Dynamics of a radially rotating beam with impact: Implications for robotics.

Abstract

Theoretical and experimental results on the dynamics of a radially rotating beam with impact are presented. The governing equations of motion are coupled, in that the elastic motion influences the rigid body motion and vice versa. Impact is treated using the momentum balance method together with a velocity dependent coefficient of restitution. A spring-dashpot model of impact is also implemented and compared with the momentum balance method. Galerkin's method and numerical integration are used to obtain the theoretical results. Experiments are performed to investigate the validity of the model for flexible systems on a radially rotating flexible beam attached to a rigid shaft. The elastic motion of the beam is measured using strain gages, and an optical incremental encoder is utilized to measure the rigid body angular velocity. Torque input to the rigid shaft is measured using a Hall effect current transducer. The results from the simulation are compared with the experiments. Excellent agreement is found for response frequencies, peak strains and rigid body angular velocities. Multiple impacts are detected in both simulations and experiments. Sensitivity studies are employed to generalize the results of the experiments. It is found that the model will give good results over a wide range of system parameters. An important conclusion of this study is that the momentum balance model using a velocity dependent coefficient of restitution works quite well for systems which consist of both rigid and flexible links.