Algorithm for the Inverse Kinematics Calculation of Cross Rods Parallel Machine Tools Based on Lie-Algebras

2011 ◽  
Vol 697-698 ◽  
pp. 282-287
Author(s):  
X.F. Fang ◽  
Y.H. Tong ◽  
R.Y. Zhao ◽  
S.W. Zhang ◽  
Tong Yue Wang ◽  
...  
Keyword(s):  
Lie Algebras ◽  
Error Compensation ◽  
Machine Tools ◽  
Inverse Kinematics ◽  
Parallel Machine ◽  
Parallel Machine Tools ◽  
Exponential Formula ◽  
Parallel Machine Tool ◽  
Analysis Of Error ◽  
Direct Kinematics

In order to solve the problems that traditional kinematics model built by the method of D-H parameters can only reflect relative movements between adjacent components and can't express directly the spatial poses of every component relative to static platform, Lie-algebras is used this paper to establish the product of exponential formula of forward direct kinematics of every branch chains. The elimination method and Paden - kahan sub-problems are used to calculate joint variables. Then the quick and intuitive inverse algorithm of cross rods parallel machine tools is acquired. The algorithm provides reliable proofs for the analysis of error compensation, kinematics interference and singularity. Finally we prove our theory with an example of an actual parallel machine tool.

Contour Controller Design for Cubic Parallel Machine Tool

Manufacturing ◽  
2003 ◽  
Author(s):  
Sungsoo Kim ◽  
Seung Hwan Lee ◽  
Daehie Hong ◽  
Woo Chun Choi ◽  
Jae-Bok Song
Keyword(s):  
Machine Tool ◽  
Machine Tools ◽  
Estimation Method ◽  
Parallel Machine ◽  
Control Algorithms ◽  
Contour Error ◽  
Contour Control ◽  
Contouring Accuracy ◽  
Parallel Machine Tools ◽  
Parallel Machine Tool

In machining processes, contouring accuracy is usually more important than tracking performance. In order to reduce the contour error, there have been many contour control algorithms for conventional machine tools, which noticeably improve their contouring accuracy. However, the available contour control algorithms cannot be directly applied to the parallel machine tools. The dynamic characteristics of the parallel machine tools are not consistent inside workspace and unsymmetrical disturbances can be imposed on any axis. Due to these, mismatched dynamics cause unwanted contour error. In this paper, we present a contour control algorithm for the cubic parallel machine tool that employs the parallel mechanism for its moving table, which can be also applied to a general parallel manipulator. The contour error estimation method for free-formed curve trajectory is proposed and the relation between the contour error vectors in joint and Cartesian spaces is considered. In order to show the validity of the algorithm, the contour control simulations and experiments are made for various contour trajectories with the cubic parallel machine tool. The results show that the proposed controller reduces the contour error considerably both in joint and Cartesian spaces.

Manipulability Analyses of the 3-DOF Parallel Machine Tool

2009 ◽  
Vol 16-19 ◽  
pp. 1351-1354
Author(s):  
Ming Hu ◽  
Wen Yuan Tian ◽  
Jia Shun Shi
Keyword(s):  
Machine Tool ◽  
Machine Tools ◽  
Jacobian Matrix ◽  
Parallel Machine ◽  
Parallel Machine Tools ◽  
Parallel Machine Tool

A 3-DOF in-parallel machine tools based on a tripod mechanism is developed and studied, the kinematic is analytically performed, the workspace is derived, Analysis of the a number of conditions of the Jacobian matrix and manipulability is carried, The manipulability analytical of the parallel machine tool is investigated

The Kinematics Analysis of the 3-PTT Parallel Machine Tools

2014 ◽  
Vol 701-702 ◽  
pp. 784-787
Author(s):  
Ming Hu ◽  
Jia Shun Shi
Keyword(s):  
Machine Tool ◽  
Machine Tools ◽  
Jacobian Matrix ◽  
Parallel Machine ◽  
Kinematics Analysis ◽  
Kinematic Coupling ◽  
Parallel Machine Tools ◽  
Parallel Machine Tool

This paper presents the kinematics for 3-PTT parallel machine tools, the kinematic is analytically performed, the forward and inverse position kinematic equations are explicit functions and workspace is derived and there is no singularity configuration and kinematic coupling in the whole workspace. The manipulability analytical of the parallel machine tool is investigated by the Jacobian matrix.

Dimensional Synthesis of a 2UPS-UPR Parallel Machine Tool

2009 ◽  
Vol 16-19 ◽  
pp. 554-558
Author(s):  
Liang Zhao ◽  
Ya Dong Gong ◽  
Jian Ye Guo ◽  
Guang Qi Cai
Keyword(s):  
Condition Number ◽  
Performance Index ◽  
Machine Tools ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Structural Parameters ◽  
Parallel Machine ◽  
Dimensional Synthesis ◽  
Parallel Machine Tools ◽  
Parallel Machine Tool

This paper deals with the dimensional synthesis of a 2UPS-UPR parallel mechanism tool newly designed by Northeastern University. On the basis of establishing kinematics equations and obtaining Jacobian matrix, the performance index of dimensional synthesis is given which is the average of 729 values of the condition number of Jacobian matrix corresponding to 729 positions in the workspace. With MATLAB software, the effects are simulated which the structural parameters of parallel machine tools have on dimensional synthesis, their change laws are gained, and then dimensional synthesis of parallel machine tools is conducted based on these laws.

Development of a Virtual Axis Cutter Grinder

2006 ◽  
Vol 304-305 ◽  
pp. 483-487
Author(s):  
Xian Guo Han ◽  
Wu Yi Chen ◽  
B. Huang ◽  
Shao Hong Wang
Keyword(s):  
Machine Tool ◽  
Machine Tools ◽  
Design Method ◽  
Parallel Machine ◽  
Design Parameters ◽  
Good Precision ◽  
Program System ◽  
Parallel Machine Tools ◽  
Parallel Machine Tool ◽  
New Machine

The development of a virtual axis cutter grinder was introduced. The main contents of this paper include layout design, parameters design method, control system and program system. The purpose of the development of the parallel machine tools is for cutter grinding. The dimension of the cutter and the translation workspace for cutter grinding usually is small and is therefore suitable for the parallel machine tool application. The new machine tool has high rigidity and good precision.

Workspace Comparison Study of Two Plane-Symmetry Parallel Machine Tools

2013 ◽  
Vol 321-324 ◽  
pp. 1700-1703
Author(s):  
Yan Shi ◽  
Peng Cheng Zhang ◽  
Hong Xin Yue ◽  
Lian He Guo
Keyword(s):  
Machine Tool ◽  
Machine Tools ◽  
Parallel Machine ◽  
Comparison Study ◽  
Plane Symmetry ◽  
Spherical Joint ◽  
Computer Aided ◽  
Parallel Machine Tools ◽  
Geometric Technique ◽  
Parallel Machine Tool

Workspaces of two plane-symmetry parallel machine tools whose limbs are composed of the revolute joint, the prismatic joint and the spherical joint were studied comparatively in this paper. Firstly, manipulators of the plane-symmetry 3-RPS parallel machine tool and the plane-symmetry 3-SPR parallel machine tool were introduced, and their simulation manipulators were given. Secondly, the workspaces of the plane-symmetry 3-RPS parallel machine tool and the plane-symmetry 3-SPR parallel machine tool were solved and expressed in the same figure on the basis of the computer aided geometric technique method, respectively. Lastly, indices measuring the workspace were defined, and workspaces of the plane-symmetry 3-RPS parallel machine tool and the plane-symmetry 3-SPR parallel machine tool were analyzed comparatively from two aspects: positional workspace and posture angle.

Analysis on Influence of the Position Error of Joint Points in the Fixed Platform of 3-UPS Parallel Machine Tool

2012 ◽  
Vol 459 ◽  
pp. 203-206
Author(s):  
Jian Ye Guo ◽  
Yan Jin ◽  
Zhong Qi Sheng ◽  
Liang Zhao
Keyword(s):  
Machine Tool ◽  
Error Compensation ◽  
Inverse Kinematics ◽  
Theoretical Foundation ◽  
Mathematical Expression ◽  
Parallel Machine ◽  
Position Error ◽  
Kinematics Analysis ◽  
Independent Function ◽  
Parallel Machine Tool

This paper took one kind of 3-TPT Parallel Machine Tool (PMT) as the object of research. It mainly analyzed the influences of the position error of joint points in the fixed platform to the position error of tool of this PMT. Firstly, on the basis of introducing the structure of PMT, the kinematics of this machine was analyzed, and the inverse kinematics equation of this PMT was obtained. Then the influence situation of the position error of joint points in the fixed platform to the position error of tool was studied based on the kinematics analysis results and the error independent function principle, and the corresponding mathematical expression of error influence was established. Thus the theoretical foundation was laid for the comprehensive establishment of error model and the error compensation of this PMT

Study on the Accuracy of 3-RPS Parallel Machine Tools

2009 ◽  
Vol 407-408 ◽  
pp. 89-93
Author(s):  
Jun Xiong ◽  
Xian Guo Han ◽  
Wu Yi Chen
Keyword(s):  
Error Compensation ◽  
Geometrical Parameter ◽  
Machine Tools ◽  
Parallel Mechanism ◽  
Synthesis Method ◽  
Parallel Machine ◽  
Error Model ◽  
Geometrical Errors ◽  
Inverse Solutions ◽  
Parallel Machine Tools

According to the inverse solutions of 3-RPS parallel machine tools, the mapping relationship between the geometrical errors built on the 3-RPS parallel machine tools and errors of out posture has been created, then the error model of direct solutions including all the geometrical parameter errors has been built, and this model can be directly used to analyse the accuracy of parallel mechanism. On this basis, the algorithm about error compensation has been proposed. Moreover, accuracy synthesis of 3-RPS parallel machine tools was made respectively in probabilistic synthesis method and extreme synthesis method, and at last these two methods were compared.

The Prediction of Surface Roughness of Parallel Machine Tools Based on the Neural Network

2014 ◽  
Vol 556-562 ◽  
pp. 1328-1331
Author(s):  
Chang Long Zhao ◽  
Xue Song Guan
Keyword(s):  
Neural Network ◽  
Machine Tool ◽  
Machine Tools ◽  
High Speed ◽  
Parallel Machine ◽  
Processing Parameter ◽  
The Neural Network ◽  
Roughness Prediction ◽  
Parallel Machine Tools ◽  
Parallel Machine Tool

Because the parallel machine tool have high speed, high precision, high rigidity and the mechanical structure is simple, the parallel machine tool have been used in many field widely. In the research and application of parallel machine, the effect of processing parameter on machine processing is the most important problem. In the paper the improved artificial neural network is applied to the roughness prediction model of parallel machine tools, the model predict the roughness when the feed rate, spindle speed, processing angle and machining force are changed effectively.

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