Kinematic Error Analysis of Parallel Machine Tool Based on Rigid Body Dynamics

2015 ◽  
Vol 743 ◽  
pp. 71-78
Author(s):  
Xiao Gang Chen ◽  
Zhao Tang Xu ◽  
Hai Bing Wu
Keyword(s):  
Rigid Body ◽  
Machine Tool ◽  
Parallel Machine ◽  
Position Error ◽  
Rigid Body Dynamics ◽  
Friction Forces ◽  
Analytical Expression ◽  
Body Dynamics ◽  
Position And Orientation ◽  
Parallel Machine Tool

To estimate influence of velocity on kinematic accuracy for a cross-linked Stewart type Parallel Machine Tool, position and orientation errors of the moving tool platform are researched. Based on rigid body dynamics, inertial and friction forces and moments are considered. Firstly, analytical expression of driving force is derived for each link. Secondly, change of length is derived using Hooke’s Law for each link. Then mapping matrix between change of link length and change of platform position and orientation is derived based on both Euler angle and revolving angle around a spatial axis. Finally, analytical expression of position and orientation errors of the moving platform is derived. Figures of distribution of position and orientation errors in workspace under two velocities are obtained respectively. The results show that, in frequently used workspace, all of the three components of position error are less than 3.5μm. All of them increase with z coordinate of platform center. Position error is influenced slightly by velocity. The difference of position error between two velocities is less than 2%.

scholarly journals Slipping–rolling transitions of a body with two contact points

2021 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Rigid Body ◽  
Contact Point ◽  
Static Friction ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Friction Forces ◽  
Contact Points ◽  
Body Dynamics ◽  
Coulomb Model ◽  
Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

Kinematic Analysis of a Four Degreed-of-Freedoms Hybrid Machine Tool

2011 ◽  
Vol 204-210 ◽  
pp. 1651-1654
Author(s):  
Yan Fei Zhang ◽  
Jin Liang Gong ◽  
Xiu Ting Wei
Keyword(s):  
Machine Tool ◽  
Machine Tools ◽  
Parallel Machine ◽  
Spherical Joint ◽  
Kinematic Modeling ◽  
Hybrid Machine Tool ◽  
Hybrid Mechanism ◽  
Hybrid Machine ◽  
Position And Orientation ◽  
Parallel Machine Tool

On one hand, parallel machine tool enjoys many advantages over conventional serial counterpart, on the other hand, it also suffers from the disadvantages of coupled position and orientation, difficulty in kinematic modeling, strict requirements for components and difficulty in manufacturing of the spherical joint adopted in some limbs. Hybrid mechanism, however, will serve the turn in some cases. By using a three degree-of-freedoms parallel mechanism and a slide worktable which will fulfill one movement, a novel four degree-of-freedoms hybrid machine tool is put forward. The kinematic solutions are analyzed and closed-form kinematic solutions are given. The methods and theories adopted here can be used for design of other types of hybrid machine tools.

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

New solutions of classical problems in rigid body dynamics

2015 ◽  
Vol 69 ◽  
pp. 40-44
Author(s):  
H.M. Yehia ◽  
E. Saleh ◽  
S.F. Megahid
Keyword(s):  
Rigid Body ◽  
Rigid Body Dynamics ◽  
Body Dynamics
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