Joseph Pegna

Exploratory investigation of solid freeform construction

A radical departure from generally accepted concepts in construction robotics is proposed in this paper. A new process derived from the emerging field of additive manufacturing processes is investigated for its potential effectiveness in construction automation. In essence, complex assemblies of large construction components are substituted with a large number of elemental component assemblies. The massive complexity of information processing required in construction is replaced with a large number of simple elemental operations which lend themselves easily to computer control. This exploratory work is illustrated with sample masonry structures that cannot be obtained by casting. They are manufactured by an incremental deposition of sand and Portland cement akin to Navajo sand painting. A thin layer of sand is deposited, followed by the deposition of a patterned layer of cement. Steam is then applied to the layer to obtain rapid curing. A characterization of the resulting material properties shows rather novel anisotropic properties for mortar. Finally, the potential of this approach for solid freeform fabrication of large structures is assessed.

Surface Curve Design by Orthogonal Projection of Space Curves Onto Free-Form Surfaces

A novel technique for designing curves on surfaces is presented. The design specifications for this technique derive from other works on curvature continuous surface fairing. Briefly stated, the technique must provide a computationally efficient method for the design of surface curves that is applicable to a very general class of surface formulations. It must also provide means to define a smooth natural map relating two or more surface curves. The resulting technique is formulated as a geometric construction that maps a space curve onto a surface curve. It is designed to be coordinate independent and provides isoparametric maps for multiple surface curves. Generality ofthe formulation is attained by solving a tensorial differential equation formulated in terms of local differential properties of the surfaces. For an implicit surface, the differential equation is solved in three-space. For a parametric surface the tensorial differential equation is solved in the parametric space associated with the surface representation. This technique has been tested on a broad class of examples including polynomials, splines, transcendental parametric and implicit surface representations.

Geometrical Criteria to Guarantee Curvature Continuity of Blend Surfaces

Computer Aided Geometric Design (CAGD) of surfaces sometimes presents problems that were not envisioned in classical differential geometry. This paper presents mathematical results that pertain to the design of curvature continuous blending surfaces. Curvature continuity across normal continuous surface patches requires that normal curvatures agree along all tangent directions at all points of the common boundary of two patches, called the linkage curve. The Linkage Curve theorem proved here shows that, for the blend to be curvature continuous when it is already normal continuous, it is sufficient that normal curvatures agree in one direction other than the tangent to a first order continuous linkage curve. This result is significant for it substantiates earlier works in computer aided geometric design. It also offers simple practical means of generating second order blends for it reduces the dimensionality of the problem to that of curve fairing, and is well adapted to a formulation of the blend surface using sweeps. From a theoretical viewpoint, it is remarkable that one can generate second order smooth blends with the assumption that the linkage curve is only first order smooth. The geometric criteria presented may be helpful to the designer since curvature continuity is a technical requirement in hull or cam design problems. The usefulness of the linkage curve theorem is illustrated with a second order blending problem whose implementation will not be detailed here.

Software calibration of the multifringe pattern analysis of circular zone plates.

The linearized perturbation method for fringe pattern analysis and its extension to multifringe analysis have been recently introduced [ Hilaire , Ph.D. dissertation (Rensselaer Polytechnic Institute, Troy, N.Y., 1993)]. For isolating the error component that is due to information processing—as opposed to image-acquisition errors—experimental calibration experiments were conducted by use of computer-generated fringe patterns. The effects of noise, fringe completeness, image resolution, illumination, quantization, and displacement magnitude are tested and discussed in evaluating the software’s performance and accuracy.

Generalized Abbe Principle: Position Error Propagation in Machine Elements

In the quest for ever finer levels of technology integration, mechanical linkages reach their precision limits at about 5 micrometers per meter of workspace. Beyond this physical limit, all six dimensional degrees offreedom need to be precisely ascertained to account for mechanical imperfections. This paper substantiates Wus vision of precision machines without precision machinery. A formulation and statistical characterization of position and orientation error propagation in rigid bodies are presented for two extreme models of measurement. It is shown that error distribution is uniquely dependent upon the design of the measurement plan. The theoretical foundations presented were evolved in the course of designing precision machinery. Other potential applications include: fixture design, metrology, and geometric tolerance verification.

Multifringe pattern analysis of circular zone plates

We introduce the linearized perturbation method to find the center of a set of concentric circular fringes. The mathematical foundations of the method presented here are instrumental in the design of a two-dimensional interferometric position sensor, which uses the geometry of the fringe pattern rather than the wavelength. A wavelength-independent physical characteristic of the fringe pattern is derived, which relates the radii of successive fringes. The linearized perturbation method is formulated for multiple fringes as a constrained quadratic optimization problem. Experimental calibrations have shown that using physical constraint information significantly improves the precision on the center position.

Teaching Tolerances: A Comparison between the Conventional and Reverse Engineering Approaches

Over the last decade Geometric Dimensioning and Tolerancing (GD&T) has gone from black art to the forefront of computer aided design research. Despite a prominent position in industrial and academic research, GD&T is seldom taught at university level. This paper offers a glimpse at two of those courses, and compares the pedagogy adopted to introduce the fundamental concepts. The conventional approach taken to tolerance education at the Ecole Polytechnique of Montreal is integrated through the curriculum in a two course sequence, respectively as required sophomore and elective senior courses. An elective senior design course at Rensselaer Polytechnic Institute introduces GD&T by way of reverse engineering of existing mechanical systems. Both approaches are presented and a comparison is drawn from the point of view of course contents and integration within a Mechanical Engineering curriculum. To illustrate the two different approaches, concrete examples taken from the course contents are included.

Software calibration of the multifringe pattern analysis of circular zone plates

The linearized perturbation method for fringe pattern analysis and its extension to multifringe analysis have been recently introduced [Hilaire, Ph.D. dissertation (Rensselaer Polytechnic Institute, Troy, N.Y., 1993)]. For isolating the error component that is due to information processing-as opposed to image-acquisition errors-experimental calibration experiments were conducted by use of computer-generated fringe patterns. The effects of noise, fringe completeness, image resolution, illumination, quantization, and displacement magnitude are tested and discussed in evaluating the softwares performance and accuracy.