Direct volumetric error evaluation for multi-axis machines

Abstract

A generalized methodology, referred to as direct error analysis, for the evaluation of the position and orientation errors in the workspace of a multi-axis machine of arbitrary configuration was formulated based on two important new concepts. First, a modified coordinate frame assignment rule was defined. This rule offers the ability to assign the origins of the joint frames at the physical joint so that the corresponding homogeneous transformation matrices can overcome the problem with the conventional Denavit-Hartenberg rule with respect to small variations in link geometry. Second, the concepts of fixed and moving error reference frames for kinematic error motions were introduced. Depending on the joint configuration these frames facilitate the representation of the true kinematic error motions at both ends of the physical link.