Sensitivity analysis and prediction of the orientation error of a three translational parallel manipulator

Abstract

This paper deals with the sensitivity analysis and the prediction of the orientation error limits of a three-DoF translational parallel manipulator (3-TPM). An analytical model relating the robot accuracy to the design parameters uncertainties, the joints clearances, the nominal pose, and the external load is developed. Based on this model, an analytical sensitivity analysis is performed to show the influence of each parameter on the orientation error. An algorithm based on the interval analysis is used to predict the bounds of the translator orientation error. Using the RAF robot as an example, it is shown that the pin length of the revolute joint, the width of the parallelogram structure and the radial clearance in the revolute joints are the most influential parameters on the orientation error of the manipulator. Moreover, one of the main results of this analysis is that an increase of the tolerances on certain parameters does not necessarily lead to an increase of the orientation error of the robot, for this specific example.

Genetic Algorithm Coupled with the Krawczyk Method for Multi-Objective Design Parameters Optimization of the 3-UPU Manipulator

“…where C is a preconditioning non-singular matrix that improves the convergence properties. 13,14,27 Introducing the uncertainties of the different parameters in the form of intervals, the mathematical concept of the Krawczyk operator can be written as where…”

“…This iterative process is repeated until the maximum number of iterations is reached or the intersection of the two sets [K]([x ]) and [x ] is [x ], that is, [x ] ⊆ [K]([x ]). If this intersection is empty, then there is no solution to the problem 27,. The error prediction algorithm.…”

Precision comparison of two 3-DoF translational parallel manipulators based on the orientation errors due to joint clearances

“…The accuracy of parallel mechanism can be altered by the uncertainties of the geometric parameters, joint clearances or both of them [4,5,[8][9][10][11][12][13][14]. Indeed, Al-Widyan et al [4] proposed a statistical approach to determine the optimum clearances of the unactuated cylindrical joints for the 3-DOF spherical manipulators.…”

“…In fact, the Interval Analysis method has been used to verify the efficiency of this method. The static model of the isostatic parallel manipulator and the virtual work principle have been adopted to determine an analytical model of the pose error of the platform due to the clearance in the passive joints [2,[9][10][11]. Sun et al [12] considered the epistemic and random uncertainty to introduce a general method of kinematic accuracy analysis of mechanisms with clearance.…”

“…The 3-DOF TPM (RAF) was proposed by Romdhane et al [1]. Chebbi et al [9] presented a sensitivity analysis and prediction of the orientation error limits of the RAF robot. An algorithm based on the interval analysis was used to predict the bounds of the orientation error of the manipulator.…”