Accuracy Analysis and Calibration of a Special 3-DOF Parallel Mechanism

Abstract In order to improve the low output accuracy caused by the elastic deformations of the branch chains, a finite element-based dynamic accuracy analysis method for parallel mechanisms is proposed in this paper. First, taking a 5–prismatic–spherical–spherical (PSS)/universal–prismatic–universal (UPU) parallel mechanism as an example, the error model is established by a closed vector chain method while its influence on the dynamic accuracy of the parallel mechanism is analyzed through numerical calculation and simulation. According to the structural and error characteristics of the parallel mechanism, a vector calibration algorithm is proposed to reduce the position and pose errors along the whole motion trajectory. Then, considering the elastic deformation of the rod, the rigid-flexible coupling dynamic equations of the mechanism are established by combining the finite element method with the Lagrange method, and the equations are vectorially superimposed by means of internal force cancellation to synthesize the elastic dynamics equation of the connecting rod. Based on the constraint condition of each moving part, the elastodynamic model of the whole machine is obtained. Furthermore, the effect of component flexibility on the dimensionless root mean square error of the displacement, velocity and acceleration of the moving platform is investigated by using a Newmark method, and the dynamic accuracy influenced by these dimensionless root mean square errors is further studied. The research work establishes an important theoretical foundation for the development of the prototype.

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Accuracy analysis of three degrees of parallel mechanism based on Monte Carlo Simulation

10.1117/12.2625290 ◽

2021 ◽

Author(s):

Haiqiang Zhang ◽

Jianglong Tang ◽

Kan Shi ◽

Yan'an Yao

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Parallel Mechanism ◽

Accuracy Analysis

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Positioning Accuracy Analysis of the Parallel Mechanism Near Singular Positions

International Journal of Applied Mechanics and Engineering ◽

10.1515/ijame-2015-0001 ◽

2015 ◽

Vol 20 (1) ◽

pp. 5-18 ◽

Cited By ~ 1

Author(s):

J. Bałchanowski

Keyword(s):

Numerical Modelling ◽

Parallel Mechanism ◽

Degrees Of Freedom ◽

Accuracy Analysis ◽

Parallel Mechanisms ◽

Contact Interactions ◽

Positioning Accuracy ◽

Singular Configurations ◽

Positioning Errors ◽

Three Degrees Of Freedom

Abstract This paper presents a method of numerical modelling of parallel mechanisms with clearances in their kinematic pairs taken into account. The pairs with clearances are modelled as shape connections based on constraints in the form of contact interactions. Using the created models simulations were run to determine the positioning errors of the links in a parallel mechanism with three degrees of freedom (MR2120). In particular, the accuracy of positioning the links close to the mechanism singular configurations was studied.

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The Accuracy Analysis of Parallel Mechanism Assembly Robot

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.423-426.2769 ◽

2013 ◽

Vol 423-426 ◽

pp. 2769-2775 ◽

Cited By ~ 2

Author(s):

Xin Rong Liu

Keyword(s):

Parallel Mechanism ◽

Joint Angle ◽

Parallel Robot ◽

Accuracy Analysis ◽

Analysis Model ◽

Error Sources ◽

Positioning Accuracy ◽

Moving Platform ◽

Position And Orientation ◽

High Repeatability

Parallel robot has the advantages of high rigidity,high bearing capacity and high repeatability of positioning accuracy,and make it more and more widely used in the field of industrial applications.In this paper,the 3-RRR parallel mechanism assembly robot was used as the research object;introduced the sources of error in the parallel mechanism operation platform's position and orientation,furthermore,analyzed the factors of the error sources;then built up that parallel robot's error analysis model,solved the error model with the differential equation,and analyzed the error of parallel robot's structural in rod length,joint angle,the moving platform and the base platform's radius of circle,then simulated with MATLAB.Research shows that All structure errors in parallel mechanism increased by the X axis monotone increasing.

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Accuracy analysis and synthesis of asymmetric parallel mechanism based on Sobol-QMC

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406220920702 ◽

2020 ◽

Vol 234 (21) ◽

pp. 4200-4214

Author(s):

Mengli Wu ◽

Xianqu Yue ◽

Weibin Chen ◽

Qi Nie ◽

Yue Zhang

Keyword(s):

Parallel Mechanism ◽

Closed Loop ◽

Jacobian Matrix ◽

Mapping Function ◽

Error Modeling ◽

Accuracy Analysis ◽

Vector Method ◽

Evaluation Indexes ◽

Quasi Monte Carlo ◽

Analysis And Synthesis

Aiming at the aircraft composite skin grinding, a new three degree-of-freedom (DOF) parallel mechanism with asymmetrical structure (TAM) is proposed to replace manual grinding. The TAM is achieved by integrating one of active limbs into the passive limb while keeping the required DOF unchanged, which is divided into two closed-loop chains: telescopic rod and parallelogram. The inverse kinematics models of the two chains are established according to closed-loop vector method. Thus, the actuation and the constraint Jacobian matrix are obtained. Based on the perturbation principle, the error modeling of the TAM is built. Adopting the constraint Jacobian matrix, 15 uncompensated errors are distinguished from the error model. In order to improve the working accuracy of the TAM, accuracy analysis and synthesis are necessary for all the uncompensated errors. The mapping function reflects the influence of uncompensated errors on the pose accuracy. The global sensitivity evaluation indexes are established by mapping function. Since Sobol sequences are superior in uniformity and convergence, the Quasi-Monte Carlo method based on Sobol sequences (Sobol-QMC) is introduced for sensitivity analysis. Taking the minimum manufacturing and installation costs as the optimization target, the objective function of accuracy synthesis is constructed. Ultimately, the reasonable tolerance zone of each uncompensated error is calculated by genetic algorithm. Simulation is performed by Sobol-QMC to verify the rationality of the optimization. The results show the probability is above 97% where most pose errors are in [[Formula: see text], [Formula: see text]] within the workspace. Therefore, accuracy synthesis is correct and practical.

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