Abstract
It is crucial to determine the mobility in regular and singular configurations of a mechanism. At a configuration space singularity, a mechanism can branch between different motion modes. All reported approaches to the local mobility analysis aim to identify possible finite motions, more precisely tangents to these motions. The latter is formalized by the concept of a kinematic tangent cone. It is shown how this can be used to identify the motion modes meeting at a singularity. A rigorous definition of motion modes is introduced, and smooth motion modes are defined as such were smooth finite motions are possible. An example is given for singularities leading to a smooth and a non-smooth motion mode.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. Connelly and H. Servatius. Higher-order rigidity–what is the proper definition? Discrete. Comput. Geom., 11:193–200, 1994.
J. Gallardo-Alvarado and J.M. Rico-Martinez. Jerk influence coefficients via screw theory, of closed chains. Meccanica, 36:213–228, 2001.
C. Galleti and P. Fangella. Single-loop kinematotropic mechanisms. Mech. Mach. Theory, 36:743–761, 2001.
X. He, X. Kong, S. Caro D. Chablat, and G. Hao. Kinematic analysis of a single-loop reconfigurable 7r mechanism with multiple operation modes. Robotica, 32:1171–1188, 2014.
C.H. Kuo, J.S. Dai, and H.S. Yan. Reconfiguration principles and strategies for reconfigurable mechanism. ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots, pages 1–7, 22-24 June, 2009.
J. Lerbet. Analytic geometry and singularities of mechanisms. ZAMM, Z. angew. Math. Mech., 78(10b):687–694, 1999.
P.C. López-Custodio, A. Müller, and J.M. Ricoand J.S. Dai. A synthesis method for 1-dof mechanisms with a cusp in the configuration space. Mech. Mach. Theory, DOI: https://doi.org/10.1016/j.mechmachtheory.2018.09.008, 2018.
J.M. Rico Martinez, J. Gallardo, and J. Duffy. Screw theory and higher order kinematic analysis of open serial and closed chains. Mech. Mach. Theory, 34(4):559–586, 1999.
A. Müller. Local kinematic analysis of closed-loop linkages -mobility, singularities, and shakiness. ASME J. of Mech. and Rob., 8, 2016.
A. Müller. Higher-order constraints for linkages with lower kinematic pairs. Mech. Mach. Theory, 100:33–43, 2016.
A. Müller. Higher-order analysis of kinematic singularities of lower pair linkages and serial manipulators. ASME J. Mech. Rob., 10(1), 2018.
A. Müller. Local investigation of mobility and singularities of linkages. In A. Müller and D. Zlatanov, editors, Singular Configurations of Mechanisms and Manipulators, CISM 589. Springer, 2019.
A. Müller. A screw approach to the approximation of the local geometry of the configuration space and of the set of configurations of certain rank of lower pair linkages. ASME J. Mech. Rob., to appear 2019.
A. Müller and S. Piipponen. On regular kinematotropies. 14th World Congress in Mechanism and Machine Science, Taipei, Taiwan, pages 1–8. IFToMM, 25-30 October, 2015.
D.B. O’Shea and L.C. Wilson. Limits of tangent spaces to real surfaces. American Journal of Mathematics, 126(5):951–980, 2004.
H. Whitney. Local properties of analytic varieties. Differential and Combinatorial Topology, A Symposium in Honor of M. Morse. Princeton, 1965.
K. Wohlhart. Kinematotropic linkages. In V. Parent-Castelli J. Lenarčič editor, Recent Advances in Robot Kinematics, pages 359–368. Springer, 1996.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Müller, A. (2019). Kinematic Tangent Cone – A useful Concept for the local Mobility and Singularity Analysis. In: Uhl, T. (eds) Advances in Mechanism and Machine Science. IFToMM WC 2019. Mechanisms and Machine Science, vol 73. Springer, Cham. https://doi.org/10.1007/978-3-030-20131-9_34
Download citation
DOI: https://doi.org/10.1007/978-3-030-20131-9_34
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-20130-2
Online ISBN: 978-3-030-20131-9
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)