Stiffness modeling for perfect and non-perfect parallel manipulators under internal and external loadings

Abstract

International audienceThe paper presents an advanced stiffness modeling technique for perfect and non-perfect parallel manipulators under internal and external loadings. Particular attention is paid to the manipulators composed of non-perfect serial chains, whose geometrical parameters differ from the nominal ones and do not allow to assemble manipulator without internal stresses that considerably affect the stiffness properties and also change the end-effector location. In contrast to other works, several types of loadings are considered simultaneously: an external force applied to the end-effector, internal loadings generated by the assembling of non-perfect serial chains and external loadings applied to the intermediate points (auxiliary loading due to the gravity forces and relevant compensator mechanisms, etc.). For this type of manipulators, a non-linear stiffness modeling technique is proposed that allows to take into account inaccuracy in the chains and to aggregate their stiffness models for the case of both small and large deflections. Advantages of the developed technique and its ability to compute and compensate the compliance errors caused by the considered factors are illustrated by an example that deals with parallel manipulators of the Orthoglide family

Stiffness of serial and quasi-serial manipulators: comparison analysis

“…A stiffness model of a robotic manipulator (both serial and quasi-serial) describes the manipulator behavior under loading [16], [17]. In addition to the conventional robot parameters (i.e., geometric ones), it includes a number of elastic parameters which describe flexibility of the manipulator links and joints.…”

Comparison of Serial and Quasi-Serial Industrial Robots for Isotropic Tasks

“…This example deals with two manipulators (serial and quasi-serial ones) with the same basic geometric parameters l 2 = 1 m, l 3 = 0.8 m and similar joint compliances k = 10 − 6 rad ̸N m. These values are typical for industrial robots that are used in machining (Dumas et al, 2012). To compare stiffness behavior, let us compute the compliance errors caused by an external force 1.0 kN applied to the end-effector (details of related technique are presented in (Klimchik et al 2014)). Relevant results have been obtained for two different external loadings and are presented in Fig.…”

“…The stiffness model of a robotic manipulator describes manipulator behavior under loading (Klimchik et al 2014;Pashkevich et al 2011;Yan et al 2016). In addition to the conventional robot parameters (geometric ones), it includes a number of elastic parameters describing flexibility of manipulator links and joints.…”

Stiffness analysis and experiment of a novel 5-DoF parallel kinematic machine considering gravitational effects

“…It is worth pointing out that the stiffness or compliance modeling is a research hotspot and an essential foundation for the stiffness or compliance analysis, design and estimation in the preliminary and final design stages of 5-DoF PKMs. Literature reviews [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] show that there are three main methods for the formulation of stiffness or compliance model: numerical approach based on finite element analysis (FEA) software, analytical approaches based on structural matrix, and semi-analytical approach based on virtual work principle.…”