ParallelPlatform Directory Reference

A couple of 6-6 parallel robots.

Files
file	Dietmeier.world [code]
	A 6-6 parallel platform with 40 solutions.
file	Griffis-Duffy.world [code]
	An architecturally singular 6-6 parallel platform.

Detailed Description

[Introduction] [Geometry] [Formulations]

Introduction

This device is a generalization of a mechanism originally proposed by Stewart as a flight simulator. It consists of two rigid bodies, a fixed "base" and a moving "platform", which are held fixed one to the other by means of six legs. The legs are connected to the base and platform bodies via spherical joints, and their lengths can be changed by means of linear actuators. No further geometric constraints are assumed for the device. In particular, the base and platform joints need not be coplanar.

While the inverse kinematics of this mechanism is straightforward (given the platform pose, derive the leg lengths) the converse problem (given the leg lengths, derive the platform pose) is by no means trivial and can have many different solutions. In fact, for a long time, it has been considered one of the most difficult problems of robot kinematics.

Geometry

The geometry of a parallel platform is given by the leg lengths $l_i$ and by the anchor points of the legs on the base $A_i$ and on the platform $B_i$ , for $i=1..6$ .

Formulations

This directory includes formulatins for two different parallel platforms:

Dietmeier.world A parallel platform with 40 solutions, the maximum possible number of solutions for a parallel platform.
Griffis-Duffy.world An architecturally singular parallel platform.

ParallelPlatform Directory Reference

Files

Detailed Description

Introduction

Geometry

Formulations