Abstract
Increasingly, light and fast robots are in demand, and the flexibility of their links are no longer negligible. For such robots, which are often called fllexible arms, it is necessary to compensate for deformations and to supress vibrations caused by the elasticity of the links. In general, some mathematical models are required for the analysis or control of flexible arms. There have been many studies about planar motions of flexible arms, but not so many about 3D motions. In this paper, a 3D spring/mass model is proposed to describe an elastic link with a heavy lumped mass and a light beam in 3D motion. A flexible arm which has three joints and two elastic links is modeled in this way. The equation of motion and then the state equation are derived to describe the dynamics of the flexible arm under certain assumptions. It is shown that we can determine the end-of-arm position and orientation from the output of accelerometers installed at the tips of the elastic links. Experimental results demonstrate that a controller designed using optimal regulator theory can suppress the vibration significantly.
