A Unified Approach to Modelling of Flexible Robot Arms

Summary

Increasing demands on velocity and accuracy of robot motions require the consideration of the elasticity of robot arms in the controller and structural design. The first and most essential step is the mathematical modeling. The transmission flexibility and the torquer dynamics can easily be modeled by proven rigid body formalisms. The structural elasticity of robot arms, however, has to be regarded with more detail.

There have been numerous papers concerning the modelling approach which can be summarized essentially in three categories:

• i) A series of rigid bodies and elastic springs.

• ii) A series of finite elements.

• iii) One continuous element subject to modal analysis.

For an optimal design it is hard to find out which model is the best one. A comparison is usually omitted in literature.

This paper presents a unified approach including all the mentioned models. For this purpose the method of multibody systems is extended summarizing the rigid body motions as well as the elastic motions. The three different. approaches are compared using a simple example. It turns out that the different methods are strongly related to each other. Moreover, for a sufficient number of degrees of freedom even the numerical results are equivalent.