Abstract
The paper addresses the constraint singularities in connection with the structural parameters of parallel robots. The new formulae of mobility, connectivity, overconstraint and redundancy of parallel robots, recently proposed by the author, are used to characterize the constraint singularities. By using these formulae, we demonstrate that in a constraint singularity the instantaneous values of the mobility, connectivity of the moving platform and degree of overconstraint increase with no changes in limb connectivity. The constraint singularities are easily identified by inspection without Jacobian calculation.
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References
Di Gregorio, R., Parenti-Castelli, V. (2002), Mobility analysis of the 3-UPU parallel mechanism assembled for a pure translational motion, Transactions of the ASME Journal of Mechanical Design 124, 259-264.
Gogu, G. (2005a), Mobility of mechanisms: A critical review, Mechanism and Machine Theory 40,1068-1097.
Gogu, G. (2005b), Chebychev-Grubler-Kutzbach’s criterion for mobility calculation of multi-loop mechanisms revisited via theory of linear transformations, European Journal of Mechanics, A - Solids 24, 427-441.
Gogu, G. (2005c), Mobility and spatiality of parallel robots revisited via theory of linear trans-formations, European Journal of Mechanics, A - Solids 24, 690-711.
Gogu G. (2005d), Mobility criterion and overconstraints of parallel manipulators, in Proceedings of International Workshop on Computational Kinematics, Cassino, Italy.
Gogu, G. (2008), Structural Synthesis of Parallel Robots, Springer, Dordrecht.
Han, C., Kim, J., Kim, J., Park, F.C. (2002), Kinematic sensitivity analysis of the 3-UPU parallel mechanism, Mechanism and Machine Theory 37, 787-798.
Ionescu, T.G. (2003), Terminology for mechanisms and machine science, Mechanism and Machine Theory 38, 597-901.
Joshi, S.A., Tsai, L.W. (2002), Jacobian analysis of limited-DOF parallel manipulators, Transactions of the ASME Journal of Mechanical Design 124, 254-258.
Liu, G., Lou, Y., Li, Z. (2003), Singularities of parallel manipulators: A geometric treatment, IEEE Trans Robotics Automation 19(4), 579-594.
Tsai, L.-W. (1996), Kinematics of a three-dof platform with three extensible limbs, in Recent Ad-vances in Robot Kinematics, Lenar či č , J., Parenti-Castelli, V. (Eds), Kluwer Academic Pub-lishers, Dordrecht, pp. 401-410.
Wolf, A., Shoham, M. (2003), Investigation of parallel manipulators using linear complex approximation, Transactions of the ASME Journal of Mechanical Design 125, 564-572.
Wolf, A., Shoham, M., Park, F.C. (2002) Investigation of singularities and self-motions of the 3-UPU robot, in Advances in Robot Kinematics: Theory and Applications, Lenar či č J., Thomas F. (Eds), Kluwer Academic Publishers, Dordrecht, pp. 165-174.
Zlatanov, D., Bonev, I.A., Gosselin, C.M. (2002a), Constraint singularities of parallel mechanisms, in Proceedings of the IEEE International Conference on Robotics and Automation, Washing-ton, D.C., USA, pp. 496-502.
Zlatanov, D., Bonev, I.A., Gosselin, C.M. (2002b), Constraint singularities as configuration space singularities, in Lenar či č J., Thomas F. (Eds), Advances in Robot Kinematics: Theory and Applications, Kluwer Academic Publishers, Dordrecht.
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Gogu, G. (2008). Constraint Singularities and the Structural Parameters of Parallel Robots. In: Lenarčič, J., Wenger, P. (eds) Advances in Robot Kinematics: Analysis and Design. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8600-7_3
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DOI: https://doi.org/10.1007/978-1-4020-8600-7_3
Publisher Name: Springer, Dordrecht
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