ABSTRACT
370The purpose of this chapter is to illustrate a relatively simple, structured approach for modelling precision systems that can be used to evaluate a broad variety of instrument and machine designs. A number of case studies and examples show how, when used in conjunction with the design principles discussed in other chapters, relatively simple mathematical techniques can be employed to determine critical aspects of a given design. In this chapter it is assumed that mechanisms are comprised from perfect rigid bodies that translate or rotate by means of a guided mechanism (slideways, crossed-roller bearings, air bearings, etc.) that, although not providing ideal rectilinear motions, are repeatable. Specifically, rigid body motions and the inclusion of error sources will be described in detail. With this in mind, the following represents a method for evaluating the combined effects of errors in a mechanism comprised from an assembly of translation and rotation axes. In particular, a method utilising homogeneous transformation matrices for assessing propagation of uncertainties will be developed.
