On the Study of the Kinematic Position Errors Due to Manufacturing and Assembly Tolerances

Abstract

This work deals with the kinematic position errors analysis of planar multibody mechanical systems when considering tolerances associated with manufacturing and assemble processes. For this purpose, the generalized Cartesian coordinates are utilized to mathematically formulate kinematic constraints and equations of motion of the multibody systems. The systems are defined by a set of generalized coordinates, which represents the instantaneous positions of all bodies, together with a set of generalized dimensional parameters that defines the functional dimensions of the system under analysis. The generalized dimensional parameters can take into account the tolerances associated with the lengths, fixed angles, diameters and distance between centers. This work emphasizes the relation among kinematic constraints, dimensional parameters and output kinematic parameters. Based on the theory of dimensional tolerances, the variation of the geometrical dimensions is regarded as a tolerance grade with an interval associated with each dimension and, consequently, a kinematic amplitude variation for the position of bodies.