Bracing to Increase the Natural Frequency of a Manipulator: Analysis and Design

Abstract

The dynamic behavior of braced manipulators is analyzed. A braced manipulator is a manipulator that has been constrained by contact with the environment at a point other than the robot end effector, tool, or gripper. The analysis is restricted to manipulators with links that are rigid but joints that may be compliant. An expression is developed for the undamped natural frequency of an unbraced manipulator for small am plitudes of vibration. The kinematics of braced manipulators is described using admissible variables (i.e., variables that define the constrained admissible motion space), and the natural fre quency analysis is extended to braced manipulators. Dynamic analysis is used to design the ideal geometry of constraint to optimize the vibration characteristics of a robotic manipulator. It is shown that the lowest braced natural frequency is always greater than or equal to unbraced lowest natural frequency and thus can improve the dynamic performance of the robot. It is shown that there is a range of directions of bracing constraints that have the greatest effect in increasing the lowest natural frequency, and of this range it is possible to choose the most practically convenient. The results of the analysis and design are illustrated by their application to a grinding robot.