Angles between Subspaces of Wrenches in Parallel Mechanisms

The possibility of a theoretical analysis of the proximity of parallel mechanisms to singularities in the case when the group of all wrenches of the mechanism includes linearly dependent wrenches is considered. It is proposed to consider separate groups of wrenches as subspaces of a six-dimensional...

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Bibliographic Details
Published in:Journal of machinery manufacture and reliability 2022-12, Vol.51 (6), p.502-510
Main Author: Laryushkin, P. A.
Format: Article
Language:English
Subjects:
Engineering
Machines
Manufacturing
Mechanics of Machines
Processes
Singularities
Subspaces
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Summary:The possibility of a theoretical analysis of the proximity of parallel mechanisms to singularities in the case when the group of all wrenches of the mechanism includes linearly dependent wrenches is considered. It is proposed to consider separate groups of wrenches as subspaces of a six-dimensional linear space. In this case, the angle between the subspaces can serve as a criterion of proximity to a singularity. The relation of this angle to the value of the generalized reaction associated with the corresponding wrench is noted. Using the example of a 4-RRR mechanism, it is shown that this measure is continuous, in contrast to the rank of the wrench matrix, which changes only in a singularity.
ISSN:1052-6188
1934-9394
DOI:10.3103/S1052618822060061