Geometric Theorems and Application of the DOF Analysis of the Workpiece Based on the Constraint Normal Line

Luo, Guojun; Wang, Xiaohui; Yan, Xianguo

doi:10.1155/2021/1014708

Cited by 3 publications

(7 citation statements)

References 21 publications

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“…Through equations (20) to (22), 𝐶𝐼 2→1,1 = 0.0147 , 𝑅𝐼 2→1,1 = 1.12 , 𝐶𝑅 2→1,1 = 0.0131 < 0.1 , meeting the consistency requirement.…”

Section: Case Study On Planar Feature Part Locating Strategymentioning

confidence: 95%

“…Positioning normal lines [20]- [22] refer to the normal lines at the contact points between a workpiece and locating components, as depicted in Fig. 2(a).…”

Section: Relationship Between Positioning Normal Lines and Workpiece ...mentioning

confidence: 99%

“…Hence, the normalized eigenvector of the judgment matrix 𝑩 𝟐→𝟏,𝟏 yields the weight vector through equation ( 23) is as follows: Generate the CR values for the scheme layer to the criteria layer according to equations (20) to (22), as shown in Table 8. From Table 8, it's evident that the judgment matrices generated from the scheme layer to the criteria layer meet the consistency requirements.…”

Section: Case Study On Planar Feature Part Locating Strategymentioning

confidence: 99%

See 2 more Smart Citations

Locating Scheme Planning Algorithm based on Positioning Normal Line and Analytical Hierarchy Process

Zhang,

Wang,

Wang

et al. 2024

Preprint

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Planning methods tailored for individual stages of locating schemes often fall short of achieving overall optimization. Therefore, by employing the positioning normal line as a medium and based on the geometric theorem of workpiece locating concerning the positioning normal line, the relationship between workpiece degrees of freedom and the positioning normal line can be deduced. This enables the acquisition of positioning normal line information for the freedom constraint model, consequently deriving an initial layout for the locating points. This initial layout sieves through all surfaces of the workpiece, establishing a set of candidate locating references. The intrinsic conditions of the workpiece surfaces, alongside the corresponding clamping surface quality, are utilized as measures to gauge their locating capabilities. Aiming for optimal locating capabilities, the Analytic Hierarchy Process (AHP) is employed to ascertain a comprehensive, optimal vector encompassing the combined locating capabilities of various workpiece surfaces, aiding in the selection of locating references. The feasibility of this method is validated through practical examples. Results demonstrate that the layout of locating points planned using this method, in conjunction with the positioning normal information provided by different characteristic types as summarized in this paper, effectively guides machining personnel in formulating locating schemes.

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“…Through equations (20) to (22), 𝐶𝐼 2→1,1 = 0.0147 , 𝑅𝐼 2→1,1 = 1.12 , 𝐶𝑅 2→1,1 = 0.0131 < 0.1 , meeting the consistency requirement.…”

Section: Case Study On Planar Feature Part Locating Strategymentioning

confidence: 95%

“…Positioning normal lines [20]- [22] refer to the normal lines at the contact points between a workpiece and locating components, as depicted in Fig. 2(a).…”

Section: Relationship Between Positioning Normal Lines and Workpiece ...mentioning

confidence: 99%

Section: Case Study On Planar Feature Part Locating Strategymentioning

confidence: 99%

See 1 more Smart Citation

Locating Scheme Planning Algorithm based on Positioning Normal Line and Analytical Hierarchy Process

Zhang,

Wang,

Wang

et al. 2024

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Wang et al [23][24][25] analyzed the DOF of the workpiece in the fxture in the early stage and simplifed the positioning of the workpiece in the fxture with several contact points. According to the number of common normal lines at the constraint point and its geometric relationship, a geometric theorem for judging the DOF and over-constraint of the workpiece was established.…”

Section: Introductionmentioning

confidence: 99%

DOF Calculation Method of Planar Mechanisms Based on Constraint Normal Line

Luo

Wang

Yan

2023

Mathematical Problems in Engineering

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In the analysis and calculation of the degree of freedom (DOF) of mechanisms, it is generally a complicated problem to judge the virtual constraint correctly. Under what conditions do virtual constraints exist, and how many virtual constraints are there? Understanding these problems can contribute to effectively tackling the difficulty of calculating the DOF. With planar mechanisms as a research object, the constraints among various components are simplified into point constraints, and the common normal at a constraint point is referred to as normal. According to whether a constraint point can move relative to the frame in its normal direction, normals are divided into different categories. Based on the geometric theorem for judging the DOF of a workpiece, a set of geometric theorems for judging the DOF of components and their nature, over-constraint, and quantity are established. After the correlation between virtual constraints and over-constraints is clarified, the total number of virtual constraints in a mechanism is calculated. The analysis and calculation of the DOF of several typical planar mechanisms demonstrate that the new method is logically rigorous, simple, and intuitive, and the DOF of a mechanism can be accurately calculated.

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“…Luo et al [29] developed geometric theorems and applied DOF workpiece analysis based on a normal constraint line to avoid repositioning when a complex workpiece is installed on many different surfaces.…”

Section: Introductionmentioning

confidence: 99%

Development of Flexible Fixtures with Incomplete Locating: Connecting Rods Machining Case Study

et al. 2022

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The rapid development of manufacturing in recent years has led to a significant expansion of the technological capabilities of modern metal-cutting equipment. Therefore, the modern approach to intensifying production requires an advanced fixture design. Design and manufacture of flexible fixtures capable of machining similar shapes and sizes of complex geometry parts reduce setup time. The article aims to design flexible fixtures for parts such as one-piece connecting rods under incomplete locating conditions. The advantages are the minimum number of parts and tool availability for multi-axis machining connecting rods in one setup. This approach, combined with up-to-date machining centers and industrial robots, can increase the production efficiency of manufacturing non-removable connecting rods. This effectiveness is in a decrease in the number of operations by 5–7 times, fixtures—by 3–4 times, and machine tools—by 3–5 times, depending on the type of a non-removable connecting rod and its design features. The numerical simulation results of the proposed fixture design confirmed the comprehensive technological capabilities and dynamic characteristics. Particularly, a decrease in displacements and oscillation amplitudes up to 7% compared to the full-basing locating chart was provided. It is determined that the system “fixture–workpiece” entirely meets all the strength, accuracy, and rigidity parameters, which allows you to perform machining with intensive cutting modes. The amplitudes of oscillations do not exceed the tolerances on the dimensions of these surfaces, established by requirements for non-removable connecting rods, and all displacements are elastic. During numerical simulation, the workpiece position remained stable at all machining steps.

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Geometric Theorems and Application of the DOF Analysis of the Workpiece Based on the Constraint Normal Line

Cited by 3 publications

References 21 publications

Locating Scheme Planning Algorithm based on Positioning Normal Line and Analytical Hierarchy Process

Locating Scheme Planning Algorithm based on Positioning Normal Line and Analytical Hierarchy Process

DOF Calculation Method of Planar Mechanisms Based on Constraint Normal Line

Development of Flexible Fixtures with Incomplete Locating: Connecting Rods Machining Case Study

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