# On local real algebraic geometry and applications to kinematics

## TL;DR

This paper develops an algebraic criterion to identify non-smooth points in real algebraic varieties and applies it to analyze the configuration spaces of certain planar linkages.

## Contribution

It introduces a new algebraic criterion for non-smooth points and demonstrates its application to kinematic configuration spaces.

## Key findings

- Criterion effectively identifies non-smooth points in real algebraic varieties.
- Application to planar linkages clarifies their configuration space structure.
- Provides tools for analyzing kinematic mechanisms using algebraic geometry.

## Abstract

We address the question of identifying non-smooth points in affine real algebraic varieties. A simple algebraic criterion will be formulated and proven. As an application we can answer several questions about the configuration spaces of some class of planar linkages.