Various Approaches for the Modeling 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 control 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 with respect to the modeling 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 multihody systems is extended summarizing the rigid body motions as well as the elastic motions. Particularly, the development of a finite beam element is considered with respect to the large nonlinear movements of robot arms. 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. Further, two examples show some characteristic errors resulting from the linear kinematical description of finite beam elements. For large rigid body motions, a refined description of the elastic motions must be used.