Workspace, Joint space and Singularities of a family of Delta-Like Robot

Ranjan Jha (1) , Damien Chablat (2, 3) , Luc Baron (4) , Fabrice Rouillier (5) , Guillaume Moroz (6)

1 CSIR - Council of Scientific and Industrial Research [India]
2 LS2N - Laboratoire des Sciences du Numérique de Nantes
3 LS2N - équipe ReV - Robotique Et Vivant
4 EPM - École Polytechnique de Montréal
5 OURAGAN - OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs
6 GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm

This paper presents the workspace, the joint space and the singularities of a family of delta-like parallel robots by using algebraic tools. The different functions of SIROPA library are introduced, which is used to induce an estimation about the complexity in representing the singularities in the workspace and the joint space. A Groebner based elimination is used to compute the singularities of the manipulator and a Cylindrical Algebraic Decomposition algorithm is used to study the workspace and the joint space. From these algebraic objects, we propose some certified three-dimensional plotting describing the shape of workspace and of the joint space which will help the engineers or researchers to decide the most suited configuration of the manipulator they should use for a given task. Also, the different parameters associated with the complexity of the serial and parallel singularities are tabulated, which further enhance the selection of the different configuration of the manipulator by comparing the complexity of the singularity equations.

Mots clés: Workspace; Groebner basis; Singularities; Delta-like robot; Cylindrical algebraic decomposition; Parallel robot

Domaines: Robotique [cs.RO]

Ranjan Jha, Damien Chablat, Luc Baron, Fabrice Rouillier, Guillaume Moroz. Workspace, Joint space and Singularities of a family of Delta-Like Robot. Mechanism and Machine Theory, 2018, 127, pp.73-95. ⟨10.1016/j.mechmachtheory.2018.05.004⟩. ⟨hal-01796066⟩