Optimal synthesis of a spatial RRSS mechanism for path generation. (English) Zbl 1520.70002
In this article the authors use a special property of the trajectories of arbitrary coupler points for the synthesis of an RRSS mechanism to guide a point on the coupler through specified positions. When the trajectory of a point connected to the R-S link is orthographically projected to a plane orthogonal to the base link (R-S link), then its picture is an ellipse. The dimensions of this ellipse are given in the paper for arbitrary design of the linkage and an arbitrary point on the coupler.
This opens the opportunity for a stepwise synthesis method. First, an orthographic projection is searched for, where the feature points are best fitting to a previously specified type of ellipse, using an optimization method. In this step, only the direction of the base link and linkage angles are specified. In a second step, link length parameters are computed using a genetic algorithm. In the third step, the remaining parameters that specify the complete mechanism, namely its position in space and the point connected to the coupler and generating the optimal trajectory in space are calculated based on the previous results.
Using this approach of reducing the complexity of the whole problem to partial ones, that can be solved stepwise with fewer unknowns, decreases the computational time of the overall process and increases the accuracy. This is proven at hand of some examples known in the literature.
This opens the opportunity for a stepwise synthesis method. First, an orthographic projection is searched for, where the feature points are best fitting to a previously specified type of ellipse, using an optimization method. In this step, only the direction of the base link and linkage angles are specified. In a second step, link length parameters are computed using a genetic algorithm. In the third step, the remaining parameters that specify the complete mechanism, namely its position in space and the point connected to the coupler and generating the optimal trajectory in space are calculated based on the previous results.
Using this approach of reducing the complexity of the whole problem to partial ones, that can be solved stepwise with fewer unknowns, decreases the computational time of the overall process and increases the accuracy. This is proven at hand of some examples known in the literature.
Reviewer: Martin Pfurner (Innsbruck)
MSC:
| 70B15 | Kinematics of mechanisms and robots |
| 70-08 | Computational methods for problems pertaining to mechanics of particles and systems |
Keywords:
dimensionality reduction synthesis method; orthographic projection; link length parameter; genetic algorithm; optimal spatial trajectoryReferences:
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