Analysis of the Kinematic Accuracy Reliability of a 3-DOF Parallel Robot Manipulator

This paper presents a novel parallel manipulator with one translational and two rotational (1T2R) degrees of freedom that can be employed to form a five-degree-of-freedom hybrid kinematic machine tool for large heterogeneous complex structural component machining in aerospace field. Compared with serial or parallel machine, hybrid machine has the merits of high stiffness, high speed, large workspace, and complicated surface processing ability. To increase stiffness, three-degree-of-freedom redundantly actuated and overconstrained 2PRU-PRPS parallel manipulator (P denotes the active prismatic joint) is proposed, which is utilized as the main body of hybrid machine. By resorting to the screw theory, the degree of freedom of the proposed mechanism is briefly addressed including the initial configuration and general configuration and validated by Grübler-Kutzbach (G-K) equation. Next, kinematic inverse solution and parasitic motion of the parallel manipulator are deduced and the transformational relations between the Euler angle and Tilt-Torsion (T-T) angle are identified. Thirdly, the performance evaluation index of orientation workspace is introduced, and the reachable workspace and joint workspace are formulated. Through specific examples, the reachable workspace, task workspace, and joint workspace of the redundant actuation parallel manipulator are depicted. Compared with overstrained 2PRU-PRS parallel manipulator, corresponding analyses illustrate that the proposed parallel manipulator owns much better orientation capability and is very meaningful to the development of the five-axis hybrid machine tool.

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“…Position inverse solution of the 2PRU-PRPS parallel manipulator about s i in (25) can be expressed as follows [34].…”

Section: Position Inverse Analysismentioning

confidence: 99%

Workspace Analysis of a Hybrid Kinematic Machine Tool with High Rotational Applications

Zhang

Fang

et al. 2018

Mathematical Problems in Engineering

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“…The issue of uncertainties plays a significant role in the actual performance of a mechanism. In mechanism literature, their effects are generally studied using statistical and probabilistic approaches [10][11][12][13] or interval analysis [14][15][16][17] approaches. In the four-bar linkage, uncertainties make it no longer possible to obtain an exact solution for the coupler point and thus exact synthesis is not applicable.…”

Section: Introduction To Linkage Synthesismentioning

confidence: 99%

Appropriate synthesis of the four-bar linkage

Pickard

Carretero

Merlet

2020

Mechanism and Machine Theory

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The uncertainties arising from the fabrication and operation of mechanisms, specifically the four-bar linkage, significantly affect the expected performance of the mechanism. To accommodate uncertainties during the dimensional synthesis of the four-bar linkage, the desired coupler curve response is described by any number of precision point elements and trajectory elements, where each element is specified with an allowable error. A design description which accounts for bounded uncertainties is termed an appropriate design. An appropriate synthesis method is developed to synthesize the entire set of appropriate design solutions corresponding to the desired response. This method is able to completely explore the continuous design space and each synthesized appropriate design guarantees that the resulting four-bar linkage has a corresponding coupler point which lies inside each precision point response element, and a corresponding set of continuous coupler points which remain inside the trajectory response elements from start to finish.

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“…Therefore, we need to conduct a sensitivity analysis and an optimization process to meet the reliability requirement for the path planning. To measure the kinematic sensitivity of a parallel manipulator, Cui et al 18 used the random probability theory to construct a mathematical model. Li et al 19 applied the dimensionality reduction method to analyze the reliability sensitivity for a vibration system.…”

Section: Introductionmentioning

confidence: 99%

A moment estimation–based method for the path planning of manipulators with kinematic system reliability constraints

Wang

et al. 2019

Advances in Mechanical Engineering

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Since the path planning plays a significant role in the manipulator's control, the system reliability evaluation and optimization for path planning are studied with consideration of the joint clearance. A simple moment estimation-based method is proposed; a linear performance function is first established using the extreme value distribution theory. Based on the maximum entropy principle, the first four moments of variables are utilized to derive a best-fit probability density function to feature the characteristics of the system distribution rather than an empirical assumption of the normality. To meet the system reliability criterion constraints, a sensitivity analysis is conducted using the direct linearization method. With modification in the tolerance of sensitive parameters, the reliability can be improved efficiently. Traditional methods, such as the first-order second moment method, the first-order reliability method, and Monte Carlo simulation, are popular in this research field and therefore they are applied as benchmark methods for comprehensive comparisons in the accuracy and efficiency. A typical serial manipulator is applied as an example to validate the feasibility of our proposed method.

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Analysis of the Kinematic Accuracy Reliability of a 3-DOF Parallel Robot Manipulator

Cited by 37 publications

References 23 publications

Workspace Analysis of a Hybrid Kinematic Machine Tool with High Rotational Applications

Workspace Analysis of a Hybrid Kinematic Machine Tool with High Rotational Applications

Appropriate synthesis of the four-bar linkage

A moment estimation–based method for the path planning of manipulators with kinematic system reliability constraints

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