Federico ThomasBarcelona. Spain

A Reconfigurable 5-DoF 5-SPU Parallel Platform

Júlia Borràs, Federico Thomas, Erika Ottaviano, and Marco Ceccarelli

Outline

1 – Introduction

5 DoF 5-SPU parallel platformPrevious worksGoal

2 – Singularity-invariant leg rearrangements

3 – The proposed robot

Architectural singularitiesThe effect of reconfiguringSimulations

5 - Conclusions

5-DoF 5-SPU Parallel Platform

Let us consider a Stewart platform containing a line-plane subassembly

We propose a reconfigurable 5-leg 5-SPU parallel plaform

Robots with axisymmetric tool (Ex: 5-axis milling machine)

Previous works

First closed-form solution for the forward kinematics of Stewart platforms containing a line-plane subassembly

Algebraic architecturally singular condition for the line-plane subassembly

Singularity-invariant leg rearrangements in line-plane subassemblies.

Geometrical interpretation of the architectural singularities

Goal

To change leg attachment locations in such a way that:

The robot geometry is modified Singularity locus remains unaltered

There exists a one-to-one mapping between the leg lengths before and

after the reconfiguration

Reconfigurations without increasing the control of the

platform

It can be adapted it to particular tasks

Reducing the risk of collisions between legs

Improving the stiffness of the robot, in a given region of its

workspace

Singularity-invariant leg rearrangements

Same singularities

Different behavior even near a singularity

Modify the location of the attachments

Coefficients depend on the location of the attachments

Singularities of a Stewart-Gough platform

Unknowns: position and orientation parameters

Singularity polynomial is the same

(up to a constant multiple)

Singularity-invariant leg rearrangement

Pose defined by

Plücker coordinates of the leg lines

Factorization of the jacobian determinant: Stewart platform containing a line-plane subassembly

Singularity-invariant leg rearrangements

Hypersurface inSingularity polynomial

of the line-plane subassembly

Singularity-invariant leg rearrangements

(x1,y1,z1)

(x2,y2,z2)

(x3,y3,z3)

(x4,y4,z4)

(x5,y5,z5)

Hypersurface inSingularity polynomial

Singularity-invariant transformation!!!

New point (x’,y’,z’)

Singularity-invariant leg rearrangements

Giving values for z

Giving values to (x,y)

What does it mean?

One-to-one correspondence

points in the line

lines in theplane

Lines in the base plane

Points in the line

Singularity-invariant leg rearrangements

Base attachments Platform attachments

Singularity-invariant leg rearrangements

B-lines as radial guides arranged passing though the vertices of a regular pentagon

The proposed robot

B point placed at the origin

Reconfiguration of the attachments along the B-lines

Architectural singularities

A line-plane subassembly is architecturally singular iff

Any 4 base attachments are collinear

or

The 5 base attachments and B lie on a conic

Architectural singularities

The design avoids all possible architectural singularities

The proposed robot

Singularity locus

Coordinates Cofactors

The proposed robot

Singularity locus:

For a fixed orientation For a fixed position

The effect of reconfiguring

Singularity locus:

Multiplying factor:

The proposed robot

Prototype

Conclusions

Thank youFederico Thomas (fthomas@iri.upc.edu)Institut de robòtica i informàtica industrial.

Barcelona