Calibration of Parallel Kinematic Machines: Theory and Applications

Abstract

Introduction\nAs already stated in the chapter addressing the calibration of serial manipulators, kinematic calibration is a procedure for the identification and the consequent compensation of the geometrical pose errors of a robot. This chapter extends the discussion to Parallel Manipulators (also called PKM Parallel Kinematic Machines). As described in the following (Section 2) this extension is not obvious but requires special care.\nAlthough for serial manipulators some procedures for the calibration based on automatic generation of a MCPC (Minimum Complete Parametrically Continuos) model exist, for PKMs only methodologies for individual manipulators have been proposed but a general strategy has not been\npresented since now. A few examples of the numerous approaches for the calibration of individual PKMs are proposed in (Parenti-Castelli & Di Gregorio, 1995), (Jokiel et al., 2000) for direct calibration and (Neugebauer et al., 1999), (Smollett, 1996) for indirect or self calibration techniques.\nThis paper makes one significant step integrating available results with new ones and reordering them in simple rules that can be automatically applied to any PKM with general kinematic chains. In all the cases a MCPC kinematic model for geometrical calibration is automatically obtained.\nIn Section 2 the main features of PKMs calibration is pointed out and the total number of the necessary parameters is determined; this is an original contribution. In Sections 3 and 4 two novel approaches for the generation of a MCPC model are described. Sections 5 and 6 are dedicated to the analysis of the singular cases and to the procedure for the elimination of the\nredundant parameters respectively; actual cases are discussed. Section 7 presents several examples of application of the two proposed procedures to many existing PKMs. Section 8 eventually draws the conclusions.