Capturing Articulation in Assemblies from Component Geometry

This paper presents a method to extract instantaneous articulation from part geometry, based on surface mating constraints as well as constraints imposed by other incidental contacts. Many assemblies contain joints, each of which have degrees of freedom associated with them. These joints allow the relative positions of parts in the mechanism to change as the joints are articulated. Being able to represent these joints and their behavior is important from the designers perspective because it enables him or her to verify whether kinematic requirements have been met.Therefore, it is useful to be able to obtain such joint information directly from part geometry and contact physics. The method presented here handles all lower pairs of kinematic joints. Surface mating contacts are classied into one of three types: planar, spherical and cylindrical. The contacts are represented by algebraic inequalities describing the translational and angular velocities at the contact. Non-penetration conditions are written for a nite set of points on the boundary of each contact face, and it is shown that the nite set of conditions is representative of the entire boundary and the region enclosed by the boundary. Simultaneous satisfaction of the non-penetration conditions at all the contact surfaces between a pair of bodies is represented by a 6-dimensional simplex, which can be solved using linear programming.