An improved method for on‐line calculation and compensation of the static deflection at a robot end‐effector

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Abstract
Traditionally, robotic deflection analysis for a low‐weight robot has been performed based on an assumption that each link is treated as a cantilever beam, which leads to no angular deflection at a joint. In practice, a robotic intermediate joint is linearly and angularly deflected when a load is applied at the end‐effector. It is found in this study that the additional link deflection resulting from the angular deflection of a robotic revolute joint substantially contributes to the end‐effector's total deflection. This article presents an improved method via a combination of classical beam theory, energy methods and the concepts of differential relationships to more accurately calculate the static deflection at the end‐effector. A systematic approach to deflection calculation through three different Jacobians are presented. The study also shows that the end‐effector's deflection heavily depends on robotic arm configurations. The deflection is then compensated based on the selected optimum configuration. The theoretical deflection analysis is verified by experimental results. A planar two‐link robot and a six‐degree‐of‐freedom Elbow Manipulator are used for numerical illustration and calculation procedure.

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