Elastodynamic modeling and parameter sensitivity analysis of a parallel manipulator with articulated traveling plate

Abstract

This paper deals with the elastodynamic modeling and parameter sensitivity analysis of a parallel manipulator with articulated traveling plate (PM-ATP) for assembling large components in aviation and aerospace. In the elastodynamic modeling, the PM-ATP is divided into four levels, i.e., element, part, substructure, and the whole mechanism. Herein, three substructures, including translation, bar, and ATP, are categorized according to the composition of the PM-ATP. Based on the kineto-elastodynamic (KED) method, differential motion equations of lower levels are formulated and assembled to build the elastodynamic model of the upper level. Degrees of freedom (DoFs) at connecting nodes of parts and deformation compatibility conditions of substructures are considered in the assembling. The proposed layer-by-layer method makes the modeling process more explicit, especially for the ATP having complex structures and multiple joints. Simulations by finite element software and experiments by dynamic testing system are carried out to verify the natural frequencies of the PM-ATP, which show consistency with the results from the analytical model. In the parameter sensitivity analysis, response surface method (RSM) is applied to formulate the surrogate model between the elastic dynamic performances and parameters. On this basis, differentiation of performance reliability to the parameter mean value and standard variance are adopted as the sensitivity indices, from which the main parameters that greatly affect the elastic dynamic performances can be selected as the design variables. The present works are necessary preparations for future optimal design. They can also provide reference for the analysis and evaluation of other PM-ATPs.

Static and dynamic optimization of a pose adjusting mechanism considering parameter changes during construction

“…First of all, kinematic differentiation equation of element is formulated. Herein, Euler-Bernoulli beam is adopted as the basis element, whose differential motion equation is referred to [38]. Then, kinematic differentiation equation of part is assembled from the elements.…”

Natural frequency prediction of the 3-RPS parallel manipulator using the substructure synthesis technology

“…Wu et al [17] established the elastodynamic model of hybrid robots based on the substructure synthesis technology. Lian et al [18][19] investigated the natural frequency distribution in the workspace by elastodynamic modeling in terms of the FEM and substructure synthesis technology. Shankar et al [20] studied the first natural frequency of a 2-DOF translational parallel robot.…”

An approach to predict lower-order dynamic behaviors of a 5-DOF hybrid robot using a minimum set of generalized coordinates

“…The methods available at hand can roughly be classified into three categories, i.e. full order Finite Element Analysis (FEA) [4][5][6][7], lumped parameter methods [8][9][10][11] and semi-analytical methods [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Combining fundamental robotics with structural dynamics, it has been well recognized that the semi-analytical approach is particularly useful for the predesign stage thanks to its much lower computational cost compared to full order FE models.…”

“…Combining fundamental robotics with structural dynamics, it has been well recognized that the semi-analytical approach is particularly useful for the predesign stage thanks to its much lower computational cost compared to full order FE models. Along this track, several approaches have been proposed, known as Matrix Structure Analysis (MSA) [12][13][14][15][16], Virtual Joint Method (VJM) [17][18][19][20] and Component Mode Synthesis (CMS) [21][22][23][24]. In the MSA method, the flexible links are frequently treated as spatial beam elements.…”