On singularities of real algebraic sets and applications to kinematics

Abstract

We address the question of identifying non-smooth points in Vℝ(I){{\bf{V}}}_{{\mathbb{R}}}(I) the real part of an affine algebraic variety. Two simple algebraic criteria will be formulated and proven. As an application, we investigate the configuration spaces of the planar four-bar linkage and the delta robot and prove that all singularities are CS-singularities.

Keywords

• real algebraic geometry
• singularities
• planar linkages
• kinematics
• 14b05
• 14p05
• 14p15
• 13p25
• 70b15