Kinematic Interpretation of the Study Quadric’s Ambient Space

Nawratil, Georg

doi:10.1007/978-3-319-93188-3_1

Cited by 3 publications

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

On Homotopy Continuation Based Singularity Distance Computations for 3-RPR Manipulators

Kapilavai

Nawratil

2020

Mechanisms and Machine Science

Self Cite

View full text Add to dashboard Cite

We present an efficient algorithm for computing the closest singular configuration to each non-singular pose of a 3-RPR planar manipulator performing a 1-parametric motion. By considering a 3-RPR manipulator as a planar framework, one can use methods from rigidity theory to compute the singularity distance with respect to an intrinsic metric. There are different design options as the platform/base can be seen as a triangular plate or as a pin-jointed triangular bar structure. Moreover, we also allow the additional possibility of pinning down the base/platform triangle to the fixed/moving system thus it cannot be deformed. For the resulting nine interpretations, we compute the corresponding intrinsic metrics based on the total elastic strain energy density of the framework using the physical concept of Green-Lagrange strain. The global optimization problem of finding the closest singular configuration with respect to these metrics is solved by using tools from numerical algebraic geometry. The proposed algorithm is demonstrated based on an example.

show abstract