Fundamental equation of mechanism kinematic geometry: Mapping curve in se(3) to counterpart in SE(3)

Zhang, Leilei; Zhao, Yanzhi; Zhao, Tieshi

doi:10.1016/j.mechmachtheory.2019.103732

Cited by 7 publications

(2 citation statements)

References 23 publications

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“…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%

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: Introductionmentioning

confidence: 99%

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

2022

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“…5 For example, for gear pairs with centre-distance separability, their transmission ratios are not affected by the centre distance error. 6,7 Involute gear pairs have centre distance separability. 8 The arc gear pair and cycloid gear pair have no centre distance separability, and their transmission performances are badly affected by the centre distance error.…”

Section: Introductionmentioning

confidence: 99%

Research on the centre distance separability of parallel shaft line gear pair

Chen

Lin

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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For gear pairs with centre-distance separability, transmission ratios are not affected by centre distance error. Based on space curve meshing theory, the centre distance separability of a line gear pair was studied. A novel line gear pair called the separable and pure rolling parallel shaft line gear pair (SPRPSLG) was proposed, which has centre-distance separability characteristics and pure rolling transmission. The basic design theory of the SPRPSLG pair was established. A design method of the SPRPSLG pair with an eccentric arc tooth profile was given. An SPRPSLG pair example was designed and manufactured using the form milling method. Kinematic experiments and meshing efficiency experiments were conducted. Gear contact spot testing and gear contact simulation analysis were carried out. The SPRPSLG pair was shown to have centre distance separability, which provides a further theoretical basis for the popularization and application of line gears.

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Analysis of structural design defects in parallel overloading mechanisms with cam transmission mechanism

Lan

Fan

2022

Applied Mathematical Modelling

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Fundamental equation of mechanism kinematic geometry: Mapping curve in se(3) to counterpart in SE(3)

Cited by 7 publications

References 23 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

Research on the centre distance separability of parallel shaft line gear pair

Analysis of structural design defects in parallel overloading mechanisms with cam transmission mechanism

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