presented a set of PRS-XY hybrid PMT, made up of a set of 3-PRS parallel mechanism and an X-Y table. For advancing the motion accuracy of the PRS-XY type hybrid CNC machine tool, the forward kinematics model and inverse kinematics model have been made, and main error sources affect to machine tool’s precision was established. The relative position of workpiece and the tool of PRS-XY PMT wad discussed, and the coordinate of tool surface was calculated in various process models. The chamfer shape with variation of main error sources was drawn in simulation software, and the processing experiment results prove the correctness of analysis and simulation.

Parasitic motion comparison of 3-PRS parallel mechanism with different limb arrangements

The 3-PRS parallel mechanism (PM) is an important category of lower-mobility parallel mechanisms. Because it can undergo one translational degree of freedom (DOF) and two rotational DOFs, the 3-PRS PM has great potential in practical application and has received extensive attention. Parasitic motion occurring in the constrained DOFs of a 3-PRS PM is a key issue affecting its application. First, the 3-PRS PM is classified into seven subcategories based on the geometrical arrangements of limbs. Then, parasitic motion of each subcategory is discussed in detail and case studies are presented. It is illustrated that the complexity of parasitic motion of the 3-PRS PM is determined by the limb arrangement. The architecture of the 3-PRS PM without parasitic motion is also identified.

Inverse dynamics analysis for a 3-PRS parallel mechanism based on a special decomposition of the reaction forces

In this paper, a novel approach is proposed to analyze the inverse dynamics of a 3-PRS (Prismatic, Revolute, Spherical) parallel mechanism. The dynamic equations of the actuated legs and the moving platform are formulated in the joint and the task space, respectively. The reaction forces applied at the spherical joints are utilized to integrate the complete equations and a special decomposition is proposed for efficient calculation. By employing the Jacobian analysis, the constraint forces in the joint coordinates are recognized to be the internal forces for the moving platform and lead to the special decomposition. The proposed algorithm can provide higher computational efficiency as compared to the conventional approach. Computer simulations on tracking circular motion are performed to analyze the inverse dynamics of the 3-PRS mechanism and it is shown that the proposed decomposition of the reaction forces could be utilized to provide a deeper understanding for the interactions between the legs and moving platform. Since the closed-loop kinematic constraints are inherent for parallel manipulators, the proposed methodology could also be applied to other parallel mechanisms. In real-time control, the proposed algorithm with high computational efficiency might be utilized for dynamic compensation.

Structural Condition for [PP]S Parallel Mechanism without Parasitic Motion

The family of [PP]S parallel mechanism consists of 3-PRS, 3-RPS, 3-RRS and 3-PPS parallel mechanisms, which can undergo one translational degree of freedom (DOF) and two rotational DOFs, and thus, has great potential in practical application. Parasitic motion is the motion occurring in the non-independent DOFs of a [PP]S parallel mechanism, which is a key issue affecting its application. The kinematic model of the parasitic motion of the general 3-PRS parallel mechanism is established, revealing the inherent link between the geometrical structural parameters and the parasitic motion. The sufficient and necessary structural condition for a 3-PRS parallel mechanism without parasitic motion is proved. Based on the structural condition, the 3-PRS parallel mechanism without parasitic motion can be constructed. Local mobility in the 3-PRS parallel mechanism without parasitic motion is identified. Actuation selection considering the local mobility is presented. Mobility analysis of the 3-PRS parallel mechanism without parasitic motion is performed and the two finite rotational axes of the moving platform are identified. The sufficient and necessary structural condition is applicable to all [PP]S parallel mechanisms.

Analysis and simulation for a parallel drill point grinder

Based on the 3-PRS parallel mechanism, a new drill point grinder is presented in this paper. The relationship between the drill point geometry parameters and the grinding kinematic parameters are described for the most commonly used conical twist drill, and the grinding kinematic equation is also derived accordingly. The virtual prototype modeling and the kinematic simulation using MSC/ADAMS are then carried out for the proposed parallel drill point grinder. The related kinematic analysis, such as the displacement and velocity analysis of the drill point and grinding wheel, the rotation angle analysis of the ball joints with respect to the initial position, etc., is obtained. From the simulation results, we can see that the proposed structure is capable of implementing the function of drill point grinding. The virtual prototype simulation can help in the parametric design and the structural design for the new grinder.

Kinematics and inverse dynamics analysis for a general 3-PRS spatial parallel mechanism

In this paper, the kinematics and inverse dynamics of a novel kind of mechanism called a general 3-PRS parallel mechanism is investigated. In the kinematics study, the inverse kinematics solution is derived in closed form, and the forward kinematics problem is resolved by the Newton iterative method seeking for an on-line solution to this issue. The inverse dynamics analysis is approached with two methods: Lagrangian formulations and principle of virtual work. After deriving the dynamic model by a Lagrangian formulation approach, the simulation results of two introduced examples quantitatively and qualitatively verify the accuracy of the derived dynamic equations. By introducing a simplifying hypothesis, a simplified dynamic model is set up using principle of virtual work, also a computer simulation is performed on this reduced model. The simulation results demonstrate that the simplified dynamic model is reasonable under such kind of assumptions through comparison with the precise model derived from the Lagrangian formulation. The inverse dynamics analysis provides a sound basis to develop controllers for controlling over a general 3-PRS parallel robot.

Direct kinematic analysis of a 3-PRS parallel mechanism

This paper presents the direct kinematics solutions for a novel 3-PRS parallel mechanism. The geometric method is applied to formulate three coupled trigonometric equations. One algorithm for solving the three coupled equations is to use the Bezout’s elimination method which leads to a total of 64 solutions. By categorizing the 64 solutions into six groups and further examining the corresponding configuration for each group, the preferred solution to the direct kinematics problem can be obtained. The other approach for solving the coupled equations is to apply the optimization techniques with side and behavior constraints set by analyzing undesired configurations. This approach can obtain the preferred solution without checking all the possible solutions. Moreover, it can perform more efficiently than the elimination method.