scholarly journals A Kinematic Calibration Method of a 3T1R 4-Degree-of-Freedom Symmetrical Parallel Manipulator

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 357
Author(s):  
Fengxuan Zhang ◽  
Silu Chen ◽  
Yongyi He ◽  
Guoyun Ye ◽  
Chi Zhang ◽  
...  
Keyword(s):  
Parallel Manipulator ◽  
Kinematic Model ◽  
Calibration Method ◽  
Error Modeling ◽  
Degree Of Freedom ◽  
Least Square ◽  
Kinematic Calibration ◽  
Recursive Least Square ◽  
Local Product ◽  
Branched Chain

This paper proposes a method for kinematic calibration of a 3T1R, 4-degree-of-freedom symmetrical parallel manipulator driven by two pairs of linear actuators. The kinematic model of the individual branched chain is established by using the local product of exponentials formula. Based on this model, the model of the end effector’s pose error is established from a pair of symmetrical branched chains, and a recursive least square method is applied for the parameter identification. By installing built-in sensors at the passive joints, a calibration method for a serial manipulator is eventually extended to this parallel manipulator. Specifically, the sensor installed at the second revolute joint of each branched chain is saved, replaced by numerical calculation according to kinematic constraints. The simulation results validate the effectiveness of the proposed kinematic error modeling and identification methods. The procedure for pre-processing compensation on this 3T1R parallel manipulator is eventually given to improve its absolute positioning accuracy, using the inverse of the calibrated kinematic model.

CALIBRATION OF THE 3-PRS PARALLEL MANIPULATOR USING A MOTION CAPTURE SYSTEM

2005 ◽  
Vol 29 (4) ◽  
pp. 645-654
Author(s):  
C.G. van Driel ◽  
Juan A. Carretero
Keyword(s):  
Motion Capture ◽  
Parallel Manipulator ◽  
Kinematic Model ◽  
Calibration Method ◽  
Kinematic Calibration ◽  
Virtual Model ◽  
Motion Capture System ◽  
Parallel Mechanisms ◽  
Kinematic Parameters ◽  
Preliminary Testing

In this paper, a kinematic calibration method for the 3-PRS parallel manipulator using a motion capture system is presented. Although parallel mechanisms present numerous advantages over their serial counterparts, an accurate kinematic model must be developed to facilitate their operation. Kinematic calibration is used to accurately determine the kinematic parameters of the kinematic model to improve the overall accuracy of the mechanism. The kinematic calibration of the 3-PRS parallel manipulator will be examined by identification of the manipulator's kinematic parameters, an introduction to the motion capture system used, and the presentation of die calibration method itself. For preliminary testing purposes, a virtual model of the manipulator has been generated in CAD to validate the calibration method. The calibration method initially determines the joint locations and orientations, from which the remaining kinematic parameters can be resolved. Preliminary testing using the virtual model indicates the method is valid and can accurately determine the modelled parameters. Once the physical manipulator is operational, alterations the calibration method will be required to account for manufacturing and assembly tolerances/errors, joint offsets and noise during the static captures.

Kinematic calibration and error compensation of a hexaglide parallel manipulator

2017 ◽  
Vol 233 (1) ◽  
pp. 215-225 ◽  
Author(s):  
Jiangzhen Guo ◽  
Dan Wang ◽  
Rui Fan ◽  
Wuyi Chen ◽  
Guohua Zhao
Keyword(s):  
Error Compensation ◽  
Parallel Manipulator ◽  
Least Squares Method ◽  
Orthogonal Design ◽  
Kinematic Model ◽  
Calibration Method ◽  
High Accuracy ◽  
Geometric Error ◽  
Kinematic Calibration ◽  
Parallel Mechanisms

A calibration method of a hexaglide parallel manipulator is presented to improve its accuracy. A prototype of the hexaglide parallel manipulator is first proposed and its kinematics is analyzed. Through differentiating kinematic equations, 54 geometric error parameters are generated to present the pose error of the moving platform, on which an iterative algorithm for the calibration is based. The experiment starts with the data acquisition. All of measuring poses are newly selected based on the orthogonal design, and the deviations in each pose are measured by a laser tracker. Subsequently, 54 actual geometric parameters are identified by least squares method and compensated to the nominal kinematic model, which is assessed by 25 configurations to obtain the accuracy of the calibrated hexaglide parallel manipulator. It is discovered that the pose errors of the calibrated hexaglide parallel manipulator are significantly reduced and illustrate the validity of the calibration method to improve its accuracy. Finally, we discussed the feasibility of implementing this method in high-accuracy calibration of variant-scale parallel mechanisms.

Error Modeling and Analysis of Articulated Arm Coordinate Measuring Machines

2013 ◽  
Vol 798-799 ◽  
pp. 464-467
Author(s):  
Jian Lu ◽  
Guan Bin Gao ◽  
Hui Ping Yang
Keyword(s):  
Kinematic Model ◽  
Coordinate Measuring Machine ◽  
Calibration Method ◽  
Error Model ◽  
Error Modeling ◽  
Modeling And Analysis ◽  
Low Weight ◽  
New Type ◽  
Measuring Machine ◽  
Value Decomposition

The Articulated Arm Coordinate Measuring Machine (AACMM) is a new type of non-orthogonal system precision instrument with the advantages of large measuring range, small volume, low weight and portability. To improve the measurement accuracy of AACMMs, an error analysis and calibration method for AACMMs is proposed. The kinematic model of the AACMM was established with D-H model, and then the error model of the AACMM was established on the basis of kinematic model with total differential transforming method and the singular value decomposition of Jacobian matrix and the decomposition of orthogonal matrix elementary row transform. Finally, the error model was validated by position error residual calculation. The error model provides a theoretical foundation for calibration and compensation of the AACMM.

A Method for Modal Parameter Identification of Time Varying Vibration Systems

2012 ◽  
Vol 479-481 ◽  
pp. 688-693
Author(s):  
Zi Ying Wu ◽  
Kun Shi
Keyword(s):  
Linear Time ◽  
Least Square Method ◽  
Degree Of Freedom ◽  
Least Square ◽  
Modal Parameters ◽  
Time Varying ◽  
Recursive Least Square ◽  
Modal Parameter ◽  
Linear Time Invariant ◽  
Prony Method

In this paper a new time varying multivariate Prony (TVM-Prony) method is put forward to identify modal parameters of time varying (TV) multiple-degree-of-freedom systems from measured vibration responses. The proposed method is based on the classical Prony method that is often used to identify modal parameters of linear time invariant systems. The main advantage of the propose approach is that it can analyze multi-dimensional nonstationary signals simultaneously. A modified recursive least square method based on the traditional one is presented to determine the TV coefficient matrices of the multivariate parametric model established in the proposed method. The efficiency and accuracy of the identification approach is demonstrated by a numerical example, in which a TV mass-string system with three-degree-of-freedom is investigated. Satisfied results are obtained.

Stiffness-based trajectory planning of a 6-DOF cable-driven parallel manipulator

2016 ◽  
Vol 231 (21) ◽  
pp. 3999-4011 ◽  
Author(s):  
Wenjia Zhang ◽  
Weiwei Shang ◽  
Bin Zhang ◽  
Fei Zhang ◽  
Shuang Cong
Keyword(s):  
Velocity Profile ◽  
Trajectory Planning ◽  
Parallel Manipulator ◽  
Kinematic Model ◽  
Degree Of Freedom ◽  
Performance Indices ◽  
Curved Trajectories ◽  
Quintic Polynomial ◽  
Point To Point ◽  
Six Degree Of Freedom

The stiffness of the cable-driven parallel manipulator is usually poor because of the cable flexibility, and the existing methods on trajectory planning mainly take the minimum time and the optimal energy into account, not the stiffness. To solve it, the effects of different trajectories on stiffness are studied for a six degree-of-freedom cable-driven parallel manipulator, according to the kinematic model and the dynamic model. The condition number and the minimum eigenvalue of the dimensionally homogeneous stiffness matrix are selected as performance indices to analyze the stiffness changes during the motion. The simulation experiments are implemented on a six degree-of-freedom cable-driven parallel manipulator, to study the stiffness of three different trajectory planning approaches such as S-type velocity profile, quintic polynomial, and trigonometric function. The accelerations of different methods are analyzed, and the stiffness performances for the methods are compared after planning the point-to-point straight and the curved trajectories. The simulation results indicate that the quintic polynomial and S-type velocity profile have the optimal performance to keep the stiffness stable during the motion control and the travel time of the quintic polynomial can be optimized sufficiently while keeping stable.

A Simple Two-step Geometric Approach for the Kinematic Calibration of the 3-PRS Parallel Manipulator

Robotica ◽  
2019 ◽  
Vol 37 (5) ◽  
pp. 837-850
Author(s):  
Genliang Chen ◽  
Lingyu Kong ◽  
Qinchuan Li ◽  
Hao Wang
Keyword(s):  
Parameter Identification ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Calibration Method ◽  
Kinematic Parameter ◽  
Geometric Constraints ◽  
Kinematic Calibration ◽  
Kinematic Parameters ◽  
Positioning Accuracy ◽  
Kinematic Parameter Identification

SummaryKinematic calibration plays an important role in the improvement of positioning accuracy for parallel manipulators. Based on the specific geometric constraints of limbs, this paper presents a new kinematic parameter identification method for the widely studied 3-PRS parallel manipulator. In the proposed calibration method, the planes where the PRS limbs exactly located are identified firstly as the geometric characteristics of the studied parallel manipulator. Then, the limbs can be considered as planar PR mechanisms whose kinematic parameters can be determined conveniently according to the limb planes identified in the first step. The main merit of the proposed calibration method is that the system error model which relates the manipulator’s kinematic errors to the output ones is not required for kinematic parameter identification. Instead, only two simple geometric problems need to be established for identification, which can be solved readily using gradient-based searching algorithms. Hence, another advantage of the proposed method is that parameter identification of the manipulator’s limbs can be accomplished individually without interactive impact on each other. In order to validate the effectiveness and efficiency of the proposed method, calibration experiments are conducted on an apparatus of the studied 3-PRS parallel manipulator. The results show that using the proposed two-step calibration method, the kinematic parameters can be identified quickly by means of gradient searching algorithm (converge within five iterations for both steps). The positioning accuracy of the studied 3-PRS parallel manipulator has been significantly improved by compensation according to the identified parameters. The mean position and orientation errors at the validation configurations have been reduced to 1.56 × 10−4 m and 1.13 × 10−3 rad, respectively. Further, the proposed two-step kinematic calibration method can be extended to other limited-degree-of-freedom parallel manipulators, if proper geometric constraints can be characterized for their kinematic limbs.

An improved kinematic calibration method for serial manipulators based on POE formula

Robotica ◽  
2018 ◽  
Vol 36 (8) ◽  
pp. 1244-1262 ◽  
Author(s):  
Chenguang Chang ◽  
Jinguo Liu ◽  
Zhiyu Ni ◽  
Ruolong Qi
Keyword(s):  
High Precision ◽  
Least Square Method ◽  
Calibration Method ◽  
Error Model ◽  
Least Square ◽  
Identification Accuracy ◽  
Kinematic Calibration ◽  
Serial Manipulators ◽  
Serial Robots ◽  
Generic Modeling

SUMMARYExisting measurement equipments easily determine position with high precision. However, they evaluate orientation with low precision. It is necessary to minimize the effect of measurement error on identification accuracy. In this study, a method for kinematic calibration based on the product of exponentials (POE) is presented to improve the absolute positioning accuracy of a sliding manipulator. An error model with uniform and generic modeling rules is established in which the tool frame is selected as the reference frame. Furthermore, the redundant parameters of the error model are removed. Subsequently, the actual kinematic parameters are identified by using the least square method. Finally, the process of the improved method is discussed. Kinematic calibration simulations of a sliding manipulator are implemented. The results indicate that the proposed method significantly improves the precision of the sliding manipulator. The improved POE kinematic calibration method offers convenience, efficiency, and high precision. The proposed method can be applied to all types of serial robots with n-DOF

Self-calibration of three-legged modular reconfigurable parallel robots based on leg-end distance errors

Robotica ◽  
2001 ◽  
Vol 19 (2) ◽  
pp. 187-198 ◽  
Author(s):  
Guilin Yang ◽  
I-Ming Chen ◽  
Wee Kiat Lee ◽  
Song Huat Yeo
Keyword(s):  
Calibration Method ◽  
Parallel Robots ◽  
Least Square ◽  
Fine Tuning ◽  
Robot Kinematics ◽  
Calibration Model ◽  
Kinematic Calibration ◽  
Linear Calibration ◽  
Self Calibration ◽  
End Distance

A class of three-legged modular reconfigurable parallel robots is designed and constructed for precision assembly and light machining tasks by using standard active and passive joint modules in conjunction with custom designed links and mobile platforms. Since kinematic errors, especially the assembly errors, are likely to be introduced, kinematic calibration becomes particularly important to enhance the positioning accuracy of a modular reconfigurable robot. Based on the local frame representation of the Product-Of-Exponentials (Local POE) formula, a self-calibration method is proposed for these three-legged modular reconfigurable parallel robots. In this method, both revolute and prismatic joint axes can be uniformly expressed in twist coordinates by their respective local (body) frames. Since these local frames can be arbitrarily defined on their corresponding links, we are able to calibrate them, and yet retain the nominal local description of their respective joints, i.e., the nominal twist coordinates and nominal joint displacements, to reflect the actual kinematics of the robot. The kinematic calibration thus becomes a procedure of fine-tuning the locations and orientations of the local frames. Using mathematical tools from differential geometry and group theory, an explicit linear calibration model is formulated based on the leg-end distance errors. An iterative least-square algorithm is employed to identify the error parameters. A simulation example of calibrating a three-legged (RRRS) modular parallel robot shows that the robot kinematics can be fully calibrated within two to three iterations.

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