The worrnscrew gearset provides a potential advantage for some robot manipulator designs because of its simplicity, compactness, and capacity for large speed-reduction ratios. However, an oscillatory behavior has been observed in such implementations that, depending on the extension and loading of the manipulator, tends to grow as the manipulator is lowered under the influence of gravity and disappears as the manipulator is raised. The oscillations can become quite large, crippling the utility of the manipulator The growing oscillations are indicative of an instability. However, it is not immediately apparent why such a system should be unstable. The objectives of this work were to find the source of the oscillatory behavior and to determine whether feedback control can be employed to stabilize such a system.
Worm gear transmissions are capable of high velocity ratios as well as redirection of rotation. Both of these features are desirable for some robot geometries. A problem has been encountered in several robot designs; however, where a self-excited vibration occurs for some configurations of the manipulator in the joint containing the worm gear. In this work, a system which exhibits this type of undesirable motion is examined. The system consists of a DC servo motor which is used to position a flexible cantilever arm through a worm gear transmission. A nonlinear model is developed to describe the motion of the system. The model is then validated by comparing the predicted response to the observed response of an experimental system. It is demonstrated that the model accurately predicts the onset of the unstable vibration. The model is then linearized and it is shown that the linear model will predict the occurrence of the instability as well.
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