A New Kinematic Error Modelling and Identification Method of the Parallel Manipulator

2020 ◽  
Author(s):  
Weitao Li ◽  
Liping Wang
Keyword(s):  
Parallel Manipulators ◽  
Kinematic Error ◽  
Basic Error ◽  
Error Identification ◽  
Partial Differentiation ◽  
Differentiation Method ◽  
Modelling Method ◽  
Error Terms ◽  
Kinematic Error Model ◽  
Identification Model

Abstract Parallel manipulators have broad application prospects on hybrid machine tools. Kinematic error modelling and identification are two key processes to improve the accuracy of parallel manipulators. The traditional kinematic error modelling method adopts the partial differentiation of the ideal kinematic model. However, the partial differentiation method is pure mathematical calculation, which ignores physical meaning of error terms corresponding to each link. In the process of error identification, the Jacobian matrix obtained from the partial differentiation method is usually ill-conditioned, which leads to non-convergence of the identification process. In order to solve the above problems, this paper proposes a new kinematic error modelling method and an error identification model. Firstly, the basic error terms for single link are analyzed. Based on basic error terms, the kinematic error model is established by using the practical connection point of two adjacent links. Then, a new error identification model is derived from the kinematic error model. Finally, as a study case, a 3-DOF parallel tool head is used to verify the correctness of the proposed method. The numerical results show that the proposed method is effective and the accuracy of the 3-DOF parallel tool head improves significantly after compensation of error terms.

Unified Solving Jacobian∕Hessian Matrices of Some Parallel Manipulators With n SPS Active Legs and a Passive Constrained Leg

2006 ◽  
Vol 129 (11) ◽  
pp. 1161-1169 ◽  
Author(s):  
Yi Lu ◽  
Bo Hu
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Hessian Matrix ◽  
Parallel Manipulators ◽  
Simple Approach ◽  
Spherical Joint ◽  
Load Bearing ◽  
Prismatic Joint ◽  
First Order ◽  
Partial Differentiation

Some parallel manipulators with n spherical joint-prismatic joint-spherical joint (SPS)-type active legs and a passive constrained leg possess a larger capability of load bearing and are simple in structure of the active leg. In this paper, a unified and simple approach is proposed for solving Jacobian∕Hessian matrices and inverse∕forward velocity and acceleration of this type of parallel manipulators. First, a general parallel manipulator with n SPS-type active legs and one passive constrained leg in various possible serial structure is synthesized, and some formulae for solving the poses of constrained force∕torque and active∕constrained force matrix are derived. Second, the formulae for solving extension of active legs, the auxiliary velocity∕acceleration equation are derived. Third, the formulae for solving inverse∕forward velocity and acceleration and a Jacobian matrix without the first-order partial differentiation and a Hessian matrix without the second-order partial differentiation are derived. Finally, the procedure is applied to three parallel manipulators with four and five SPS-type active legs and one passive constrained leg in different serial structures and to illustrate.

Complete, Minimal and Continuous Kinematic Error Models of Perfect Multi-DOF Joints for Parallel Manipulators

2020 ◽  
Author(s):  
Lingyu Kong ◽  
Genliang Chen ◽  
Zhuang Zhang ◽  
Anhuan Xie ◽  
Hao Wang ◽  
...  
Keyword(s):  
Parallel Manipulators ◽  
Error Model ◽  
Parallel Robots ◽  
Kinematic Error ◽  
Kinematic Calibration ◽  
Calibration Result ◽  
Calibration Methods ◽  
Manufacturing Errors ◽  
The One ◽  
Serial Chains

Abstract Kinematic error model plays an important role in improving the positioning accuracy of robot manipulators by kinematic calibration. In order to get a better calibration result, the error model should satisfy complete, minimal and continuous criteria. In order to meet the complete requirement, the multi degree-of-freedom (DOF) joints, such as universal or spherical joint in parallel robots, have to be regarded as serial chains formed by multiple independent single DOF joints, such that the manufacturing errors of these joints can be considered. However, several previous work found that these manufacturing errors for some parallel manipulators have little effect on the accuracy improvement. Besides, considering these kind of errors will cause the kinematics to be much more complicated. Therefore, under the assumptions of perfectly manufactured universal, spherical and cylinder joints, a complete, minimal and continuous (CMC) error model is presented in this paper. The identifiability of the kinematic errors of these multi-DOF joints are analytically analyzed. In order to verify the correctness and effectiveness of the proposed method, a numerical simulation of kinematic calibration is conducted on a 6-UPS parallel manipulator. The calibration result is also compared to the one derived from the error model with 138 error parameters. Since the error model and calibration methods are described uniformly, it can be applied to most parallel manipulators.

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.

Mathematical Model for the Effect of Dynamic Parameter Posed on Free Floating Space Manipulator’s Kinematic Accuracy

2011 ◽  
Vol 216 ◽  
pp. 254-260 ◽  
Author(s):  
Yue Sheng Tan
Keyword(s):  
Screw Theory ◽  
Error Model ◽  
Space Robot ◽  
Structural Parameter ◽  
Kinematic Error ◽  
Space Manipulator ◽  
Error Sources ◽  
Kinematic Accuracy ◽  
Mass Error ◽  
Kinematic Error Model

Aiming at kinematic accuracy and its’ error sources of a free floating space robot, a mathematical kinematic error model based on the concept of virtual manipulator and screw theory is proposed in this paper for a free-floating space robot. Based on screw theory, structural parameters in the form of motion screw and their error expressions derived from various error sources are deduced. The effect of mass error, CM (Center of Mass) error and structural parameter error on the kinematic accuracy of the free-floating space manipulator is analyzed. A simulation is demonstrated for verifying the correctness of the kinematic error model and the effect of various error sources on the free-floating space robot. The error model and the result deriving from analyzing are vital for studying the kinematic accuracy of the space manipulator when it is under a free-floating mode, and for controlling and assigning various errors when a space robot is developed.

Characterization of Kinematic Error Model Consistency for Five-Axis Machine Tools

2018 ◽  
Author(s):  
Le Ma ◽  
Douglas A. Bristow ◽  
Robert G. Landers
Keyword(s):  
Machine Tool ◽  
Machine Tools ◽  
Error Model ◽  
Data Sets ◽  
Kinematic Error ◽  
Interior Space ◽  
Error Models ◽  
Wide Range ◽  
Kinematic Error Model ◽  
Five Axis

New metrology tools, such as laser trackers, are enabling the rapid collection of machine tool geometric error over a wide range of the workspace. Error models fit to this data are used to compensate for high-order geometric errors that were previously challenging to obtain due to limited data sets. However, model fitting accuracy can suffer near the edges of the measurable space where obstacles and interference of the metrology equipment can make it difficult to collect dense data sets. In some instances, for example when obstacles are permanent fixtures, these locations are difficult to measure but critically important for machining, and thus models need to be accurate at these locations. In this paper, a method is proposed to evaluate the model accuracy for five-axis machine tools at measurement boundaries by characterizing the statistical consistency of the model fit over the workspace. Using a representative machine tool compensation method, the modeled Jacobian matrix is derived and used for characterization. By constructing and characterizing different polynomial order error models, it is observed that the function behavior at the boundary and in the unmeasured space is inconsistent with the function behavior in the interior space, and that the inconsistency increases as the polynomial order increases. Also, the further the model is extrapolated into unmeasured space, the more inconsistent the kinematic error model behaves.

Research on the Hybrid Modelling Method Based on Mechanism and Identification for Marine Diesel

2012 ◽  
Vol 241-244 ◽  
pp. 1514-1519 ◽  
Author(s):  
Qing Fu Kong ◽  
Fan Ming Zeng ◽  
Jia Ming Wu ◽  
Jie Chang Wu
Keyword(s):  
Neural Network ◽  
Hybrid Model ◽  
System Modelling ◽  
Hybrid Modelling ◽  
Mechanism Model ◽  
Modelling Method ◽  
Marine Diesel ◽  
Network Identification ◽  
Accuracy Performance ◽  
Identification Model

Mechanism method and neural network identification method are widely used for system modelling. Due to the complexity of actual investigated objects, models built with individual method are usually not good enough for the problems to be solved. Therefore, a hybrid modelling method based on mechanism and identification is presented in the paper. In the hybrid model, the mechanism model is applied as the fundamental model in order to ensure the overall coincidence performance and the identification model is adopted as the compensated model in order to ensure the accuracy performance. The developing process of the hybrid model of a marine turbo-charged diesel is demonstrated in detail in the paper. Testing result shows that the hybrid modelling method is very suitable for modelling complex investigated objects.

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