A Formulation for Automated Computer-Aided Design of Machine Parts.

Abstract

A mathematical formulation for the automated design of parts and assemblies is presented as a numerical algorithm and its accompanying experimental code. A mechanical part is modeled as an assembly of links connected via joints. Constraints are imposed by the designer such that some dimensions are specified as variables while others are allowed to propagate due to a design change. Graph theory is used to model the assembly where the method of cut-joint constraints is used to obtain a spanning tree. Joint constrains between the various links are introduced and their variations are computed. A velocity transformation matrix is introduced and the Jacobian of for each constraint is developed. The Jacobian of the constraint is transformed to joint coordinate space. Finally, because the resulting system of equations has a non-square Jacobian, the Moore-Penrose inverse is used to compute an assembled configuration, hence, redesigning the assembly. The formulation is extended to include various methods for computing an assembled configuration. While the accompanying numerical code is only experimental, the formulation presented herein is believed to form the basis of a new methodology for automated computer-aided design of parts and systems. The significance of this work is characterized by the formulation’s ability to automatically design and redesign parts.