Delta robot forward kinematics method with one root

Gritsenko, Igor; Seidakhmet, Askar; Abduraimov, A.; Gritsenko, Pavel; Abay, Bekbaganbetov

doi:10.1109/icras.2017.8071913

Cited by 3 publications

(3 citation statements)

References 1 publication

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“…Tsai et al [2] transformed the kinematic problems into geometric intersection problems. By using virtual connecting rods, Gritsenko et al [25] transformed the forward kinematics of the non-offset-type Delta mechanism into the problem of solving for the vertex of a triangular pyramid. However, for the offset-type Delta mechanism, some geometric methods are no longer applicable.…”

Section: Introductionmentioning

confidence: 99%

Research on fast forward kinematics of an offset-type flexible micro-motion Delta parallel mechanism

Li¹,

Song²,

Zhang³

et al. 2023

Phys. Scr.

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In this paper, a fast numerical iterative algorithm is proposed based on the Pseudo-Rigid-Body-Model and geometric method to deal with the problem of the offset-type flexible Delta mechanism forward kinematics with multiple solutions and without analytical solutions. In forward kinematics, the quartic kinematic equations are reduced to quadratic ones by variable substitution. As the simplest nonlinear equations, quadratic equations can be represented by the coefficient matrices which is suitable for computer calculation. And due to the operational properties of the matrix, the updating and iterative process in the steps of Newton’s method can be simplified and improved to solve the forward kinematics more efficiently. The convergence and singularity of the proposed iterative algorithm are also analysed. By controlling the offset-type flexible micro-motion Delta parallel mechanism to move along three different expected spatial trace curves and measuring the displacements, the experiment results show that the Root Mean Square Error between the measured values and the expected values of linear positioning is 0.9177 μm for 37.4166 μm. Moreover, it is proved by numerical examples that the proposed iterative algorithm takes only 0.53 ms on average to solve the forward kinematic problems. The calculation time is reduced by 90.3% on average compared to the traditional Newton’s method, which provides a feasible solution for real-time control based on forward kinematics.

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Section: Introductionmentioning

confidence: 99%

Research on fast forward kinematics of an offset-type flexible micro-motion Delta parallel mechanism

Li¹,

Song²,

Zhang³

et al. 2023

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…Due to the complexity of the closed-loop structure and kinematic constraints of the robot, the robot model is a multi-variable, multiparameter, coupling, and multi-degree-of-freedom nonlinear system. Many studies have shown the significance of kinematic [3][4][5] and dynamic models [6][7][8][9] on path planning and tracking precision. Accordingly, numerous model-based control techniques are employed to improve the performance of parallel robots.…”

Section: Introductionmentioning

confidence: 99%

Robust Adaptive Finite-Time Synergetic Tracking Control of Delta Robot Based on Radial Basis Function Neural Networks

Pham

Kuo

2022

Applied Sciences

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This paper presents a robust proportional derivative adaptive nonsingular finite-time synergetic tracking control (PDAFS) for a parallel Delta robot system. First, a finite-time synergetic controller combined with a proportional derivative (PD) control is constructed based on an object-oriented model to fulfill the robust tracking control of the robot. Then, an adaptive radial basis function approximation neural network (RBF) is designed to compensate for the effects of uncertainty parameters and external disturbances. Second, a second-order sliding mode (SOSM) differentiator is implemented to reduce the chattering noises due to the low-resolution encoders. Third, the stability theorems of the proposed control scheme are provided, where the Lyapunov stability theory is used to prove the theorems. Then, simulations of the helix trajectory tracking and the pick-and-place task are demonstrated on the Delta robot to validate the advantages of the proposed control scheme. Based on the advances, an implementing control system of the proposed controller is performed to improve the Delta robot’s performance in the experiments.

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“…Igor Gritsenko stated that there is a new method for calculating the Forward Kinematics (FK) of a Parallel Robot (PR), which relies on the verification of the analytical and the numerical method. This method had also shown its ability to calculate the workspace of the PR in about 150 microseconds [8].…”

Section: Introductionmentioning

confidence: 99%

Investigation of Using ANN and Stereovision in Delta Robot for Pick and Place Applications

Youssef¹,

Bayoumy²,

Atia³

2021

MMEP

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Delta robot forward kinematics method with one root

Cited by 3 publications

References 1 publication

Research on fast forward kinematics of an offset-type flexible micro-motion Delta parallel mechanism

Research on fast forward kinematics of an offset-type flexible micro-motion Delta parallel mechanism

Robust Adaptive Finite-Time Synergetic Tracking Control of Delta Robot Based on Radial Basis Function Neural Networks

Investigation of Using ANN and Stereovision in Delta Robot for Pick and Place Applications

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