Extending a gear CAD application with special space feature objects

The Surface Constructor gear CAD application developed by the author is intended for creation and investigation of new contacting surface pairs. The main capability of the software is the generation of surfaces by surfaces using enveloping. The applied original Reaching Model theory provides many unique capabilities, like detection of local undercut situations and global cut problems. Beside usual 3D surface and contact line visualisation there is a need in development of kinematical surfaces for visualisation of special locus of the velocity space, because the special formations and singularities plays important role in the successful development of new gear surfaces having excellent contacting characteristics. As the contact points characterised by the orthogonality of the relative speed vectors and the surface normals it is evident that the exploration of the special loci of the velocity space is also informative and advantageous. One of the most important instantaneous geometrical formation is the axis of the velocity screw and the axoid evolving in the process of motion. The aim of the presented developments is to improve the visualisation capabilities of Surface Constructor with new velocity space objects, like the linear complex of normals in the velocity screw, the reciprocal polars and the linear congruence of reciprocal polars. Taking the advantage of dynamic 3D visualisation capability of today's computers these objects can be analysed along their formation process and the singularities of the velocity space can be discovered. The detection of problematic spatial regions and the revealing of healthy regions will aid the development of better gears having optimal contacting characteristics.