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.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“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]
Citations
Cites
Ideals, Varieties, and Algorithms
Cox, D., Little, J. B., & O’Shea, D. (2007) · Undergraduate texts in mathematics · doi:10.1007/978-0-387-35651-8 · Cited by 2,401
Stable Mappings and Their Singularities
Golubitsky, M., & Guillemin, V. (1973) · Graduate texts in mathematics · doi:10.1007/978-1-4615-7904-5 · Cited by 1,969
Singularity analysis of closed-loop kinematic chains
Gosselin, C., & Angeles, J. (1990) · IEEE Transactions on Robotics and Automation · doi:10.1109/70.56660 · Cited by 1,752
Bochnak, J., Coste, M., & Roy, M.-F. (2014) · Choice Reviews Online · doi:10.5860/choice.51-3296 · Cited by 1,319
Singular Configurations of Parallel Manipulators and Grassmann Geometry
Merlet, J. (1989) · The International Journal of Robotics Research · doi:10.1177/027836498900800504 · Cited by 563
Singular configurations of parallel manipulators and grassmann geometry
Merlet, J. (1989) · Lecture notes in computer science · doi:10.1007/3-540-51683-2_31 · Cited by 500
Geometric Fundamentals of Robotics
(2005) · Monographs in Computer Science · doi:10.1007/b138859 · Cited by 495
McCarthy, J. M., & Soh, G. S. (2000) · Springer eBooks · doi:10.1007/b98861 · Cited by 470
Robotic manipulators and the product of exponentials formula
Brockett, R. W. (2005) · Springer eBooks · doi:10.1007/bfb0031048 · Cited by 315
Singularity Analysis of 3-DOF Planar Parallel Mechanisms via Screw Theory
Bonev, I. A., Zlatanov, D., & Gosselin, C. (2003) · Journal of Mechanical Design · doi:10.1115/1.1582878 · Cited by 306
Differential and Combinatorial Topology
Cairns, S. S. (1965) · Princeton University Press eBooks · doi:10.1515/9781400874842 · Cited by 283
Singular points of smooth mappings
Gibson, C. G. (1979) · Medical Entomology and Zoology · Cited by 245
Singularity Analysis of Closed Kinematic Chains
Park, F. C., & Kim, J. W. (1999) · Journal of Mechanical Design · doi:10.1115/1.2829426 · Cited by 234
Special configurations of spatial mechanisms and robot arms
Sugimoto, K., Duffy, J., & Hunt, K. H. (1982) · Mechanism and Machine Theory · doi:10.1016/0094-114x(82)90042-8 · Cited by 165
A Unifying Framework for Classification and Interpretation of Mechanism Singularities
Zlatanov, D., Fenton, R. G., & Benhabib, B. (1995) · Journal of Mechanical Design · doi:10.1115/1.2826720 · Cited by 146
Gibson, C. G., & Hunt, K. H. (1990) · Mechanism and Machine Theory · doi:10.1016/0094-114x(90)90103-q · Cited by 129
Identification and classification of the singular configurations of mechanisms
Zlatanov, D., Fenton, R. G., & Benhabib, B. (1998) · Mechanism and Machine Theory · doi:10.1016/s0094-114x(97)00053-0 · Cited by 125
Gibson, C. G., & Hunt, K. H. (1990) · Mechanism and Machine Theory · doi:10.1016/0094-114x(90)90104-r · Cited by 102
Special configurations of robot-arms via screw theory
Hunt, K. H. (1986) · Robotica · doi:10.1017/s0263574700009358 · Cited by 101
Differential analysis of bifurcations and isolated singularities for robots and mechanisms
Kieffer, J. (1994) · IEEE Transactions on Robotics and Automation · doi:10.1109/70.285580 · Cited by 101
Type synthesis and reconfiguration analysis of a class of variable-DOF single-loop mechanisms
Kong, X., & Pfurner, M. (2014) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2014.10.011 · Cited by 95
Analysis of configuration space singularities of closed-loop mechanisms and parallel manipulators
Bandyopadhyay, S., & Ghosal, A. (2004) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2003.08.003 · Cited by 90
A Study of the Singular Configurations of Serial Manipulators
Wang, S.-L., & Waldron, K. J. (1987) · Journal of Mechanisms Transmissions and Automation in Design · doi:10.1115/1.3258779 · Cited by 81
Singularities, Configurations, and Displacement Functions for Manipulators
Litvin, F. L., Zhang, Y., Castelli, V. P., & Innocenti, C. (1986) · The International Journal of Robotics Research · doi:10.1177/027836498600500206 · Cited by 73
Higher derivatives of the kinematic mapping and some applications
Müller, A. (2014) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2014.01.007 · Cited by 70
Self-citationHigher-order rigidity—What is the proper definition?
Connelly, R., & Servatius, H. (1994) · Discrete & Computational Geometry · doi:10.1007/bf02574003 · Cited by 66
Local Kinematic Analysis of Closed-Loop Linkages—Mobility, Singularities, and Shakiness
Müller, A. (2016) · Journal of Mechanisms and Robotics · doi:10.1115/1.4032778 · Cited by 63
Self-citationGenericity and singularities of robot manipulators
Pai, D. K., & Leu, M.-C. (1992) · IEEE Transactions on Robotics and Automation · doi:10.1109/70.163780 · Cited by 58
Singularity-theoretic methods in robot kinematics
Donelan, P. (2007) · Robotica · doi:10.1017/s0263574707003748 · Cited by 54
Analytic Geometry and Singularities of Mechanisms
Lerbet, J. (1998) · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · doi:10.1002/(sici)1521-4001(199810)78:10 · Cited by 50
Singularity Analysis of Serial Robot-Manipulators
Karger, A. (1996) · Journal of Mechanical Design · doi:10.1115/1.2826922 · Cited by 49
Alon Wolf, A., Ottaviano, E., Shoham, M., & Ceccarelli, M. (2003) · Mechanism and Machine Theory · doi:10.1016/s0094-114x(03)00105-8 · Cited by 45
(1995) · Solid mechanics and its applications · doi:10.1007/978-94-011-0333-6 · Cited by 39
Wohlhart, K. (1999) · Mechanism and Machine Theory · doi:10.1016/s0094-114x(98)00027-5 · Cited by 38
Kinematic topology and constraints of multi-loop linkages
Müller, A. (2018) · Robotica · doi:10.1017/s0263574718000619 · Cited by 37
Self-citationRecursive higher-order constraints for linkages with lower kinematic pairs
Müller, A. (2016) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2016.01.012 · Cited by 36
Self-citationLimits of tangent spaces to real surfaces
O’Shea, D., & Wilson, L. C. (2004) · American Journal of Mathematics · doi:10.1353/ajm.2004.0040 · Cited by 32
The order of local mobility of mechanisms
Chen, C. (2011) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2011.04.007 · Cited by 27
Representation of the kinematic topology of mechanisms for kinematic analysis
Müller, A. (2015) · Mechanical sciences · doi:10.5194/ms-6-137-2015 · Cited by 26
Self-citationA family of mixed double-Goldberg 6 R linkages
Song, C., & Chen, Y. (2011) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2011.0345 · Cited by 23
Rico, J. M., Gallardo-Alvarado, J., & Duffy, J. (1995) · Solid mechanics and its applications · doi:10.1007/978-94-011-0333-6_15 · Cited by 20
Implementation of A Geometric Constraint Regularization For Multibody System Models
Müller, A. (2014) · Archive of Mechanical Engineering · doi:10.2478/meceng-2014-0021 · Cited by 15
Self-citationLocal Analysis of Helicoid–Helicoid Intersections in Reconfigurable Linkages
López-Custodio, P. C., Rico, J. M., & Cervantes‐Sánchez, J. J. (2017) · Journal of Mechanisms and Robotics · doi:10.1115/1.4035682 · Cited by 13
On the Manifold Property of the Set of Singularities of Kinematic Mappings: Genericity Conditions
Müller, A. (2012) · Journal of Mechanisms and Robotics · doi:10.1115/1.4005524 · Cited by 11
Self-citationConstraint graphs for combinatorial mobility determination
Müller, A., & Shai, O. (2016) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2016.10.012 · Cited by 10
Self-citationA remarkable structure of Leonardo and a higher-order infinitesimal mechanism
Tarnai, T., & Lengyel, A. (2011) · Journal of mechanics of materials and structures · doi:10.2140/jomms.2011.6.591 · Cited by 7
Research works printed but not linked: 1
- 2002, Constraint Singularity as C-Space Singularities, 183
Cited by
Sorted by citations
Müller, A. (2019) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2019.103594 · Cited by 60
Self-citationCondurache, D. (2022) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2022.104999 · Cited by 28
A synthesis method for 1-DOF mechanisms with a cusp in the configuration space
López-Custodio, P. C., Müller, A., Rico, J. M., & Dai, J. S. (2019) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2018.09.008 · Cited by 24
Self-citationWu, L., Müller, A., & Dai, J. S. (2020) · Mechanism and Machine Theory · doi:10.1016/j.mechmachtheory.2019.103776 · Cited by 18
Self-citationLocal Investigation of Mobility and Singularities of Linkages
Müller, A. (2019) · Courses and lectures · doi:10.1007/978-3-030-05219-5_5 · Cited by 13
Self-citation
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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
