Screw rolling between moving and fixed axodes traced by lower-mobility parallel mechanism

Zhang, Leilei; Zhao, Yanzhi; Ren, Jianlin

doi:10.1016/j.mechmachtheory.2021.104354

Cited by 3 publications

(3 citation statements)

References 29 publications

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“…Although Equation ( 19) is just the formula of the striction point of ruled surfaces, it can be used to derive the ∞ 3 striction points of the general three-system. Substituting S, P, λ 2 = f (λ 1 ), and k into Equation (19) and rearranging lead to…”

Section: S S S Smentioning

confidence: 99%

“…To develop intuitive and visual methods of axode planning, we especially study the distribution regularity of the screw axes of the general three-system in Euclidean three-space. Furthermore, to build a bridge between axode planning and the motion planning of parallel mechanisms, we have developed a kinematic model of screw rolling between fixed and moving axodes [19,20], which solves the problem, "Given a pair of fixed and moving axodes, how to reproduce the associated continuous rigid motion?" For the distribution zone of the screw axes of higherorder screw systems, perhaps it can be decomposed into that of lower-order screw systems, as Chen [2] has decomposed the four-, five-, and six-systems into the direct sums of several two-and three-systems by the decomposition of the positive semidefinite (PSD) method.…”

Section: Introductionmentioning

confidence: 99%

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Distribution Characteristics of Screw Axes Belonging to General Three-System of Screws

2022

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The cylindroid describes the exact distribution of the ∞1 screw axes of the general two−system of screws. For the general three−system, this article introduces the surface on which lies the position vector endpoints of its ∞2 screw axes, and then develops the finite distribution zone in which they most densely distribute. In particular, this paper explores the inner structure of the zone by partitioning the general three−system into ∞1 two−subsystems, and then reveals the principle of constructing the distribution space of the general three−system by that of the general two−system in Euclidean three−space. In pursuit of a generalized decomposition method, we propose the varying−pitch ruled surface carrying the screws whose pitch value continuously varies according to any desired function rule, based on the pitch−hyperboloid carrying all the equal−pitch screws. This investigation provides some useful guides for the axode planning and then the motion planning of three degree−of−freedom parallel mechanisms.

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Section: S S S Smentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Distribution Characteristics of Screw Axes Belonging to General Three-System of Screws

2022

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“…It is important to note that even recent papers wrongly indicate the foundations of the generalization of the Aronhold-Kennedy theorem to the spherical and spatial cases, called the Three-Axes Theorem. Zhang et al [23] indicate "...Sugimoto and Duffy firstly obtained the IS of planar 4R and spatial RCCC mechanisms by the reciprocal screw theory. Aronhold-Kennedy Theorem is an effective geometrical method computing the IS of planar mechanism and was generalized to the spatial case using the reciprocal screw theory...".…”

Section: Application Of the Killing And Klein Forms To Planar Linkagesmentioning

confidence: 99%

A Screw Theory Approach to Computing the Instantaneous Rotation Centers of Indeterminate Planar Linkages

Valderrama-Rodríguez¹,

Rico

Cervantes-Sánchez

et al. 2021

Robotics

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This paper presents a screw theory approach for the computation of the instantaneous rotation centers of indeterminate planar linkages. Since the end of the 19th century, the determination of the instantaneous rotation, or velocity centers of planar mechanisms has been an important topic in kinematics that has led to the well-known Aronhold–Kennedy theorem. At the beginning of the 20th century, it was found that there were planar mechanisms for which the application of the Aronhold–Kennedy theorem was unable to find all the instantaneous rotation centers (IRCs). These mechanisms were denominated complex or indeterminate. The beginning of this century saw a renewed interest in complex or indeterminate planar mechanisms. In this contribution, a new and simpler screw theory approach for the determination of indeterminate rotation centers of planar linkages is presented. The new approach provides a simpler method for setting up the equations. Furthermore, the algebraic equations to be solved are simpler than the ones published to date. The method is based on the systematic application of screw theory, isomorphic to the Lie algebra, se(3), of the Euclidean group, SE(3), and the invariant symmetric bilinear forms defined on se(3).

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Two second order instantaneous invariants of axodes

Dooner

García-García²,

Rico³

2023

Mechanism and Machine Theory

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Screw rolling between moving and fixed axodes traced by lower-mobility parallel mechanism

Cited by 3 publications

References 29 publications

Distribution Characteristics of Screw Axes Belonging to General Three-System of Screws

Distribution Characteristics of Screw Axes Belonging to General Three-System of Screws

A Screw Theory Approach to Computing the Instantaneous Rotation Centers of Indeterminate Planar Linkages

Two second order instantaneous invariants of axodes

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