The dynamic dexterity is an important issue for manipulator design, some indices were proposed for analyzing dynamic dexterity, but they can evaluate the dynamic performance just at one pose in the workspace of the manipulator, and can’t be applied to dynamic design expediently. Much work has been done in the kinematic optimization, but the work in the dynamic optimization is much less. A global dynamic condition number index is proposed and applied to the dynamic optimization design the parallel manipulator. This paper deals with the dynamic manipulability and dynamic optimization of a two degree-of-freedom (DOF) parallel manipulator. The particular velocity and particular angular velocity matrices of each moving part about the part’s pivot point are derived from the kinematic formulation of the manipulator, and the inertial force and inertial movement are obtained utilizing Newton-Euler formulation, then the inverse dynamic model of the parallel manipulator is proposed based on the virtual work principle. The general inertial ellipsoid and dynamic manipulability ellipsoid are applied to evaluate the dynamic performance of the manipulator, a global dynamic condition number index based on the condition number of general inertial matrix in the workspace is proposed, and then the link lengths of the manipulator is redesigned to optimize the dynamic manipulability by this index. The dynamic manipulability of the origin mechanism and the optimized mechanism are compared, the result shows that the optimized one is much better. The global dynamic condition number index has good effect in evaluating the dynamic dexterity of the whole workspace, and is efficient in the dynamic optimal design of the parallel manipulator.
This paper presents a novel step kinematic calibration method for a 3 degree-of-freedom(DOF) planar parallel kinematic machine tool,based on the minimal linear combinations(MLCs) of error parameters.The method using mapping of linear combinations of parameters in error transfer multi-parameters coupling system changes the modeling,identification and error compensation of geometric parameters in the general kinematic calibration into those of linear combinations of parameters.By using the four theorems of the MLCs,the sets of the MLCs that are respectively related to the relative precision and absolute precision are determined.All simple and feasible measurement methods in practice are given,and identification analysis of the set of the MLCs for each measurement is carried out.According to the identification analysis results,a step calibration including step measurement,step identification and step error compensation is determined by taking into account both measurement costs and observability.The experiment shows that the proposed method has the following merits:(1) the parameter errors that cannot influence precision are completely avoided;(2) it reflects the mapping of linear combinations of parameters more accurately and enhances the precision of identification;and(3) the method is robust,efficient and effective,so that the errors in position and orientation are kept at the same order of the measurement noise.Due to these merits,the present method is attractive for the 3-DOF planar parallel kinematic machine tool and can be also applied to other parallel kinematic machine tools with weakly nonlinear kinematics.
CHANG Peng,WANG JinSong,LI TieMin,LIU XinJun & GUAN LiWen Department of Precision Instruments and Mechanology,Tsinghua University,Beijing 100084,China
