Configuration Space Singularities of The Delta Manipulator

TL;DR

This paper analyzes the configuration space of the Delta manipulator, identifying singular points where the Jacobian loses rank and demonstrating these are non-manifold points in the algebraic set.

Contribution

It provides a detailed algebraic analysis of singularities in the Delta manipulator's configuration space, revealing their non-manifold nature.

Findings

Identified 24 singular points in the configuration space.

Proved these points are not manifold points of the algebraic set.

Enhanced understanding of the manipulator's kinematic singularities.

Abstract

We investigate the configuration space of the Delta-Manipulator, identify 24 points in the configuration space, where the Jacobian of the Constraint Equations looses rank and show, that these are not manifold points of the Real Algebraic Set, which is defined by the Constraint Equations.