A systematic optimization approach for the calibration of parallel kinematics machine tools by a laser tracker

Wu, Jiafeng; Zhang, Rui; Wang, Ruihe; Yao, Yingxue

doi:10.1016/j.ijmachtools.2014.06.003

Cited by 64 publications

(17 citation statements)

References 17 publications

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“…and ½r i 3 are the skew matrix of r i . Combining equations (16) with (18), the velocity of the mass center D i and the angular velocity of the ith UPS limb can be written in a matrix form as follows…”

Section: Velocity Analysismentioning

confidence: 99%

Coupling analysis of a 5-degree-of-freedom hybrid manipulator based on a global index

et al. 2020

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Parallel kinematic machines have been applied in aerospace and automotive manufacturing due to their potentials in high speed and high accuracy. However, there exists coupling in parallel kinematic machines, which makes dynamic analysis, rigidity enhancement, and control very complicated. In this article, coupling characteristics of a 5-degree-of-freedom (5-dof) hybrid manipulator are analyzed based on a local index and a global index. First, velocity analysis as well as acceleration analysis of the robot is conducted to provide essential information for dynamic modeling. Then the dynamic model is built based on the principle of virtual work. Whereas the mass matrix is off-diagonal, a local coupling index as well as a global index is defined, based on which coupling characteristics of the robot are analyzed. Results show that distributions of coupling indices are symmetric due to its structural features. And dimensional parameters, structural parameters, as well as mass parameters have a large influence on the system’s coupling characteristics. Research conducted in the article is of great help in optimal design and control. Meanwhile, the method proposed in the article can be applied to other types of parallel kinematic machines or hybrid manipulators.

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Section: Velocity Analysismentioning

confidence: 99%

Coupling analysis of a 5-degree-of-freedom hybrid manipulator based on a global index

et al. 2020

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“…The sixth and seventh equations in Eq. (15) can be modified as the standard form for the Newton iterative method, which gives:…”

Section: Kinematics Modelmentioning

confidence: 99%

“…Finally, with the objective function of minimizing the deviation between actual and theoretical joint variables of the parallel mechanism, the actual parameters including the hinge positions and the length of the limbs can be obtained by the optimization [13,14]. Wu et al [15] developed a new inverse kinematics model considering the influence of inaccurate motion of joints, and a high-accuracy and high-efficient approach is proposed to reduce the positioning error of parallel mechanism due to inaccurate joint motion. However, when the calibration method of the inverse kinematics is used to calibrate the parallel mechanism, the absolute position/posture of the upper platform relative to the lower platform needs to be measured precisely, which makes a high demand on the measuring equipment.…”

Section: Introductionmentioning

confidence: 99%

Calibration of a parallel mechanism in a serial-parallel polishing machine tool based on genetic algorithm

Fan

Zhao

et al. 2015

Int J Adv Manuf Technol

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The calibration is very important to improve the accuracy of the parallel mechanism. This paper proposed a new calibration approach for the parallel mechanism based on the direct kinematics model and the genetic algorithm. The proposed calibration approach avoids the measurement of the absolute position/posture of the moving platform in the calibration. Firstly, the ideal kinematics model, as well as the kinematics model with errors, of the parallel mechanism in the hybrid machine tool is established. Due to the absence of an analytical solution to the direct kinematics, the Newton iterative method is used to provide a solution. Since the calibration of the parallel mechanism can be regarded as a discrete optimization problem of multiple designed variables, the genetic algorithm is specifically used to identify the parameters in the kinematics model. Finally, the calibration experiment is carried out to verify the effectiveness of the proposed method. According to the experimental results, the positioning error of the parallel mechanism is largely reduced from 0.083 to 0.018 mm.

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“…However, neither the self-calibration method nor the constraint calibration method can identify all parameters. External calibration, which employs devices such as laser trackers [11], ball bars [12,13], and vision systems [14][15][16] to acquire the pose of a parallel mechanism, is widely applied in calibration. For kinematic calibration of RA-PKMs, external calibration is a more suitable method as it does not require mechanical constraints or extra sensors on passive joints.…”

Section: Introduction 1mentioning

confidence: 99%

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

Wang

et al. 2020

Preprint

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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.

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A systematic optimization approach for the calibration of parallel kinematics machine tools by a laser tracker

Cited by 64 publications

References 17 publications

Coupling analysis of a 5-degree-of-freedom hybrid manipulator based on a global index

Coupling analysis of a 5-degree-of-freedom hybrid manipulator based on a global index

Calibration of a parallel mechanism in a serial-parallel polishing machine tool based on genetic algorithm

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

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