A General Approach for Geometric Error Modeling of Lower Mobility Parallel Manipulators

2011 ◽  
Vol 3 (2) ◽  
Author(s):  
Haitao Liu ◽  
Tian Huang ◽  
Derek G. Chetwynd
Keyword(s):  
Systematic Approach ◽  
Parallel Manipulators ◽  
Geometric Error ◽  
Error Modeling ◽  
Kinematic Calibration ◽  
Accuracy Improvement ◽  
Linear Map ◽  
Homogeneous Transformation Matrix ◽  
Lower Mobility ◽  
Source Errors

This paper presents a general and systematic approach for geometric error modeling of lower mobility manipulators. The approach can be implemented in three steps: (1) development of a linear map between the pose error twist and source errors within an individual limb using the homogeneous transformation matrix method; (2) formulation of a linear map between the pose error twist and the joint error intensities of a lower mobility parallel manipulator; and (3) combination of these two models. The merit of this approach lies in that it enables the source errors affecting the compensatable and uncompensatable pose accuracy of the platform to be explicitly separated, thereby providing designers and/or field engineers with an informative guideline for the accuracy improvement achievable by suitable measures, i.e., component tolerancing in design, manufacturing and assembly processes, and kinematic calibration. Three typical and well-known parallel manipulators are taken as examples to illustrate the generality and effectiveness of this approach.

Geometric accuracy design and error compensation of a one-translational and three-rotational parallel mechanism with articulated traveling plate

2017 ◽  
Vol 232 (12) ◽  
pp. 2083-2097 ◽  
Author(s):  
Tao Sun ◽  
Panfeng Wang ◽  
Binbin Lian ◽  
Sida Liu ◽  
Yapu Zhai
Keyword(s):  
Error Compensation ◽  
Parallel Mechanism ◽  
Screw Theory ◽  
Geometric Error ◽  
Error Modeling ◽  
Geometric Errors ◽  
Kinematic Calibration ◽  
Geometric Accuracy ◽  
Improvement Strategy ◽  
Accuracy Improvement

The demands for advanced and flexible docking equipment are increasing in the fields of aerospace, shipbuilding and construction machinery. Position and orientation accuracy is one of the most important criteria, which would directly affect the docking quality. Taking a novel one-translational and three-rotational docking equipment, referred to as PaQuad parallel mechanism as example, this article proposed an accuracy improvement strategy by geometric accuracy design and error compensation. Drawing mainly on screw theory, geometric error modeling of PaQuad parallel mechanism was first carried out via four independent routes. Joint perturbations and geometric errors were included in each route error twist. Wrenches due to articulated traveling plate were applied to eliminate joint perturbations. Then, geometric accuracy design was implemented at component and substructure levels. The basic principle was to transfer geometric errors into dimensional or geometric tolerance. High-precision machining/assembling techniques were applied to satisfy the tolerance. Finally, error compensation resorting to kinematic calibration was implemented at mechanism level. It can be summarized as identification modeling, measurement planning, and parameter identification and modification. Maximum deviations of PaQuad parallel mechanism before calibration experiment were 0.01 mm, [Formula: see text], [Formula: see text], and [Formula: see text]. And they become 0.01 mm, [Formula: see text], [Formula: see text], and [Formula: see text] after kinematic calibration. Orientation accuracy of PaQuad parallel mechanism has improved one order of magnitude. It proves the effectiveness of accuracy improvement in terms of geometric accuracy design and error compensation.

A Dual Space Approach for Force/Motion Transmissibility Analysis of Lower Mobility Parallel Manipulators

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Haitao Liu ◽  
Manxin Wang ◽  
Tian Huang ◽  
Derek G. Chetwynd ◽  
Andrés Kecskeméthy
Keyword(s):  
Systematic Approach ◽  
Local Maximum ◽  
Parallel Manipulators ◽  
Joint Space ◽  
Unified Framework ◽  
Different Types ◽  
Indeterminate Form ◽  
Lower Mobility ◽  
Space Approach ◽  
Dimensional Optimization

By drawing on the duality of twist space and wrench space, this paper presents a general and systematic approach for force/motion transmissibility analysis of lower mobility nonredundant and nonoverconstrained parallel manipulators. This leads to the formulation of a complete and justifiable model that enables the force/motion transmissibility analysis to be integrated into a unified framework under the umbrella of a homogenous and decoupled linear transformation that maps the coordinates of the platform wrench/twist in the joint space to its natural coordinates in the operation space. Utilizing the penalty method to avoid the indeterminate form “0/0” when the local maximum of a virtual coefficient approaches zero, a set of dimensionally homogeneous transmission indices is proposed which can be employed for precisely representing the closeness to different types of singularities defined in twist space as well as for dimensional optimization. An example is given to illustrate the effectiveness of this approach.

scholarly journals Error Modeling and Sensitivity Analysis of a Five-Axis Machine Tool

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Wenjie Tian ◽  
Weiguo Gao ◽  
Wenfen Chang ◽  
Yingxin Nie
Keyword(s):  
Sensitivity Analysis ◽  
Machine Tool ◽  
Screw Theory ◽  
Geometric Error ◽  
Error Modeling ◽  
Analysis Method ◽  
Precision Design ◽  
Sensitivity Analysis Method ◽  
Source Errors ◽  
Five Axis

Geometric error modeling and its sensitivity analysis are carried out in this paper, which is helpful for precision design of machine tools. Screw theory and rigid body kinematics are used to establish the error model of an RRTTT-type five-axis machine tool, which enables the source errors affecting the compensable and uncompensable pose accuracy of the machine tool to be explicitly separated, thereby providing designers and/or field engineers with an informative guideline for the accuracy improvement by suitable measures, that is, component tolerancing in design, manufacturing, and assembly processes, and error compensation. The sensitivity analysis method is proposed, and the sensitivities of compensable and uncompensable pose accuracies are analyzed. The analysis results will be used for the precision design of the machine tool.

scholarly journals Study of error modeling in kinematic calibration of parallel manipulators

2016 ◽  
Vol 13 (5) ◽  
pp. 172988141667256 ◽  
Author(s):  
Liping Wang ◽  
Yuzhe Liu ◽  
Jun Wu ◽  
Jinsong Wang ◽  
Binbin Zhang
Keyword(s):  
Parallel Manipulators ◽  
Error Modeling ◽  
Kinematic Calibration

Modeling Quasi-Static Errors in a Five-Axis Gantry Machine Tool

2012 ◽  
Vol 152-154 ◽  
pp. 781-787
Author(s):  
Jian Yin ◽  
Ming Li ◽  
Fang Yu Pan
Keyword(s):  
Machine Tool ◽  
Thermal Error ◽  
Geometric Error ◽  
Error Model ◽  
Error Modeling ◽  
Compensation Scheme ◽  
Homogeneous Transformation Matrix ◽  
Body Kinematic ◽  
Five Axis ◽  
Gantry Machine Tool

Enhancing the accuracy of machine tool is a key goal of machine tool manufactures and users. To characterize the Quasi-static errors and then use software compensation is an important step for accuracy enhancement. The effectiveness of an error compensation scheme relies heavily on the error model. The model must be concise and roust which can be applied to any machine tool. The total Quasi-static errors within the workspace of a five-axis gantry machine tool is composed of geometric error, kinematic error, thermal error. This paper presents an error model which can be used for practical compensation scheme. Homogeneous transformation matrix, rigid body kinematic and small angle approximations are used in this paper for error modeling.

A Systematic Approach for Accuracy Design of Lower-Mobility Parallel Mechanism

Robotica ◽  
2020 ◽  
Vol 38 (12) ◽  
pp. 2173-2188
Author(s):  
Wenjie Tian ◽  
Ziqian Shen ◽  
Dongpo Lv ◽  
Fuwen Yin
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Geometric Error ◽  
Error Modeling ◽  
Tolerance Allocation ◽  
Design Stage ◽  
Geometric Errors ◽  
End Effector ◽  
Allocation Method ◽  
Lower Mobility

SUMMARYGeometric accuracy is a critical performance factor for parallel robots, and regardless of error compensation, accuracy design or tolerance allocation is another way to ensure the pose accuracy of a robot at design stage. A general method of both geometric error modeling and accuracy design of lower-mobility parallel mechanisms is presented. First, a general approach for error modeling of lower-mobility parallel mechanism is proposed based on screw theory, and then the geometric errors affecting the compensatable and uncompensatable accuracy of the end-effector are separated using the properties of dual vector space. The pose error aroused by compensatable geometric errors can be compensated via kinematic calibration, while the uncompensatable geometric errors should be minimized during the manufacturing and assembly processes. Based on that, the tolerance allocation method is presented, giving each uncompensatable geometric error a proper tolerance by the use of reliability theory. Compared with the traditional tolerance allocation method, the advantages of the proposed method are as follows: the number of geometric errors to be allocated is greatly reduced; the results of serialized tolerance allocation can be obtained according to different reliability indices of pose accuracy of end-effector for designers to choose; on the premise of guaranteeing the same pose accuracy of end-effector, the allocated tolerances are loose and easy to realize. Finally, the proposed methods are successfully applied to an R(2-RPS&RP)&UPS lower-mobility parallel robot, and the effectiveness and practicability of the proposed method are verified.

scholarly journals Kinematic calibration of Delta robot using distance measurements

2015 ◽  
Vol 230 (3) ◽  
pp. 414-424 ◽  
Author(s):  
Pujun Bai ◽  
Jiangping Mei ◽  
Tian Huang ◽  
Derek G Chetwynd
Keyword(s):  
Real Time ◽  
Error Compensation ◽  
Error Modeling ◽  
Laser Tracker ◽  
Kinematic Calibration ◽  
Time Error ◽  
Distance Measurements ◽  
Positioning Accuracy ◽  
Delta Robot ◽  
Source Errors

This paper deals with kinematic calibration of the Delta robot using distance measurements. The work is mainly placed upon: (1) the error modeling with a goal to classify the source errors affecting both the compensatable and uncompensatable pose accuracy; (2) the full/partial source error identification using a set of distance measurements acquired by a laser tracker; and (3) design of a linearized compensator for real-time error compensation. Experimental results on a prototype show that positioning accuracy of the robot can significantly be improved by the proposed approach.

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