Abstract
This paper first deals with the forward kinematics (forward displacement analysis) of a class of 3-RPR planar parallel manipulator with congruent equilateral base and moving platform using an algebraic approach. Conditions on the inputs under which the manipulator has different number of solutions to the forward kinematics, including a double solution, two distinct solutions or infinite solutions (self-motion), are identified. The Type 2 singularity analysis is then performed for this parallel manipulator. The result, given in [1] without detailed proof, regarding the Type 2 singularities with a non-zero orientation angle is then proved.
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References
Chablat, D., Wenger, P. and Bonev, I.A., Self motions of a special 3RPR planar parallel robot. In Advances in Robot Kinematics, J. Lenar či č and B. Roth (Eds.), pp. 221-228, Springer (2006).
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Kong, X. and Gosselin, C.M., Uncertainty singularity analysis of parallel manipulators based on the instability analysis of structures. The International Journal of Robotics Research, 20(11), 847-856 (2001).
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Kong, X. (2008). Forward Kinematics and Singularity Analysis of a 3-RPR Planar Parallel Manipulator. 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_4
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DOI: https://doi.org/10.1007/978-1-4020-8600-7_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-8599-4
Online ISBN: 978-1-4020-8600-7
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