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Method for the Optimization of Kinematic and Dynamic Properties

of Parallel Kinematic Machines

R. Neugebauer1 (1), W.-G. Drossel1 (3), C. Harzbecker1 (3), S. Ihlenfeldt1, S. Hensel1

1Fraunhofer Institute for Machine Tools and Forming Technology IWU, Chemnitz, Germany

Abstract

The following paper introduces an approach, which allows the consideration of the kinematic as well as the

dynamic properties of parallel kinematic machines. Based on the results of a preceding kinematic

optimization, a FEM-model with arbitrary input parameters is designed. The full kinematic functionality of

struts and joints used is ensured. By coupling the FEM-model to the GNU Octave numerical program system,

a variety of movements including machining forces can be simulated. A Broyden-Fletcher-Goldfarb-Shanno

optimization algorithm, using GNU Octave, was written and coupled to the FEM-system. Now, this algorithm

is able to influence the models arbitrary input parameters during the optimization process. Thus, the model is

optimized automatically for a certain machining process and/or dynamic behavior. This procedure is

demonstrated using the example of a delta robot structure originally designed by Raymond Clavel [7].

Keywords:

Optimization; Kinematic; Dynamic

1 INTRODUCTION

Both kinematic variables (such as the quality of transmission)

and stiffness behavior towards static and

dynamic loads have a share in the optimization of parallel

kinematic machines. Therefore optimization processes

can not be limited to kinematics only. A second optimization

run based on such a kinematic optimization is

required to approximate the actual behavior of the structure

to be designed in the optimum way (see Figure 1).

2-Phase PKM-Optimization (simplified)

Geometric requirements

Initial value

Workspace size

Number of DOF...

STOP

FEM-optimization

Collisions within workspace?

Kinematic optimization

Experience

Type of PKM

Initial geom. dimensions

Drive types (rot./ transl.)

Global Performance Index

Min. distances: - strut/ strut

- strut/ tool

- strut/ base

Stiffness - tool/ base

Eigenfrequencies

Thermal behavior

Vectorized model

Changed vectorized model

FEM-model

Figure 1: Diagram of a two-step optimization process.

An initial value is created based on the minimum

requirements of the structure to be designed. This starting

point contains information on the types and number of

struts, degrees of freedom of joints, and macrostructure.

Kinematic optimization improves the macrostructure. This

can be done under various aspects such as high dynamics

or high stiffness. After a collision study and subsequent

review of the structure, a second optimization step can be

required to give an actual reflection of the physical

properties (e.g. stiffness characteristics, eigenfrequencies,

thermal behavior) of the PKM to be expected, and to

improve them.

This article introduces a method to perform a FEM

optimization based on a preceding kinematic optimization.

Thus, the dynamic properties of the parallel kinematic

machine to be designed will be improved fully optimized

and predicted in advance.

For this purpose, an algorithm is introduced that allows to

couple a script-enabled FEM-system with a mathematical

and numerical system that is script-enabled likewise. This

coupling is to enable the mathematical system to improve

a PKM model independently based on given dynamic

processes.

This process is demonstrated on a drilling/ milling machine

to be designed on the basis of a Clavel tripod structure

(see Figure 2).

Figure