This study describes the methodology for modelling a worm and worm wheel of a double enveloping worm gear with the use of a CAD system. An algorithm for generating a globoid helix is described. In addition, the methodology for modelling an hourglass worm thread with a straight axial tooth profile is presented. The shape of the hourglass worm tooth end with and without a trace modification is proposed. Moreover, a method for achieving a geometric modification of the tooth trace was developed. Next, the method for modelling the worm wheel teeth is described. A solid model of using a machining worm as a hob is applied. Owing to the limitations of a CAD system, which prevents the use of a direct machining simulation, an indirect modelling method is introduced. In the present study, different CAD techniques, both solid and surface, are applied. Knowledge of the correct modelling of the hourglass worm and worm wheel facilitates their generation and conducting various analyses, including a tooth contact analysis. CAD models are utilised to analyse the geometrical contact pattern in a CAD environment, to carry out FEM analysis, to manufacture real parts or to prototype models using the technique of rapid prototyping. They can be also used as master models for measurement, e.g. in optical technics.

Geometric deviations of free-form surfaces are attributed to many phenomena that occur during machining, both systematic (deterministic) and random in character. Measurements of free-form surfaces are performed with the use of numerically controlled CMMs on the basis of a CAD model, which results in obtaining coordinates of discrete measurement points. The spatial coordinates assigned at each measurement point include both a deterministic component and a random component at different proportions. The deterministic component of deviations is in fact the systematic component of processing errors, which is repetitive in nature. A CAD representation of deterministic geometric deviations might constitute the basis for completing a number of tasks connected with measurement and processing of free-form surfaces. The paper presents the results of testing a methodology of determining CAD models by estimating deterministic geometric deviations. The research was performed on simulated deviations superimposed on the CAD model of a nominal surface. Regression analysis, an iterative procedure, spatial statistics methods, and NURBS modelling were used for establishing the model.

The paper presents the development procedures for both virtual 3D-CAD and material models of fractured segments of human spine formulated with the use of computer tomography (CT) and rapid prototyping (RP) technique. The research is a part of the project within the framework of which a database is developed, comprising both 3D-CAD and material models of segments of thoracic-lumbar spine in which one vertebrae is subjected to compressive fracture for a selected type of clinical cases. The project is devoted to relocation and stabilisation procedures of fractured vertebrae made with the use of ligamentotaxis method. The paper presents models developed for five patients and, for comparison purposes, one for a normal spine. The RP material models have been built basing on the corresponding 3D-CAD ones with the use of fused deposition modelling (FDM) technology. 3D imaging of spine segments in terms of 3D-CAD and material models allows for the analysis of bone structures, classification of clinical cases and provides the surgeons with the data helpful in choosing the proper way of treatment. The application of the developed models to numerical and experimental simulations of relocation procedure of fractured vertebra is planned.