Kinematic Design of 3-URU Pure Rotational Parallel Mechanism with Consideration of Uncompensatable Error

Abstract

Kinematic design of a lower-dof parallel mechanism, a 3-URU pure rotational parallel mechanism, is presented that takes into account the “uncompensatable error”. The uncompensatable error is defined as the position error of the rotation center of the platform caused by errors in the kinematic constants, such as a joint axis error, that cannot be compensated for by control or calibration. Sensitivity matrices for four error sources were derived, introducing virtual revolute joints. An index for evaluating the magnitude of the uncompensatable error was developed and used to numerically investigate the effect of kinematic constants on the uncompensatable error. Finally, an optimal design for an application of the 3-URU parallel mechanism to a tool-orientating device was done in consideration of the uncompensatable error. In this design, the redundant orientation parameter was optimized together with the values of the kinematic constants to minimize the uncompensatable error. Two mechanisms optimal for different workspace specifications were derived.