Abstract
Hole drilling or contour milling for the large and complex workpieces such as automobile panels and aircraft fuselages makes a high combined demand on machining accuracy, stiffness and workspace of machining equipment. Therefore, a 5-DOF (degrees of freedom) parallel kinematic machine (PKM) with redundant constraints is proposed. Based on the kinematics analysis of the parallel mechanism using intermediate variables, the kinematics problems of the PKM are solved through equivalent kinematics model. The structural stiffness matrix method is adopted to model the stiffness of the parallel mechanism of the PKM, where the stiffness of each joint and branch component is obtained by stiffness formula and finite element analysis. And the stiffness model of the parallel mechanism is improved by correction coefficient matrix, each element of which is constructed as a polynomial function of three independent end variables of the parallel mechanism. The terminal stiffness matrices obtained by simulation result are used to determine the coefficients of polynomial function by least square fitting to describe the correction coefficient over the workspace of the parallel mechanism quantitatively. The experiment results prove that the modification method can greatly improve the stiffness model of the parallel mechanism. To enhance the machining accuracy of the PKM, the proposed kinematics model and the improved stiffness model are utilized to optimize the working stiffness of parallel machine by searching the best relative position of parallel machine and workpiece. A plate workpiece taken as example is examined in the case study section, which demonstrates the effectiveness of optimization method.
Highlights
The parallel kinematic machine (PKM) is composed of parallel mechanism and series mechanism, which have both the characteristics of these two types of mechanism
Bi et al [6, 7] proposed an Exechon parallel mechanism with redundant constraints, which had three degrees of freedom (DOF), and presented a method of solving the kinematics problem for Exechon parallel mechanism by using intermediate variables to establish the relation between joint variables and end variables
(1) To facilitate the study on kinematics, the parallel mechanism of the PKM is transformed into a joint of the PKM, which is equivalent to a 3-joint series mechanism
Summary
The parallel kinematic machine (PKM) is composed of parallel mechanism and series mechanism, which have both the characteristics of these two types of mechanism. Zhang et al [8, 9] proposed a Tricept parallel mechanism, the stiffness of which was enhanced by a passive chain, and used various intelligent algorithms to evaluate the positive kinematics solution of a 3-DOF. Fan et al [16] related to the design of PKM for optimal static stiffness using computer simulation He et al [17] proposed a new stiffness orientation method, which was used to optimize milling path and improve stability of the robotic milling system. The kinematic pairs in Exechon mechanism which connect limb to the fixed platform and to the moving platform are interchanged in the proposed PKM, which makes it possible to use one-piece precision spherical pair instead of three rotation pairs and avoid the assembly error
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