A novel geometric approach for planar motion generation based on similarity transformation of pole maps

Lin, Song; Liu, Jingshuai; Wang, Hanchao

doi:10.1016/j.mechmachtheory.2017.11.027

Cited by 6 publications

(2 citation statements)

References 18 publications

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“…In this paper, the connecting rods in the 2R open chain rod group are required to pass through several given positions in sequence according to a certain orientation. In the rigid body guidance of the linkage mechanism, the position of the linkage plane can be determined by the azimuth of any point on the linkage plane and any selected line [21][22][23][24][25][26] . As shown in Figure 3, when the plane is at the i-th position, the P point on it is P i (x i , y i ) and the azimuth of P i S i is θ i , i=1, 2, 3.…”

Section: Synthesis Of Three-position Motion Generation Structuralmentioning

confidence: 99%

Optimization design and experiment of the variable differential gear train planting mechanism

Xiong,

Ziwei,

Yuanwu

et al. 2024

International Journal of Agricultural and Biological Engineering

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In order to improve the adaptability of the planting mechanism for different plant spacings, a variable differential gear train planting mechanism based on precise pose and trajectory control was proposed by combining the open chain 2R rod group and the variable differential gear train. According to the pose requirements of receiving seedling point, transporting seedling point and planting point, three precise pose points of constrained planting trajectory were determined. Through the three-position motion generation structural synthesis method, combined with computer-aided optimization design software, a set of mechanism parameters that meet the planting requirements were optimized. Based on the optimized mechanism parameters, by only changing the coordinates of two trajectory shape control points, three planting trajectories with key point position information adapted to 300 mm, 400 mm and 500 mm plant spacing were obtained by interpolation, and three pairs of total transmission ratio of three groups of variable differential gear trains were calculated. When distributing the total transmission ratio of the mechanism, the fixed axis gear train and the differential gear train are combined. The fixed axis gear train included a pair of non-circular gear pairs and a pair of positive gear pairs, which were convenient for disassembly and assembly. The former drives the sun gear at variable speed, and the latter drives the planet carrier at uniform speed. Based on this structure, the transmission ratio of the positive gear pair is -1, and the transmission ratio of the differential gear train is 0.5. The sub-transmission ratio of the single-stage non-circular gear pair was calculated and the pitch curves of three pairs of noncircular gears were solved. Three pairs of non-circular gear pairs with different transmission ratios were replaced in turn and three sets of planting mechanisms were modeled in three dimensions. The virtual prototype motion simulation was completed by ADAMS software, and the physical prototype was built for vegetable pot seedling planting test. The theoretical solution was consistent with the attitude and trajectory of the actual test. When the test sample size was 100 plants, the actual average plant spacing was measured to be 303 mm, 402 mm, and 503 mm, with errors of 1.3%, 1.25%, and 1.88%. The width of the moving hole was 72 mm, 70 mm, and 71 mm, and the planting success rate were 94%, 96%, and 95%. The test results verified the correctness of the optimization design results of the mechanism, indicating that the variable differential gear train planting mechanism can adapt to a variety of plant spacing and has good planting effect.

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Section: Synthesis Of Three-position Motion Generation Structuralmentioning

confidence: 99%

Optimization design and experiment of the variable differential gear train planting mechanism

Xiong,

Ziwei,

Yuanwu

et al. 2024

International Journal of Agricultural and Biological Engineering

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“…Schimmels (2019, 2020) researched the synthesis method of compliant five-bar linkages and presented a geometric approach to the passive realization of any given planar compliance with a six-joint fully serial or six-spring fully parallel mechanism. Topology optimization method has been widely used in the design of distributed compliant mechanisms (Zhou and Mandala, 2012;Patiballa and Krishnan, 2017;Liu et al, 2017), but it commonly leads to complex structures that may cause higher manufacturing costs using elastic material. Diab and Smaili (2017) presented an ants-search-based method for optimum synthesis of compliant mechanisms under various design criteria.…”

Section: Introductionmentioning

confidence: 99%

Geometric synthesis method of compliant mechanism based on similarity transformation of pole maps

et al. 2021

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Abstract. This paper presents a geometric synthesis method for compliant mechanisms based on similarity transformation of pole maps. Motion generation is a typical and common mechanism synthesis task, so this study takes it as the design requirement to expound the proposed method. Most of the current research work relies on numerical solution of the nonlinear Bernoulli–Euler beam model, numerical simulations or physical experiments to study the synthesis method of compliant mechanisms. There is a lack of simpler and more efficient methods to achieve motion generation of compliant mechanisms with various topologies. This study is based on pole map which is a geometric tool to describe the motion of rigid-body mechanisms. In this paper, we first demonstrate the feasibility of applying the similarity transformation of pole map to compliant mechanisms. It is proved that the pole map of compliant mechanisms has the same characteristic as rigid-body mechanisms during similarity transformation. Then we present the procedure of synthesis method in detail and expound the establishment method of function module which can avoid the functional defects of the final designed mechanism. At last, we take the compliant geared linkages and compliant four-bar linkage as examples to illustrate the novel synthesis approach. The result is an applicable and effective synthesis method for motion generation of compliant mechanisms.

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Compliant Mechanism Synthesis for Guidance Task Based on Geometrical Similarity Transformation

Lin

Song

2019

Advances in Mechanism and Machine Science

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A novel geometric approach for planar motion generation based on similarity transformation of pole maps

Cited by 6 publications

References 18 publications

Optimization design and experiment of the variable differential gear train planting mechanism

Optimization design and experiment of the variable differential gear train planting mechanism

Geometric synthesis method of compliant mechanism based on similarity transformation of pole maps

Compliant Mechanism Synthesis for Guidance Task Based on Geometrical Similarity Transformation

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