Abstract
Continuum robots present designers with the challenges of interpreting the geometric conditions that lead to singularity. Unlike serial robots, where it is easy to relate Plücker line coordinates to physical locations fixed in each link-attached frame, such geometric understanding is hard to visualize for continuum robots. In this paper, we explore the conditions for the singularity of continuum robots comprised of two and three segments. We derive the conditions for singularity and visualize these singular configurations with their corresponding conditions of singularity. We start the analysis assuming circular curvature, and then we discuss how the same analysis can be extended to non-circular curvature cases. We also define safety regions for singularity that depend on an assumed modal shape variation due to the elastic deflections of these robots. These safety zones can be used to produce designs and path plans that guarantee singularity-free performance despite norm-bounded deflections in configuration space.
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Notes
- 1.
We use \(^{a}\mathbf {x}\) to designate the representation of vector \(\mathbf {x}\) in a frame {A} with axes \(\hat{\mathbf {x}}_a\), \(\hat{\mathbf {y}}_a\), \(\hat{\mathbf {z}}_a\).
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Shihora, N., Simaan, N. (2022). Geometric Insights into Kinematically-Singular Configurations of Planar Continuum Robots. 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_26
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