3-PRS Mechanism Research Articles

Analysis of the 2 P RU-1 P RS 3DOF parallel manipulator: kinematics, singularities and dynamics

Parallel manipulators, especially those with outputs as a translation and two rotations (1T2R), are being increasingly studied. The 3PRS mechanism is a very typical example of this category, but it has peculiar kinematic characteristics caused by parasitic motions and by low orientation capability. To overcome these problems, new mechanisms are being studied, such as the 2PRU-1PRS manipulator. As in the case of the 3PRS manipulator, the degrees of freedom of the 2PRU-1PRS are one translation along the Z-axis and two rotations about the X- and Y-axes. The advantages are that the parasitic motion appears only in one direction instead of in three and that the orientation capability is higher. In this paper we solve the kinematics, singularities and dynamics of a 2PRU-1PRS mechanism. We first analyse a general 2PRU-1PRS mechanism and then present the results for the particular case of the 2PRU-1PRS used for automobile pieces testing purposes.

Kinematics and inverse dynamics analysis for a novel 3-PUU parallel mechanism

SUMMARYThe modules of parallel tool heads with 2R1T degrees of freedom (DOFs), i.e., two rotational DOFs and one translational DOF, have become so important in the field of machine tools that corresponding research studies have attracted extensive attention from both academia and industry. A 3-PUU (P represents a prismatic joint, U represents a universal joint) parallel mechanism with 2R1T DOFs is proposed in this paper, and a detailed discussion about its architecture, geometrical constraints, and mobility characteristics is presented. Furthermore, on the basis of its special geometrical constraint, we derive and explicitly express the parasitic motion of the 3-PUU mechanism. Then, the inverse kinematics problem, the Jacobian matrix calculation and the forward kinematics problem are also investigated. Finally, with a simplified dynamics model, the inverse dynamics analysis for the mechanism is carried out with the Principle of Virtual Work, and corresponding results are compared with that of the 3-PRS mechanism. The above analyses illustrate that the 3-PUU parallel mechanism has good dynamics features, which validates the feasibility of applying this mechanism as a tool head module.

Prototype Development of a 5-DOF Series-Parallel Robot Based on 3-PRS Mechanism

Aiming at the problem that the fixed working envelope can not always satisfy the study and experiment requirements, the study has developed a 5-DOF series-parallel robot with an adjustable working envelope based on the 3-PRS mechanism. The robot system is composed of an electric hardware subsystem, a mechanical subsystem and a control system subsystem. The architecture of the robot is introduced firstly. The key components and parts of the electric hardware and mechanical component are presented secondly. The robot system adopts the open architecture mode based on the computer and the motion controller, which provides sufficient convenience for experiments at different levels. Then the control software design method is presented. And many high-level programming languages and Integrated Development Environments can be used separately or together, and even other engineering software packages can be made full use of. Finally, an experiment is presented to verify the developed robot prototype, and that shows its correctness, reliability and convenience.

Research on CNC of FSW with Serial-Parallel Structure Based on 3-PRS Mechanism

With the increase of welding thickness, Friction stir welding equipment (FSW) with traditional milling machine structure could not meet the requirements of stiffness which to support the huge axis load. Therefore, a FSW with serial-parallel mechanism based on 3-PRS platform was proposed. In order to complete real-time control and the actual and virtual axis control of the equipment, the positive solution and inverse solution (based on Newton-Euler method) of the FSW are analyzed. Then, based on the PA system, the open CNC of the equipment is designed, and the inverse kinematics and the numerical positive kinematics based on Newton-Euler method are embedded into the interpolation of NC system. According to the demand of the equipment, human-machiner interface (HMI) is developed to display the positions of actual and virtual axis for the equipment, and compiler and interpolation are designed. At the same time, online real-time 3D motion simulation is designed, space pose of spindle and whole for the equipment are deduced. In the paper, design method of CNC based on the serial-parallel mechanism is provided.

Stiffness Modeling of 3-PRS Mechanism

Stiffness Modeling of 3-PRS Mechanism

Dimensional synthesis for 3-PRS mechanism based on identifiability performance

Many performance indices for parallel mechanism are put forward in the phase of dimensional synthesis, except for identifiability index, which determines the difficulty of kinematical calibration. If the dimensional parameters are inappropriately selected, the existing methods for optimizing identifiability will not effectively work. Thus, with the aim of studying identifiability optimization in dimensional synthesis for 3-PRS mechanism, kinematics with structural errors is analyzed to provide theoretical bases for kinematical model. Then through a comparison of two 3-PRS mechanisms with different dimensional parameters, identifiability performance is proved to be necessary and feasible for optimization in the phase of dimensional design. Finally, an index δ is proposed to scale the identifiability performance. With the index, identifiability analysis and dimensional synthesis simulation in the whole workspace is completed. The index is verified to be correct and feasible, and based on the index, a procedure of dimensional synthesis, as well as an example set of non-dimensional parameters of 3-PRS mechanism, is proposed. The proposed identifiability index and design method can effectively introduce identifiability optimization into dimensional synthesis, and will obviously benefit later kinematical calibration.

Kinematical calibration of a hybrid machine tool with Regularization method

The hybrid machine tools, combining the advantages of serial and parallel type machine tools, provide more and more application opportunities for less-freedom parallel mechanism. Accuracy performance is still an important index of hybrid machine tool for industry application. In this study, configuration of a 3-P(4R)S-XY hybrid machine tool is first introduced. The 3-P(4R)S parallel mechanism can be simplified to a 3-PRS mechanism on kinematical calibration. Based on that, error model and error kinematics are derived to introduce all possible manufacturing and assembling errors into calibration. Then, identification matrix is derived by differentiating kinematical equations. Combining the advantages of calibration schemes based on both inverse and forward kinematics model, a new measurement scheme is put forward, in which not all freedoms of motions needs to be measured and error identification could be efficiently accomplished in one time measurement. In order to solve the ill-posed problem in error identification, practical Regularization methods are adopted. Finally, the kinematical calibration experiment of the prototype machine tool is performed with a combined measuring tool. The results of RTCP accuracy test reveal that the positioning accuracy is less than 0.05 mm in the 30° cone workspace. Calibration experiments for the prototype verify feasibility and effectivity of the more precise kinematical error model, the low-cost measurement scheme, and the error identification solution with Regularization method.

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.

Nonlinear dynamic analysis of a parallel mechanism with consideration of joint effects

Abstract This paper presents a nonlinear dynamic analysis of a 3-PRS series-parallel mechanism with consideration of joint effects which includes flexibility, clearance and friction. The Newtonian approach is applied to derive the equations of motion of the 3-PRS mechanism. The Runge–Kutta method and contact verification criterion are combined to solve the nonlinear piecewise differential equations. The linearization technique is applied to determine the natural frequencies and their associated mode shapes. The simulation results show that the natural frequencies of the 3-PRS mechanism shift with the position of prismatic pairs and the physical interpretations are given by using the associate mode shapes. The effects of joint clearance and friction cause the natural frequencies to decrease and significantly affect the modes of which rotational motions are dominated. It is also shown that the dynamic response becomes larger as the joint clearances increase, and the joint contact forces become larger as joint clearances and friction coefficient increase.

Identification of strut and assembly errors of a 3-PRS serial–parallel machine tool

In a serial–parallel type machine tool, the parallel spindle platform plays the key role in manipulating three directions of movement. Spatial symmetry of the 3-PRS loops is essential to the machine’s systematic accuracy. Currently, however, there is no effective instrument capable of measuring the symmetrical errors of the corresponding joints and strut lengths during structure assembly. In this study, an experimental method is proposed to identify the mechanism symmetric errors of a 3-PRS serial–parallel machine tool during the test run. It is based on the differentiation of the inverse kinematics equations. The mechanism errors could be derived by an identification model. With the aid of a developed 3D laser ball bar to detect the spatial position and orientation of the spindle platform, and three laser Doppler scales to measure three sliders’ positions simultaneously, the length errors of three struts and the symmetrical errors of the R-joints and S-joints can be identified by the optimization technique. This technique can help shop floor engineers to tune the symmetrical errors of the 3-PRS mechanism during machine assembly.