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Classification and analysis of constraint singularities for parallel mechanisms using differential manifolds

机译：差分流形并联机构约束奇异性的分类与分析

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This paper presents investigations into classification and analysis of constraint singularities for parallel mechanisms. Parallel mechanisms (also called parallel manipulators or parallel robots) have wide applications in industry. The singularities tremendously affect their applications. Existing research works show that constraint singularity causes a mechanism to have instantaneous degree-of-freedoms (DoFs) or bifurcated finite motions. However, the intrinsic differences among the conditions under which the specific constraint singularities happen have not been discussed. This paper is focused on these topics by using differential manifolds as mathematical tools. Firstly, the general mathematical models of parallel mechanisms are formulated by respectively describing their finite motions and instantaneous motions in forms of differential manifolds and their tangent spaces. Then, parallel mechanisms having bifurcated finite motions and instantaneous DoFs are modelled accordingly, and the constraint singularities are thus classified into two kinds by considering their influences on motions of mechanisms in both finite and instantaneous motion levels. Finally, two examples are given to further illustrate the theoretical analysis. This paper lays foundations for mathematical modelling and applications of parallel mechanisms with constraint singularities. (C) 2019 Elsevier Inc. All rights reserved.
机译：本文对并行机制的约束奇点分类和分析进行了研究。并行机制（也称为并行操纵器或并行机器人）在工业中具有广泛的应用。奇异性极大地影响了它们的应用。现有的研究工作表明，约束奇异性会导致一种机制具有瞬时自由度（DoF）或分叉的有限运动。但是，尚未讨论发生特定约束奇点的条件之间的固有差异。本文通过使用微分流形作为数学工具来关注这些主题。首先，通过分别描述微分流形及其切线空间形式的有限运动和瞬时运动，建立了并联机构的通用数学模型。然后，对具有分叉的有限运动和瞬时自由度的并联机构进行建模，并考虑到约束奇异性对机构在有限运动和瞬时运动水平上的运动的影响，将约束奇异性分为两种。最后，给出两个例子以进一步说明理论分析。本文为具有约束奇异性的并联机构的数学建模和应用奠定了基础。 （C）2019 Elsevier Inc.保留所有权利。

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