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 classified 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 finite set of points on the boundary of each contact face, and it is shown that the finite 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. 1Author to whom all correspondence should be addressed. INTRODUCTION Assemblies are composed from parts. The geometry of the parts imposes certain restrictions on the way that they can be assembled, and also on the way that they move relative to one another. The joints between parts are defined by the designer at the conceptual design level to meet certain functional requirements of the assembly. Thus, there can be two types of constraints between parts, namely, constraints induced by the geometry of parts, and constraints introduced by the designer to satisfy functional requirements of the assembly. Both these types of constraints interact to produce a resultant behavior of a joint. At the conceptual level, the designer knows the type and behavior of the joints in the concept design. However, the geometry still needs to be defined. At the preliminary design stage, the geometric information is defined, and the relative positions and orientations of components in the assembly are specified. Following this stage, component and joint representations are enriched to achieve a final refinement of the geometry. In order to generate assembly or disassembly plans for such assemblies, the designer needs to take articulation information into consideration. However, current methods 1 Copyright c © 1998 by ASME of representing articulation are restricted to systems which require complete specification by the user or are feature recognition based. The former are open to incorrect input by the user resulting in illegal articulation behavior. The latter do not account for incidental contacts. In this paper, we present a methodology that extends earlier work on planar contact surfaces and reasons about the degrees of freedom at each joint based on surface mating constraints, which are in turn obtained from analyzing the nature of body to body contact. Non-penetration constraints are imposed along the boundary of each contact surface in the form of algebraic inequalities. It is shown that a finite number of non-penetration conditions are representative of the entire surface in contact. Using linear programming methods, instantaneous velocities and accelerations for each pair of bodies are computed. This determines the type of joint and its features. The algorithms and analysis presented here apply to the so-called “lower” kinematic pairs, namely, the Revolute, Cylindrical, Planar, Prismatic and Spherical joint types. The types of surfaces in contact must be planar, cylindrical or spherical. Since linear programming techniques are used to find a solution, the number of constraints must be finite. We will show that for this reason, some types of patch boundaries must be approximated as “straight line segments” in its topology (straight lines on the plane; circular arcs or vertical lines on the cylinder; great arcs on the sphere). Such a methodology is useful in that it can provide useful feedback to the designer. He or she can determine which components are free to move in the assembly. The procedure can be completely automated, so that there is no user interaction. This eliminates the possibility of input errors. In addition, since the method is algebraic and uses linear programming, it is extremely fast and is valid for all possible surface contacts which fall into one of three classes, unlike other rule-based systems which operate on a feature level. This method will also account for contact surfaces with incomplete geometry (such as portions of planes, cylinders or spheres). REVIEW OF PREVIOUS WORK