scholarly journals Lagrangian Dynamics Analysis of a XY-Theta Parallel Robotic Machine Tool

2017 ◽  
Vol 61 (2) ◽  
pp. 107 ◽  
Author(s):  
Javad Enferadi ◽  
Mohammad Tavakolian
Keyword(s):  
Machine Tool ◽  
Inverse Kinematics ◽  
Good Accuracy ◽  
Inverse Dynamics ◽  
Constraint Forces ◽  
Lagrangian Multipliers ◽  
Motion Equations ◽  
The Subject ◽  
Parallel Machine Tool ◽  
Dynamics Problems

Dynamics of a highly stiff parallel machine tool is the subject of this paper. High stiffness, good accuracy, relatively large workspace and free of singularities on the whole workspace makes the manipulator suitable for machining applications as an XY-Theta precision table. First, obtaining kinematics constraints, inverse kinematics analysis and velocity analysis are performed. Next, using six redundant generalized coordinates, we obtain Lagrangian of the manipulator. Also, a Lagrangian approach is proposed to obtain dynamics equations of the machine tool using three Lagrangian multipliers. This method allows elimination of constraint forces and moments at the joints from the motion equations. Dynamic equations of the manipulator are formed as inverse dynamics and direct dynamics problems. Finally, two examples are presented that confirms the obtained dynamics equations.

Kinematic Analysis of 5-UPS Parallel Machine Tool Based on Adams

2014 ◽  
Vol 644-650 ◽  
pp. 215-219 ◽  
Author(s):  
Lin Cai
Keyword(s):  
Mathematical Model ◽  
Machine Tool ◽  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Machine ◽  
Inverse Solution ◽  
Robot Kinematics ◽  
Vector Method ◽  
Parallel Machine Tool ◽  
The Mathematical Model

In this paper, the kinematics of 5-UPS parallel machine tool is analyzed, and a kinematic analysis method combining kinematic analysis and computer kinematics software is proposed. Under the premise that the parallel machine tool sector parameters is known, firstly we use the vector method to establish a mathematical model of inverse kinematics, and in accordance with a U-shaped processing trajectory the inverse solution is calculated; Secondly, three-dimensional model of the parallel machine tool is modeled in Adams, and kinematic constraints are set correctly; Finally, the inverse kinematics solution of the mathematical model is used as the Adams drive input, then the positive solutions is carried out. Compared through the Adams simulation results with U-machining path, it is verified that the inverse solution of the mathematical model and parallel machine tool bodies both are correct, it has certain significance for Parallel machine tools and other parallel robot kinematics analysis.

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

The Kinematic Analysis of a Novel Parallel Machine Tool with 3-HSS Structure

2006 ◽  
Vol 532-533 ◽  
pp. 797-800 ◽  
Author(s):  
Tie Hong Gao ◽  
Chang Juan Yu ◽  
Jiang Bo Qi ◽  
Jun Yi Cao
Keyword(s):  
Machine Tool ◽  
Inverse Kinematics ◽  
Simple Structure ◽  
Three Dimensional ◽  
Complex Surface ◽  
Parallel Machine ◽  
Rotary Table ◽  
Kinematics Modeling ◽  
Parallel Machine Tool ◽  
Cutter Position

A novel parallel machine tool(PMT) with 3-HSS structure is presented in this paper. The three ball screws and guiding-parallels of this PMT are horizontally and parallel set. The three helix joints are driving components connected to and driven by servos, and the corresponding parameters of the cutter position can be obtained. The kinematics modeling is simple and the direct and inverse kinematics can be easily obtained for this PMT. It also has other advantages, such as spacious workspace in horizon direction, simple structure, easy controlling, etc. This PMT can be used in three-dimensional carving, milling and other machining processing. This kind of PMT has been designed and manufactured in our institution, and has also been tested successfully. Besides, it’s easy to get the 5-DOF series-parallel machine tool through fixing two more revolving structure on the mobile platform. It’s also easy to furnish complex surface processing using a rotary table. This paper studies mainly on DOF analysis, derivation of the kinematical equation, direct and inverse kinematics, workspace and other kinematical problems of the parallel machine.

Effect of guide rail profile errors on the motion accuracy for a heavy-duty hydrostatic turntable

2019 ◽  
Vol 233 (15) ◽  
pp. 5350-5362 ◽  
Author(s):  
Yongsheng Zhao ◽  
Hongchao Wu ◽  
Congbin Yang ◽  
Ligang Cai ◽  
Zhifeng Liu
Keyword(s):  
Machine Tool ◽  
Reynolds Equation ◽  
Machining Accuracy ◽  
Guide Rail ◽  
Heavy Duty ◽  
Motion Equations ◽  
Rotating Speed ◽  
Proposed Model ◽  
Reaction Forces ◽  
Profile Errors

The motion accuracy of hydrostatic turntable is the key in improving the machining accuracy of heavy-duty machine tool. However, the motion accuracy of hydrostatic turntable depends not only on the offset load but also on the rotating speed of the turntable as well as the profile errors of the guide rails. In this paper, a simulation model is developed to analyze the effect of guide rail profile errors on the motion accuracy of hydrostatic turntable. The reaction forces of preload thrust bearing and hydrostatic circular oil pads are obtained based on the Reynolds equation of the lubricant film. The motion equations of hydrostatic turntable are derived in which the profile errors of two guide rails are considered. The results show that the motion accuracy of hydrostatic turntable can be affected by wavelength, amplitude of profile errors and speed, and offset load of turntable. Finally, the motion accuracy of heavy-duty hydrostatic turntable used in XCKA28105 type turning and milling composite machine tool is obtained by using the presented method. Comparing with the experimental results, the proposed model can be used to predict the machining accuracy caused by the profile errors of guide rails for any heavy-duty hydrostatic turntable.

Effects of Dynamic Model Errors in Task-Priority Operational Space Control

Robotica ◽  
2021 ◽  
pp. 1-12
Author(s):  
Paolo Di Lillo ◽  
Gianluca Antonelli ◽  
Ciro Natale
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Null Space ◽  
Control Algorithms ◽  
Model Errors ◽  
Operational Space ◽  
Dynamic Level ◽  
Concurrent Tasks ◽  
Modeling Errors

SUMMARY Control algorithms of many Degrees-of-Freedom (DOFs) systems based on Inverse Kinematics (IK) or Inverse Dynamics (ID) approaches are two well-known topics of research in robotics. The large number of DOFs allows the design of many concurrent tasks arranged in priorities, that can be solved either at kinematic or dynamic level. This paper investigates the effects of modeling errors in operational space control algorithms with respect to uncertainties affecting knowledge of the dynamic parameters. The effects on the null-space projections and the sources of steady-state errors are investigated. Numerical simulations with on-purpose injected errors are used to validate the thoughts.

Oppositely oriented series multiple tuned mass dampers and application on a parallel machine tool

2022 ◽  
Vol 163 ◽  
pp. 108196
Author(s):  
Wenshuo Ma ◽  
Xiaoliang Jin ◽  
Jingjun Yu ◽  
Yiqing Yang ◽  
Xinjun Liu ◽  
...  
Keyword(s):  
Machine Tool ◽  
Parallel Machine ◽  
Tuned Mass Dampers ◽  
Parallel Machine Tool ◽  
Multiple Tuned Mass Dampers
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