A study of dimensional synthesis of a 3-DOF parallel manipulator with coupling of translation and rotation is carried out.The architecture of the manipulator is composed of a moving platform attached to a fixed base through three identical PRS(prismatic-revolute-spherical) serial limbs,whose unique topology leads to the physical unit inconsistency of the conventional Jacobian matrix and the emergence of the parasitic motion.Then this paper introduces a kinetostatic performance index of the manipulator based on the condition of a dimensionally homogeneous Jacobian matrix,later,the workspace of the aforementioned manipulator is searched and the influence of the crucial design variables on the workspace is analyzed.Finally,a dimensional synthesis method of the manipulator is proposed,which may be regarded as a nonlinear programming problem with subject to the parasitic motion and other several engineering constraints.
SUN Tao1,SONG YiMin1,LI YongGang2 & LIU LinShan1 1 School of Mechanical Engineering,Tianjin University,Tianjin 300072,China
A novel high-speed parallel kinematic machine (PKM) named Delta-S parallel manipulator is proposed,which consists of a fixed base connected to a moving platform through three limbs with identical topology.Each limb is composed of one driving arm and one follower arm,herein,the latter includes two strings and one middle rod,all located in a same plane.Compared with similar manipulators with uniform parameters,the novel and unique topology as well as the addition of two strings of Delta-S manipulator can remove the clearance of the spherical joints,reduce the inertial load of components further,improve the positioning accuracy and dynamic performance,and so on.In order to formulate the kineto-static model of Delta-S manipulator,the kineto-static analyses and models of the driving arm,the generalized follower and the moving platform can be carried out by the D'ALEMBERT principle.For the sake of obtaining the force analytic results of strings,the deformation compatibility condition of strings and the middle rod are determined.Furthermore,in virtue of the assumption of small deformation and the linear superposition principle,theminimal pre-tightening force of the strings is calculated.The main results include that the loads of the strings and the middle rod must be larger than "zero" and the pre-tightening force over the workspace must be larger than theminimal pre-tightening force at any time within the workspace,which lay the foundation for the dynamic analysis and the prototype manufacture of the Delta-S manipulator.
Parallel kinematic machines （PKMs） have the advantages of a compact structure,high stiffness,a low moving inertia,and a high load/weight ratio.PKMs have been intensively studied since the 1980s,and are still attracting much attention.Compared with extensive researches focus on their type/dimensional synthesis,kinematic/dynamic analyses,the error modeling and separation issues in PKMs are not studied adequately,which is one of the most important obstacles in its commercial applications widely.Taking a 3-PRS parallel manipulator as an example,this paper presents a separation method of source errors for 3-DOF parallel manipulator into the compensable and non-compensable errors effectively.The kinematic analysis of 3-PRS parallel manipulator leads to its six-dimension Jacobian matrix,which can be mapped into the Jacobian matrix of actuations and constraints,and then the compensable and non-compensable errors can be separated accordingly.The compensable errors can be compensated by the kinematic calibration,while the non-compensable errors may be adjusted by the manufacturing and assembling process.Followed by the influence of the latter,i.e.,the non-compensable errors,on the pose error of the moving platform through the sensitivity analysis with the aid of the Monte-Carlo method,meanwhile,the configurations of the manipulator are sought as the pose errors of the moving platform approaching their maximum.The compensable and non-compensable errors in limited-DOF parallel manipulators can be separated effectively by means of the Jacobian matrix of actuations and constraints,providing designers with an informative guideline to taking proper measures for enhancing the pose accuracy via component tolerancing and/or kinematic calibration,which can lay the foundation for the error distinguishment and compensation.
