Abstract
The basic parallel robotics principle of defining kinematic constraints as vector loops is transferred from the general 3T3R case to the 3T2R case by applying a nonlinear Tait-Bryan-angle rotation constraint using the intrinsic Z-\(Y'\)-\(X''\) convention. This presents an alternative way to the deduction of differential inverse kinematics by the theory of linear transformations. The resulting formulation is used in a permutational combined structural and dimensional synthesis. The modular approach allows to combine databases of serial and parallel robots without manual intervention. The validation shows the reproducibility of existing kinematic structures using the new kinematic formulation. The optimization scheme allows to obtain suitably dimensioned symmetric 3T2R parallel robots for a given task.
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Change history
14 September 2022
For chapter 15
In the original version of the book, the following correction has been updated: In Chapter 15, one of the author’s names has been changed from “Edoardo Id” to “Edoardo Idà”. The book and the chapter have been updated with the change.
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Acknowledgements
The author acknowledges the support by the Deutsche Forschungsgemeinschaft (DFG) under grant number 341489206. Matlab code to reproduce the results is available at GitHub under free license at github.com/SchapplM/robotics-paper_ark2022_3T2R.
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Schappler, M. (2022). Structural and Dimensional Synthesis of Overconstraint Symmetric 3T2R Parallel Robots Using Tait-Bryan-Angle Kinematic Constraints. In: Altuzarra, O., Kecskeméthy, A. (eds) Advances in Robot Kinematics 2022. ARK 2022. Springer Proceedings in Advanced Robotics, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-031-08140-8_21
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