Many performance indices for parallel mechanism are put forward in the phase of dimensional synthesis,except for identifiability index,which determines the difficulty of kinematical calibration.If the dimensional parameters are inappropriately selected,the existing methods for optimizing identifiability will not effectively work.Thus,with the aim of studying identifiability optimization in dimensional synthesis for 3-PRS mechanism,kinematics with structural errors is analyzed to provide theoretical bases for kinematical model.Then through a comparison of two 3-PRS mechanisms with different dimensional parameters,identifiability performance is proved to be necessary and feasible for optimization in the phase of dimensional design.Finally,an index δ is proposed to scale the identifiability performance.With the index,identifiability analysis and dimensional synthesis simulation in the whole workspace is completed.The index is verified to be correct and feasible,and based on the index,a procedure of dimensional synthesis,as well as an example set of non-dimensional parameters of 3-PRS mechanism,is proposed.The proposed identifiability index and design method can effectively introduce identifiability optimization into dimensional synthesis,and will obviously benefit later kinematical calibration.
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.
为研究机床的静刚度特性,需要得到其各部件的单元刚度矩阵。机床部件的结构往往是不规则的,因此需要将其等效简化为等截面梁单元,才能得到其单元刚度矩阵。该文对任意变截面梁等效简化为等截面梁单元的问题进行了研究,从建立梁单元的单元刚度矩阵的需要出发,推导出了完整的简化方法。为了验证该简化方法的有效性,利用有限元分析软件ABAQU S 6.51对一个力学模型进行了分析,同时用上述的简化方法对该力学模型进行了计算。将两者的计算结果进行对比,相对偏差小于5%,因此可证明该简化方法在变截面梁等效简化为等截面梁单元时的有效性。
Introduction Unlike serial machines, which suffer from the accumulation of joint errors, parallel kinematic machines (PKMs) are considered to have high accuracy[1]. However, recent investigations have shown that the PKM is not necessarily more accurate than a serial machine with the same manufacturing and
Returning home is the most important process of a parallel kinematic machine (PKM) with incremental encoders.Currently,most corresponding articles focus on the accuracy of homing process,and there lacks the investigation of the operation's safety.For a 4RRR PKM,all servoaxes would be independently driven to their zero positions at the same time based on the traditional homing mode,and that can bring serious interfere of the kinematic chains.This paper systemically investigates this 4RRR PKM's safety of homing process.A homing strategy usually contains three parts which are the home switches' locations,the platform's initial moving space,and each links' homing direction,and all of them can influence the safety of homing operation.For the purpose of evaluating and describing the safety of the homing strategy,some important parameters are introduced as follows:Safely homing ratio (SHR) is used to evaluate the probability of a machine's successfully returning home from an initial moving space;Synchronal rotational angle (SRA) is the four links' largest synchronal rotational angle with given directions from a given pose.Whether a machine can safely return home from a given pose can be judged by comparing the SRA with all four home switches' mounting angles.By meshing the initial moving space and checking the safeties of returning home from all the initial poses on the nodes,the SHR of this initial moving space can be calculate.For the sake of convenience,the platform's initial moving space should be as large as possible,and in this 4RRR PKM,a square zone in the center of the workspace with a giving initial rotation range is selected as the platform's initial moving space.The forward direction is selected as each link's homing direction according to custom,and the platform's initial rotational angle is selected as larger than 0° based on this 4RRR PKM's kinematic characteristics.The platform's initial moving space can be defined only by the side length of the initial moving square.By setting a probable searching step
