Error modeling and sensitivity analysis of a 3-P(Pa)S parallel type spindle head with parallelogram structure

The 3-P(Pa)S mechanism, based on the 3-Prismatic-Rotational-Spherical (PRS) mechanism, but with three of its revolution joints and passive links replaced by parallelogram structures, provides improved stiffness and better constraint of undesired Degree of Freedom (DOFs). The general method to establish the error model of a 3-P(Pa)S mechanism is simplifying it to a 3-PRS mechanism, which fails to account for the influence of the errors in the parallelogram structure. In this article, the error model of a spindle head based on 3-P(Pa)S mechanism was established. By projecting the structural errors of the parallelogram structure to the structural errors of a 3-PRS mechanism which is simplified from the 3-P(Pa)S mechanism, the errors of the parallelogram can be included into the model. Then, the projecting method was verified by an experiment on the spindle head to prove its correctness. Based on the error model, sensitivity analysis of the structural errors was carried out. According to the characteristic of the mechanism, two new sensitivity indexes, standardized signed local sensitivity index and standardized signed global sensitivity index, were proposed which can better reflect the influence of the structural errors on the end effector error and can also indicate whether some structural errors have similar or opposite influence on the end effector. Then, the most sensitive errors were derived and the sensitivity distribution within the workspace of the spindle head was analyzed. Additionally, two possible applications based on the sensitivity analysis were proposed to reduce the error of the spindle head.