A Systematic and General Approach to Kinematic Position Errors Due to Manufacturing and Assemble Tolerances

Abstract

A systematic and general methodology for kinematic position errors analysis of multibody systems is investigated throughout this work, taking into account the influence of the manufacturing and assemble tolerances on the performance of planar mechanisms. The generalized Cartesian coordinates are used to mathematically formulate kinematic constraints and equations of motion of the multibody systems. Thus, the systems are defined by 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. These generalized dimensional parameters take into account the tolerances associated with the lengths, fixed angles, diameters and distance between centers, among others. This paper highlights 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 bodies’ position. The methodology presented is implemented in a computational code developed for kinematic analysis of general multibody systems, capable of automatically generating and solving the equations of motion for general multibody systems. Finally, a slider-crank mechanism is used as a numerical example to demonstrate the accuracy of the presented methodology, as well as to discuss the main assumptions and procedures adopted in this work.