The DOI matches its Crossref record; 46 of the 47 references it cites were found in a registry or an index.
Higher-Order Analysis of Kinematic Singularities of Lower Pair Linkages and Serial Manipulators
Abstract
Kinematic singularities of linkages are configurations where the differential mobility changes. Constraint singularities are critical points of the constraint mapping defining the loop closure constraints. Configuration space (c-space) singularities are points where the c-space ceases to be a smooth manifold. These singularity types are not identical and can neither be distinguished nor identified by simply investigating the rank deficiency of the constraint Jacobian (linear dependence of joint screws). C-space singularities are reflected by the c-space geometry. In a previous work, a kinematic tangent cone was introduced as an approximation of the c-space, defined as the set of tangents to smooth curves in c-space. Identification of kinematic singularities amounts to analyze the local geometry of the set of critical points. As a computational means, a kinematic tangent cone to the set of critical points is introduced in terms of Jacobian minors. Closed form expressions for the derivatives of the minors in terms of Lie brackets of joint screws are presented. A computational method is introduced to determine a polynomial system defining the kinematic tangent cone. The paper complements the recently proposed mobility analysis using the tangent cone to the c-space. This allows for identifying c-space and kinematic singularities as long as the solution set of the constraints is a real variety. The introduced approach is directly applicable to the higher-order analysis of forward kinematic singularities of serial manipulators. This is briefly addressed in the paper.
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“Such singularities are the most common singularities [39, 41] found in a mechanism and here we consider the situation where they occur only at isolated points of Σ.”
From Thermal Fluctuations of Singular Bar-Joint Mechanisms (2022) · cites this paper as [41]
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Metadata
- Authors
- Müller, A.
- Affiliations
- Johannes Kepler University of Linz (AT)
- Corresponding author
- Müller, Andreas
- ORCID
- Müller, Andreas
- Venue
- Journal of Mechanisms and Robotics
- Publisher
- ASME International
- Published
- 2017-12-22
- Volume
- 10
- Issue
- 1
- ISSN
- 1942-4302 (ISSN-L)
- 1942-4310
- OpenAlex
- W2770014303
- Cited by
- 33
- References
- 47
- Citations by year
- 2026: 2 · 2025: 2 · 2024: 3 · 2023: 3 · 2022: 4 · 2021: 4 · 2020: 5 · 2019: 7 · 2018: 3
- FWCI
- 2.58
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Mechanisms and Robotics (publishedVersion)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Robotic Mechanisms and Dynamics
- Physical Sciences › Engineering › Control and Systems Engineering › Dynamics and Control of Mechanical Systems
- Physical Sciences › Engineering › Biomedical Engineering › Soft Robotics and Applications
- Keywords
- kinematic singularities, serial manipulators, constraint singularities, forward kinematics, differential mobility
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