A New Method for Error Modeling in the Kinematic Calibration of Redundantly Actuated Parallel Kinematic Machine

2020 ◽  
Author(s):  
Lei-Ying He ◽  
Zhen-Dong Wang ◽  
Qin-Chuan Li ◽  
Xin-Xue Chai
Keyword(s):  
Error Model ◽  
Error Modeling ◽  
New Method ◽  
Forward Kinematics ◽  
Kinematic Calibration ◽  
Parallel Kinematic Machine ◽  
Orientation Error ◽  
Redundantly Actuated ◽  
Parallel Kinematic ◽  
Moving Platform

Abstract This paper presents a new method for error modeling and studies the kinematic calibration of redundantly actuated parallel kinematic machines (RA-PKM). First, a n-DOF RA-PKM is split into several n-DOF non-redundantly actuated sub-mechanisms by removing actuators in limbs in an ergodic manner without changing the DOF. The error model of the sub-mechanisms is established by differentiating the forward kinematics. Then, the complete error model of the RA-PKM is obtained by a weighted summation of errors for all sub-mechanisms. Finally, a kinematic calibration experiments are performed on a 3-DOF RA-PKM to verify the method of error modeling. The positioning and orientation error of the moving platform is replaced by the positioning error of the tool center point, which was reduced considerably from 3.427 mm to 0.177 mm through kinematic calibration. The experimental results demonstrate the improvement of the kinematic accuracy after kinematic calibration using the proposed error modeling method.

Kinematic calibration of the 3-degree-of-freedom redundantly actuated spatial parallel module of a five-axis hybrid machine

2020 ◽  
Vol 234 (9) ◽  
pp. 1185-1197
Author(s):  
Xuan Luo ◽  
Fugui Xie ◽  
Xin-Jun Liu
Keyword(s):  
Error Model ◽  
Error Modeling ◽  
Kinematic Calibration ◽  
Bilinear Interpolation ◽  
Position Errors ◽  
Redundantly Actuated ◽  
Parallel Module ◽  
Hybrid Machine ◽  
Five Axis ◽  
Active Joints

As a new type of manufacturing equipment, redundant hybrid machines have the theoretical advantage over the traditional serial machines in efficiently processing large structural parts with high material removal ratio and complex parts with curved surfaces. In order to solve the accuracy problem of the redundantly actuated spatial parallel module of a five-axis hybrid machine, an improved kinematic calibration method is proposed in this article. First, different from error modeling for the corresponding non-redundant parallel module, the geometric error model of the redundantly actuated spatial parallel module considers the deformations at active joints caused by actuation redundancy as an error source. Then, the applicable error model is developed using projection technique to remove the need of active joints’ stiffness measurement or modeling. Later, the practical error model is derived from model reduction method to avoid using additional sensors or gratings. Finally, three forms of relative measurement and step identification are adopted for the calibration work, and the bilinear interpolation compensation function is introduced to ensure the calibration effect. On this basis, the kinematic calibration of the redundantly actuated spatial parallel module is conducted. The max position errors are reduced from original −0.192 to 0.075 mm after RM1 and SI1, and then further reduced to 0.014 mm after bilinear interpolation compensation, while the max orientation errors are reduced from −0.017° and 0.249° to −0.005° and −0.007° after RM2 and SI2, and RM3 and SI3, respectively. A contrasting experiment is also carried out with the previous method for the corresponding non-redundant parallel module. As a result, the proposed method shows better convergence value and speed in identifying error parameters, and therefore the effectiveness and efficiency of the proposed method for the redundantly actuated spatial parallel module are validated.

Kinematic calibration of a 5-DoF parallel kinematic machine

2016 ◽  
Vol 45 ◽  
pp. 242-261 ◽  
Author(s):  
Yimin Song ◽  
Jiateng Zhang ◽  
Binbin Lian ◽  
Tao Sun
Keyword(s):  
Kinematic Calibration ◽  
Parallel Kinematic Machine ◽  
Parallel Kinematic

Complete kinematic calibration of a 6-RRRPRR parallel kinematic machine based on the optimal measurement configurations

2019 ◽  
Vol 234 (1) ◽  
pp. 121-136 ◽  
Author(s):  
Chunyang Han ◽  
Yang Yu ◽  
Zhenbang Xu ◽  
Xiaoming Wang ◽  
Peng Yu ◽  
...  
Keyword(s):  
Kinematic Model ◽  
Inverse Kinematic ◽  
Error Model ◽  
Kinematic Calibration ◽  
Universal Joint ◽  
Parallel Kinematic Mechanism ◽  
Simulation And Experiment ◽  
Parallel Kinematic ◽  
Kinematic Mechanism ◽  
Selection Of

This paper presents a kinematic calibration of a 6-RRRPRR parallel kinematic mechanism with offset RR-joints that would be applied in space positioning field. In order to ensure highly accurate and highly effective calibration process, the complete error model, which contains offset universal joint errors, is established by differentiating inverse kinematic model. A calibration simulation comparison with non-complete error model shows that offset universal joint errors are crucial to improve the calibration accuracy. Using the error model, an optimal calibration configuration selection algorithm is developed to determine the least number of measurement configurations as well as the optimal selection of these configurations from the feasible configuration set. To verify the effectiveness of kinematic calibration, a simulation and experiment were performed. The results show that the developed approach can effectively improve accuracy of a parallel kinematic mechanism with relatively low number of calibration configurations.

Geometry and Kinematic Analysis of a Redundantly Actuated Parallel Mechanism for Rehabilitation

2007 ◽  
Author(s):  
Jody A. Saglia ◽  
Jian S. Dai
Keyword(s):  
Control System ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Forward Kinematics ◽  
Control System Design ◽  
Ankle Rehabilitation ◽  
Redundantly Actuated ◽  
Moving Platform

This paper presents the geometry and the kinematic analysis of a parallel manipulator developed for ankle rehabilitation, as the beginning of a control system design process. First the geometry of the parallel mechanism is described, secondly the equations for the inverse and the forward kinematics are obtained, then the forward kinematics is analyzed in order to define all the possible configurations of the moving platform. Finally the Jacobian matrix of the rig is obtained by differentiating the position equations and the singularities are investigated, comparing the non-redundant and redundant type of mechanism.

A Comprehensive Numerical Study on the Number of Identifiable Kinematic Parameters of Parallel Mechanisms

2021 ◽  
Author(s):  
Lingyu Kong ◽  
Genliang Chen ◽  
Guanyu Huang ◽  
Sumian Song ◽  
Anhuan Xie ◽  
...  
Keyword(s):  
Numerical Study ◽  
Error Model ◽  
Error Modeling ◽  
Kinematic Error ◽  
Kinematic Calibration ◽  
Parallel Mechanisms ◽  
Kinematic Parameters ◽  
Positioning Accuracy ◽  
Prismatic Joints ◽  
Kinematic Error Model

Abstract Kinematic error model plays an important role in improving the positioning accuracy of robot manipulators by kinematic calibration. The identifiability of kinematic parameters in the error model directly affects the positioning accuracy of the mechanism. And the number of identifiable kinematic parameters determines how many parameters can be accurately identified by kinematic calibration, which is one of the theoretical basis of kinematic error modeling. For serial mechanisms, a consensus has been reached that the maximum number of identifiable kinematic parameters is 4R + 2P + 6, where R and P represent the numbers of revolute and prismatic joints, respectively. Due to complex topologies of parallel mechanisms, there is still no agreement on the formula of the maximum number of identifiable parameters. In this paper, a comprehensive numerical study on the number of identifiable kinematic parameters of parallel mechanisms is conducted. The number of identifiable parameters of 3802 kinds of limbs with different types or actuation arrangements are analyzed. It can be concluded that the maximum number of identifiable kinematic parameters is Σ i = 1 n 4Ri + 2Pi + 6 − Ci − 2(PP)i/3(PPP1)i/(2Ri + 2Pi)(PPP)i, where Ci represents the number of joints whose motion cannot be measured and n denotes the number of limbs in a parallel mechanism; (PP)i, (PPP1)i, and (PPP)i represent two consecutive unmeasurable P joints, three consecutive P joints in which two of them cannot be measured, and three unmeasurable P joints, respectively.

Error modeling and sensitivity analysis of a novel 5-degree-of-freedom parallel kinematic machine tool

2018 ◽  
Vol 233 (6) ◽  
pp. 1637-1652 ◽  
Author(s):  
Xuan Luo ◽  
Fugui Xie ◽  
Xin-Jun Liu ◽  
Jie Li
Keyword(s):  
Sensitivity Analysis ◽  
Machine Tool ◽  
Jacobian Matrix ◽  
Error Modeling ◽  
Degree Of Freedom ◽  
Geometric Errors ◽  
Parallel Kinematic Machine ◽  
Parallel Kinematic ◽  
Position And Orientation ◽  
Five Axis

5-Degree-of-freedom parallel kinematic machine tools are always attractive in manufacturing industry due to the ability of five-axis machining with high stiffness/mass ratio and flexibility. In this article, error modeling and sensitivity analysis of a novel 5-degree-of-freedom parallel kinematic machine tool are discussed for its accuracy issues. An error modeling method based on screw theory is applied to each limb, and then the error model of the parallel kinematic machine tool is established and the error mapping Jacobian matrix of 53 geometric errors is derived. Considering that geometric errors exert both impacts on value and direction of the end-effector’s pose error, a set of sensitivity indices and an easy routine for sensitivity analysis are proposed according to the error mapping Jacobian matrix. On this basis, 10 vital errors and 10 trivial errors are identified over the prescribed workspace. To validate the effects of sensitivity analysis, several numerical simulations of accuracy design are conducted, and three-dimensional model assemblies with relevant geometric errors are established as well. The simulations exhibit maximal −0.10% and 0.34% improvements of the position and orientation errors, respectively, after modifying 10 trivial errors, while minimal 65.56% and 55.17% improvements of the position and orientation errors, respectively, after modifying 10 vital errors. Besides the assembly reveals an output pose error of (0.0134 mm, 0.0020 rad) with only trivial errors, while (2.0338 mm, 0.0048 rad) with only vital errors. In consequence, both results of simulations and assemblies validate the correctness of the sensitivity analysis. Moreover, this procedure can be extended to any other parallel kinematic mechanisms easily.

1321 A Kinematic Calibration Method under the Cancellation of Gravity-induced Errors on a Hexapod-type Parallel Kinematic Machine Tool

2005 ◽  
Vol 2005.80 (0) ◽  
pp. _13-41_-_13-42_
Author(s):  
Takeshi YOKAWA ◽  
Soichi IBARAKI ◽  
Atsushi MATSUBARA ◽  
Masao NAKAGAWA ◽  
Tetsuya MATSUSHITA
Keyword(s):  
Machine Tool ◽  
Calibration Method ◽  
Kinematic Calibration ◽  
Parallel Kinematic Machine ◽  
Parallel Kinematic
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