Verification of the higher order kinematic analyses equations

López-Custodio, P. C.; Rico, José M.; Cervantes-Sánchez, J. Jesús; Pérez-Soto, Gerardo I.; Díez-Martínez, C.R.

doi:10.1016/j.euromechsol.2016.09.010

Cited by 28 publications

(14 citation statements)

References 12 publications

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“…A velocity analysis applied to this structure would reveal that the linkage has 2 degrees of freedom since the tangent space of V in such configuration is a 2-dimensional space. A tangent cone [48,49,50,51,52,23] analysis was made for this configuration. While the first order approximation is a 2-dimensional vector space, as expected, the second order approximation is 0-dimensional, proving that the linkage is actually a structure.…”

Section: Tangent Intersections Of Concentric Singular Toroidsmentioning

confidence: 99%

“…3 π, α B2,B1 = 23 12 π, α B1,A1 = 17 36 π, a A1,A2 = 5, a B2,B1 = 6, a B1,A1 = 0 α A2,A3 = 5 3 π, α B3,B2 = 1 12 π, α A3,B3 = 55 36 π, a A2,A3 = 5, a B3,B2 = 6, a A3,B3 = 0 (14) then the linkage generates the intersection of two concentric singular toroids, such that γ A = 1 3 π, r A = 5, γ B = − 15 180 π, r B = 6 and θ = 85 180 π. These construction parameters satisfy the conditions in Eq.…”

Section: 4 Can Be Obtained From 0ŝkmentioning

confidence: 99%

“…Recent advances in reconfigurable linkages include: a closed chain with 14 states that constitute 28 configurations [14], a reconfigurable platform whose hybrid legs include a 4R diamond [15], a parallel manipulator with 15 motion branch [16], type synthesis of kinematotropic platforms [17], various reconfigurable kinematic chains with mobility one [18], a family of single-loop reconfigurable linkages with an infinity of motion branches [19]. Some advances in the study of reconfigurable linkages include: the analysis of the connections between components of the configuration space by means of algebraic geometry [20], the study of reconfigurability by means of reciprocity of screws [21], the use of morphing systemization to analyze ways of reconfiguration of linkages [22], the application of higher order kinematic analysis to prove the local mobility of kinematotropic linkages [23,24,25] and the application of dual quaternions in the analysis of reconfigurability [26,16].…”

Section: Introductionmentioning

confidence: 99%

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Branch Reconfiguration of Bricard Linkages Based on Toroids Intersections: Plane-Symmetric Case

López-Custodio

Dai

Rico

2018

Journal of Mechanisms and Robotics

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This paper for the first time reveals a set of special plane-symmetric Bricard linkages with various branches of reconfiguration by means of intersection of two generating toroids, and presents a complete theory of the branch reconfiguration of the Bricard plane-symmetric linkages. An analysis of the intersection of these two toroids reveals the presence of coincident conical singularities, which lead to design of the plane-symmetric linkages that evolve to spherical 4R linkages. By examining the tangents to the curves of intersection at the conical singularities, it is found that the linkage can be reconfigured between the two possible branches of spherical 4R motion without disassembling it and without requiring the usual special configuration connecting the branches. The study of tangent intersections between concentric singular toroids also reveals the presence of isolated points in the intersection, which suggests that some linkages satisfying the Bricard plane-symmetry conditions are actually structures with zero finite degrees-of-freedom (DOF) but with higher instantaneous mobility. This paper is the second part of a paper published in parallel by the authors in which the method is applied to the line-symmetric case.

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Section: Tangent Intersections Of Concentric Singular Toroidsmentioning

confidence: 99%

Section: 4 Can Be Obtained From 0ŝkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Branch Reconfiguration of Bricard Linkages Based on Toroids Intersections: Plane-Symmetric Case

López-Custodio

Dai

Rico

2018

Journal of Mechanisms and Robotics

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“…represents the i-th order kinematic equation. Explicit expressions for these kinematic higher-order analyses can be found in [31,33,[57][58][59]. The kinematic tangent cone is obtained as:…”

Section: A Brief Introduction To the Kinematic Tangent Cone Analysismentioning

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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“…En este trabajo se presenta un procedimiento orientado al control dinámico haciendo uso de la teoría de screws en la fase de modelado. Dicha teoría se ha aplicado en la obtención de modelos cinemáticos compactos para varios tipos de robots paralelos consiguiendo resultados satisfactorios, tal co-mo se pone de manifiesto en Mejia et al (2016), Bartkowiak and Woernle (2016), Xu et al (2017), Zhao et al (2017), Sun et al (2016) y Lopez-Custodio et al (2017). Para el caso de los robots 3RRR, Chen et al (2015) presentan la cinemática directa y la matriz jacobiana basada en teoría de screws obteniendo un modelo simple que describe las carácterísticas relevantes y puede extenderse al modelo dinámico, incluyendo las relaciones entre las variables de las juntas actuadas, y las variables del efector final.…”

Section: Introductionunclassified

Obtención de un Modelo Dinámico para un Robot 3RRR Basado en Teoría de Screws

Serrano

Rodrı́guez

Cardona

2018

Rev. iberoam. autom. inform. ind.

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En este artículo se propone una nueva técnica para la obtención de un modelo dinámico de robots 3RRR a partir de un modelo cinemático basado en teoría de screws, la cual permite obtener la cinemática de un robot ya seaésta abierta o cerrada. Primero se obtiene el modelo cinemático de una forma compacta y a partir deéste se llega al modelo dinámico aplicando el método de Euler Lagrange, con ello se transfieren las características de simplicidad y compacidad del modelo cinemático al dinámico. El modelo dinámico se obtiene inicialmente para las juntas actuadas y luego para las coordenadas del efector a través de sus interrelaciones. Para comprobar la efectividad de este desarrollo teórico se prueba el modelo obtenido con un controlador proporcional-derivativo (PD) ya que provee de una estrategia de control simple que luego puede ser extendida a controladores más efectivos.Palabras Clave: Cinemática, Dinámica, Robot Paralelo, Teoría de Screws, Robot 3RRR. Dynamic Model Derivation of a 3RRR Robot Based in Screw Theory AbstractIn this article a technique to obtain a dynamic model of a 3RRR robot from its kinematic model based on screw theory is proposed, which allows to obtain the open or closed robot kinematics. First the kinematic model is obtained in a compact form and then the dynamic model is obtained from the Euler Lagrange method, with this the simplicity and compactness characteristics are transferred to the dynamic model. The dynamic model is obtained initially for the actuated joints and then for the effector coordinates through its interrelations. To prove the effectiveness of this theoretical derivation the obtained model is tested with a proportional-derivative controller (PD) because it provides a simple control strategy that can be extended later to more effective controllers. Keywords:Kinematics, Dynamics, Parallel Robot, Screw Theory, 3 RRR Robot IntroducciónLos robots paralelos o de cadena cinemática cerrada poseen mayor precisión, rigidez, capacidad de carga y desarrollan mayores velocidades que los robots serie o de cadena cinemática abierta, estas ventajas los hacen especialmente atractivos para aplicaciones industriales como la manipulación y almacenaje de piezas. En su contra está el inconveniente de la complejidad en la obtención de sus modelos cinemático y dinámico, así como la dificultad de lograr una representación simple y compacta de los mismos. En la literatura abundan modelos orientados al control cinemático, y es mucho menor el número de publicaciones que abordan el enfoque del control dinámico del robot, siendoéste el que provee mayor robustez y rechazo a perturbaciones. En este trabajo se presenta un procedimiento orientado al control dinámico haciendo uso de la teoría de screws en la fase de modelado. Dicha teoría se ha aplicado en la obtención de modelos cinemáticos compactos para varios tipos de robots paralelos consiguiendo resultados satisfactorios, tal co- * Autor para correspondencia: serranofer@eclipso.eu Este artículo ha sido aceptado para su publicación en un futuro número d...

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Verification of the higher order kinematic analyses equations

Cited by 28 publications

References 12 publications

Branch Reconfiguration of Bricard Linkages Based on Toroids Intersections: Plane-Symmetric Case

Branch Reconfiguration of Bricard Linkages Based on Toroids Intersections: Plane-Symmetric Case

Tangential intersection of branches of motion

Obtención de un Modelo Dinámico para un Robot 3RRR Basado en Teoría de Screws

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