# PuzzleFlex: kinematic motion of chains with loose joints

## TL;DR

PuzzleFlex introduces a linear programming approach to analyze the free motions of planar rigid body assemblies with loose joints, enabling efficient analysis of large systems for robotics, stability, and control applications.

## Contribution

It models loose joints as local distance constraints and linearizes them for linear programming, allowing scalable analysis of complex mechanical systems.

## Key findings

- Efficient linear programming formulation for large assemblies.
- Applicable to modular robots, stability, and formation control.
- Enables analysis of systems with thousands of bodies.

## Abstract

This paper presents a method of computing free motions of a planar assembly of rigid bodies connected by loose joints. Joints are modeled using local distance constraints, which are then linearized with respect to configuration space velocities, yielding a linear programming formulation that allows analysis of systems with thousands of rigid bodies. Potential applications include analysis of collections of modular robots, structural stability perturbation analysis, tolerance analysis for mechanical systems, and formation control of mobile robots.