Extracting Articulation Models from CAD Models of Parts With Curved Surfaces

In an assembly, degrees of freedom are realized by creating mating features that permit relative motion between parts. In complex assemblies, interactions between individual degrees of freedom may result in a behavior different from the intended behavior. In addition, current methods perform assembly reasoning by approximating curved surfaces as piecewise linear surfaces. Therefore, it is important to be able to reason about assemblies using exact representations of curved surfaces; verify global motion behavior of parts in the assembly; and create motion simulations of the assembly by examination of the geometry and material properties. In this paper, we present a linear algebraic constraint method to automatically construct the space of allowed instantaneous motions of an assembly from the geometry of its constituent parts. Our work builds on previous work on linear contact mechanics and curved surface contact mechanics. We enumerate the conditions under which general curved surfaces can be represented using a finite number of constraints that are linear in the instantaneous velocities. We compose such constraints to build a space of allowed instantaneous velocities for the assembly. The space is then described as a set-theoretic sum of contact-preserving and contact-breaking subspaces. Analysis of each subspace provides feedback to the designer, which we demonstrate through the use of an example assembly—a 4-part mechanism. Finally, the results of the analysis of a 4-bar linkage are compared to those from mechanism theory.