Name
Abstract | ||
|---|---|---|
There exists a bijection between the configuration space of a linear pentapod and all points $(u,v,w,p_x,p_y,p_z)inmathbb{R}^{6}$ located on the singular quadric $Gamma: u^2+v^2+w^2=1$, where $(u,v,w)$ determines the orientation of the linear platform and $(p_x,p_y,p_z)$ its position. Then the set of all singular robot configurations is obtained by intersecting $Gamma$ with a cubic hypersurface $Sigma$ in $mathbb{R}^{6}$, which is only quadratic in the orientation variables and position variables, respectively. This article investigates the restrictions to be imposed on the design of this mechanism in order to obtain a reduction in degree. In detail we study the cases where $Sigma$ is (1) linear in position variables, (2) linear in orientation variables and (3) quadratic in total. The resulting designs of linear pentapods have the advantage of considerably simplified computation of singularity-free spheres in the configuration space. Finally we propose three kinematically redundant designs of linear pentapods with a simple singularity surface. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.17185/duepublico/45333 | arXiv: Robotics |
Field | DocType | Volume |
Bijection,Pure mathematics,Quadratic equation,Singularity,Control engineering,Hypersurface,SPHERES,Engineering,Quadric,Computation,Configuration space | Journal | abs/1712.06952 |
Citations | PageRank | References |
0 | 0.34 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Arvin Rasoulzadeh | 1 | 0 | 0.68 |
| Georg Nawratil | 2 | 22 | 5.94 |