A synthesis method for 1-DOF mechanisms with a cusp in the configuration space

López-Custodio, P. C.; Müller, Andreas; Rico, José M.; Dai, Jian S.

doi:10.1016/j.mechmachtheory.2018.09.008

Cited by 18 publications

(13 citation statements)

References 31 publications

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“…Analytical and numerical synthesis of planar path generator linkage mechanisms have been undertaken by many researchers in the past, 19–26 including of the five-bar type 21–24 and for the generation coupler-curves with cusps. 25,26 No reports have been found however on the optimum synthesis of linkages for the generation of paths that include a crunode.…”

Section: Kinematic Of the Planter Mechanismmentioning

confidence: 99%

Numerical optimization and experimental validation of a five-link mechanism, potato planter

Sun

Zhang

Simionescu

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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Covering with plastic film in fall and planting through the film in spring is an effective drought-resistance, potato-cultivation method. To achieve proper under-plastic-film, hill-drop potato seeding, the geometry of an existing five-link planter mechanism that is driven synchronously by two cranks rotating in the same direction has been refined through bivariate plots and numerical optimization. For this purpose, novel quantitative measures of the geometry of the crunode portion of the dibber-tip path have been introduced. The prototype planter mechanism described in detail elsewhere has then been configured according to the three optimum kinematic solutions obtained, and field tests have been carried out. All three configurations satisfied the imposed agronomic requirements of potato planting through the plastic film, with one setup performing better than the other two, and then a previously reported solution obtained through manually conducted optimization.

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Section: Kinematic Of the Planter Mechanismmentioning

confidence: 99%

Numerical optimization and experimental validation of a five-link mechanism, potato planter

Sun

Zhang

Simionescu

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…However, recently, López-Custodio et al proposed a novel approach to design 1-dof mechanisms with cuspidal [6] or tangential [5] intersection of branches of motion. Furthermore, they presented a method to detect and analyze tangential branches of motion.…”

Section: Motivationmentioning

confidence: 99%

“…Study's kinematic mapping [3] is used to derive the constraint equations of the given mechanism. Thus, the corresponding algebraic variety describes the C-space in terms of Study parameters unlike the joint parameters used in López-Custodio et al [5,6]. Then, the singularities are determined by examining the tangent space.…”

Section: Motivationmentioning

confidence: 99%

C-Space Analysis Using Tropical Geometry

Nayak

2021

Springer Proceedings in Advanced Robotics

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Configuration space (C-space) of a mechanism is a real variety describing the set of feasible configurations that it can attain. To understand the behavior of a mechanism, it is crucial to identify and scrutinize especially the singular points of its C-space. They usually appear when the variety intersects itself, leading to different branches of motion. There exist many approaches to detect those intersections if they are transversal. However, the problem remains challenging if there are tangential, cuspidal, inter-dimensional or a combination of these intersections. This paper exploits an approach acquired from tropical geometry to analyze the neighborhood of any point on C-spaces of 1-degreeof-freedom (dof ) mechanisms. This is done by finding the approximate rational parametrization of the curve(s) passing through the given point using Puiseux series. The proposed approach is shown to succesfully detect the transversal branchings in two foldable four bar mechanisms and a cusp in the configuration curve of the double Watt mechanism.

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“…In the case that such tangents are not defined, for example at cusp singularities, C K q V will fail to give a local picture of the configuration space. Examples of mechanisms whose configuration space exhibit a cusp singularity were reported in [52,53]. This planar 5-loop linkage is one of the earliest examples of kinematotropic linkages, Wohlhart [17] studied it when he introduced the term kinematotropic.…”

Section: A Brief Introduction To the Kinematic Tangent Cone Analysismentioning

confidence: 99%

“…In this regard, López-Custodio et al [53] presented a method for designing this kind of mechanisms. This method also led to the investigation of two unexplored, more complex cases of intersection of branches: cases 6 and 7 in Table 1.…”

Section: Introductionmentioning

confidence: 99%

Tangential intersection of branches of motion

López-Custodio

Müller

Kang

et al. 2020

Mechanism and Machine Theory

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The branches of motion in the configuration space of a reconfigurable linkage can intersect in different ways leading to different types of singularities. In the vast majority of reported linkages whose configuration spaces contain multiple branches of motion the intersection happens transversally, allowing local methods, like the computation of its tangent cone, to identify different branches by means of their tangents. However, if these branches are of the same dimension and they intersect tangentially, it is not possible to identify them by means of the tangent cone at the singularity as the tangent spaces to the branches are the same. Although this possibility has been mentioned by a few researchers, whether linkages with this kind of tangent intersection of branches of motion exist is still an open question. In this paper, it is shown that the answer to this question is yes: A local method is proposed for the effective identification of branches of motion intersecting tangentially, and a method for the type synthesis of linkages that exhibit this particular type of singularity is presented.

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A synthesis method for 1-DOF mechanisms with a cusp in the configuration space

Cited by 18 publications

References 31 publications

Numerical optimization and experimental validation of a five-link mechanism, potato planter

Numerical optimization and experimental validation of a five-link mechanism, potato planter

C-Space Analysis Using Tropical Geometry

Tangential intersection of branches of motion

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