The process of layered Additive Manufacture (AM) limits manufactured parts, which leads to the stair-step error, support structures and the anisotropy. CLFDM has been proposed by researchers to alleviate these problems. However, to the best of our knowledge, available CLFDM mainly focuses on filling with the uniform extruded filament in the same layer. While intricate parts usually possess small and critical features, as well as manufacturing error and assembling error. Geometry accuracy and mechanical property of Fused Deposition Modeling (FDM) parts are closely related to inter-layer and inter-road bonding. Therefore, inspired by non-uniform layers of the onion, this paper pays attention to CLFDM with VEF in the layer and between adjacent layers innovatively, whereby the direction and dimension of extruded filament are variable. The literature review of slicing and path planning is given first to make readers better understand the current status and the research gap to highlight the innovation of this paper. Then, flat layer FDM and CLFDM with VEF are modeled respectively, from the aspect of inter-layer and inter-road bonding. After that, the relationships among key process parameters are analyzed. Finally, the simulation is provided to verify the effectiveness and advantages of our method from a theoretical point of view. Generally, this research can be a foundation for CLFDM with VEF, and the preliminary research has shown broad applications.

Math models aid designers in assessing relationships between tolerances that contribute to variations of a dependent dimension that must be controlled to achieve some design function at a target (functional) feature. The Tolerance-Maps © (T-Maps © ) model for representing limits to allowable manufacturing variations is applied to identify the sensitivity of a dependent dimension to each contributing tolerance of the relationship. For each contributing feature and tolerances specified on it, the appropriate T-Map is chosen from a library of T-Maps, each represented in its own respective local reference frame. Each chosen T-Map is then transformed to the coordinate frame at the target feature, and the accumulation T-Map of these is formed with the Minkowski sum. The shape of a functional T-Map/deviation space is circumscribed (fitted) to this accumulation map. Since fitting is accomplished numerically by intersecting geometric shapes, T-Maps/deviation spaces are constructed with linear half-spaces. The sensitivity for each tolerance-and-feature combination is determined by perturbing the tolerance, refitting the functional shape to the modified accumulation map, and forming a ratio of the increment of functional tolerance to the perturbation. Taking tolerance-feature combinations one by one, sensitivities for an entire stack can be built. For certain loop equations, the same sensitivities result by fitting the functional shape to the T-Map/deviation space for each feature, without a Minkowski sum, and forming the overall result as a scalar sum. Sensitivities are used to optimize tolerance assignments by identifying the tolerances that most strongly influence the dependent dimension at the target feature. Form variations are not included in the analysis.

Mathematical tools underlie a method that has strong potential to lower the cost of fixture-setup when finishing large castings that have machined surfaces where other components are attached. One math tool, the kinematic transformation, is used for the first time to construct Tolerance-Map ® (T-Map) ® models of geometric and size tolerances that are applied to planar faces and to the axes of round shapes, such as pins or holes. For any polygonal planar shape, a generic T-Map primitive is constructed at each vertex of its convex hull, and each is sheared uniquely with the kinematic transformation. All are then intersected to form the T-Map of the given shape in a single frame of reference. For an axis, the generic T-Map primitive represents each circular limit to its tolerance-zone. Both are transformed to a central frame of reference and are intersected to form the T-Map. The paper also contains the construction for the first five-dimensional (5D) T-Map for controlling the minimum wall thickness between two concentric cylinders with a least-material-condition (LMC) tolerance specification on position. It is formed by adding the dimension of size to the T-Map for an axis. The T-Maps described are consistent with geometric dimensioning and tolerancing standards and industry practice. Finally, transformations are presented to translate between small displacement torsor (SDT) coordinates and the classical coordinates for lines and planes used in T-Maps.

For the first time, Tolerance-Maps (T-Maps) are constructed to model composite positional tolerancing applied to patterns (arrays) of features. The T-Map for a feature is a range (codomain) of points obtained by mapping all the variational possibilities (domain) of a feature within its tolerance zone to a hypothetical Euclidean point space. T-Maps have already been developed for tolerances applied to single features, such as to a simple axis (line), a plane, and a cylinder, but not for the special methods available for tolerancing patterns of features. In this paper, the different pattern tolerancing methods listed in the standards produce distinctions in geometric shape, proportions, and/or dimensions of a T-Map. The T-Map geometry is different when tolerances are specified with composite position tolerancing rather than with two-single-segment control frames. Additional changes to geometry occur when material modifiers are also specified. Two levels of T-Maps are proposed for a pattern of features. One is at the assembly level to ensure the assembly of an engaging pattern of pins and holes, such as the array of pins on an integrated circuit, which are to be inserted into a base. The second is at the part level to model the variations between the two parts that contain the engaging patterns. The assembly-level T-Maps apply to any number of engaging pin/hole features arranged in any pattern: linear, circular, rectangular, or irregular. In this paper, the part-level T-Map is restricted to linear patterns. The different specifications are also compared with a statistical analysis of misalignment for an assembly with a pattern of pins and holes.

Existing techniques for motion imitation often suffer a certain level of latency due to their computational overhead or a large set of correspondence samples to search. To achieve real-time imitation with small latency, we present a framework in this paper to reconstruct motion on humanoids based on sparsely sampled correspondence. The imitation problem is formulated as finding the projection of a point from the configuration space of a human's poses into the configuration space of a humanoid. An optimal projection is defined as the one that minimizes a back-projected deviation among a group of candidates, which can be determined in a very efficient way. Benefited from this formulation, effective projections can be obtained by using sparsely sampled correspondence, whose generation scheme is also introduced in this paper. Our method is evaluated by applying the human's motion captured by an RGB-depth (RGB-D) sensor to a humanoid in real time. Continuous motion can be realized and used in the example application of teleoperation.

Information exchange and sharing become a necessity for digital factory but they have been more challenging as the industry is computerized more. This is mainly because the capabilities of computerized systems have grown significantly in a very rapid pace in their own information structure, and they require to retrieve various data from different computer systems. ISO 10303–STEP has been developed to provide a neutral format for exchanging product data. However, implementation of STEP has several issues, including the following two: (1) the complete STEP file should be processed even for querying a small set of data, and (2) information required for realizing any functional activity (e.g., any analysis on any part of a product) is not explicitly identified. Hence, in this study, functionality-based conformance classes (FCCs) are developed to organize the current conformance classes (CCs) (which are the classes required to be implemented fully in order to be conformant to any particular STEP standard) for supporting different functional activities. Following the concept of data exchange specification (DEX)/template, several templates that are repeatedly used small information groups are introduced in order to create manageable sets of data constructs. In this study, the FCCs for 1D tolerance analysis are developed by enriching the available STEP information models with GD&T. The use of extended STEP models is illustrated with a case study.

The product assembly quality is influenced by the coupling effect of multiscale geometric errors. Acquiring the influence of dimension, tolerance and microtopography on part surface quality is the key factor of improving prediction accuracy of product assembly quality. Since the current technology of part solid modeling is difficult to represent tolerance information and surface topography information in computer aided design (CAD) model uniformly, and the accuracy of product assembly simulation and analysis is reduced, the realistic geometry based feature modeling of complex part and its application in assembly quality analysis are studied in this paper. First of all, the novel concept of realistic geometry is proposed, which integrates several geometric elements such as ideal geometry, variational geometry, and fractal geometry. Then, the hierarchical representation model of realistic geometric feature information of complex part is established, and the concrete method and steps to generate the realistic geometric solid features of complex part are proposed. Finally, the efficiency and feasibility of the proposed theory in this paper are validated by assembly quality analysis of the guide rail and sliding table of the machine tool.

Geometric and dimensional tolerances must be determined not only to ensure proper achievement of design function but also for manufacturability and assemblability of mechanical assemblies. We are investigating the degree to which it is possible to automate tolerance assignment on mechanical assemblies received only as STEP AP 203 (nominal) geometry files. In a previous paper, we reported on the preprocessing steps required: assembly feature recognition, pattern recognition, and extraction of both constraints and directions of control (DoC) for assembly. In this paper, we discuss first-order tolerance schema development, based purely on assemblability conditions. This includes selecting features to be toleranced, tolerance types, datums, and datum reference frames (DRFs), and tolerance value allocation. The approach described here is a combination of geometric analysis and heuristics. The assumption is that this initial geometric dimensioning and tolerancing (GD&T) specification will be sent to a stack analysis module and iterated upon until satisfactory results, such as desired acceptance rates, are reached. The paper also touches upon issues related to second-order schema development, one that takes intended design function into account.

Functional tolerancing must ensure the assembly and the functioning of a mechanism. This paper compares two methods of tolerance analysis of a mechanical system: the method of “analysis lines” and the method of “polytopes.” The first method needs a discretization of the ending functional surface according to various analysis lines placed on the outer-bound of the face and oriented along the normal of the surface. The second method uses polytopes. The polytopes are defined from the acceptable limits of the geometric deviations of parts and possible displacements between two parts. Minkowski sums and intersections polytopes are then carried out to take into account all geometric variations of a mechanism.

A process plan is an instruction set for the manufacture of parts generated from detailed design drawings or computer-aided design (CAD) models. While these plans are highly detailed about machines, tools, fixtures, and operation parameters, tolerances typically show up in less formal manner, if at all. It is not uncommon to see only dimensional plus/minus values on rough sketches accompanying the instructions. On the other hand, design drawings use standard geometrical and dimensional tolerances (GD&T) symbols with datums and datum reference frames (DRFs) clearly specified. This is not to say that process planners do not consider tolerances; they are implied by way of choices of fixtures, tools, machines, and operations. Process planners do tolerance charting in converting design tolerances to the manufacturing datum flow based on operation sequence, but the resulting plans cannot be audited for conformance to design specification. In this paper, we present a framework for explicating the GD&T schema implied by machining process plans. The first step is to derive DRFs from the fixturing method in each setup. Then, basic dimensions for features machined in the setup are determined with respect to the extracted DRF. Using shop data for the machines and operations involved, the range of possible geometric variations are estimated for each type (form, size, orientation, and position). The sequence of operations determines the datum flow chain. Once we have a formal manufacturing GD&T schema, we can analyze and compare it to design specification using the T-map math model.

Free-form surface features (FFSFs) extraction is one of the key issues for redesigning and reediting the surface models exported from commercial software or reconstructed by reverse engineering. In this paper, a coarse-to-fine method is proposed to robustly extract the FFSFs. First, by iterative Laplacian smoothing, a set of height functions are generated, and principal component analysis (PCA) is employed to obtain the appropriate iteration number for the feature field extraction that is then accomplished by the Gaussian mix model (GMM) with a high segmentation threshold. Second, based on the feature field, an adaptive smooth ratio for each vertex is proposed for Laplacian smoothing, which is implemented to generate a precise base surface. Thereby, with the base surface, the FFSFs can be easily extracted by using the GMM. The empirical results illustrate that the proposed method yields improved performance for extracting FFSFs compared with conventional methods.

This paper presents the design and construction of a low-cost active noncontact three-dimensional (3D) scanner using the structured light method. The applied method is a generalization of the triangulation technique using a fringe projection pattern (by Gray code technique) to achieve a higher operating speed. The hardware equipment includes a single digital camera and a video projector. matlab was used for the calibration operation, the production of images by the above method, the image processing, and data calculation; while the Geomagic Qualify software was used to estimate the accuracy of the three-dimensional model obtained after scanning and to compare it with the tested object. Regarding the point cloud of the test object, the results demonstrate the precision of the used method and the possibility of developing a 3D scanner with a dimensional accuracy of ±0.05 mm.

In the recent years, the physically based simulation has been developed and applied to various engineering processes. So far the use of this simulation method was limited to calculate the behavior of objects with large dimensions, as the calculation of small objects leads to severe inaccuracies. Thus, simulation results for small objects cannot be used in the engineering process. However, technical systems often consist of a variety of small functional components and workpieces. This paper proposes a new method to significantly improve the accuracy of physically based simulations of small objects by scaling. First, a set of scaling equations is introduced, which allow physically correct scaling of dynamic rigid body systems. Second, the equations are validated by simulating a cube with an edge length of only 20 μm. In this simulation scenario, the new method is compared to the conventional, nonscaling physically based simulation and the improvements of the simulation results are examined. With the scaling equations, technical systems of small components and workpieces can virtually be tested and optimized. This affects a significant reduction of hardware based time and cost consuming experiments.

The geometric variations in a tolerance-zone can be modeled with hypothetical point-spaces called Tolerance-Maps (T-Maps) for purposes of automating the assignment of tolerances during design. The objective of this paper is to extend this model to represent tolerances on line-profiles. Such tolerances limit geometric manufacturing variations to a specified two-dimensional tolerance-zone, i.e., an area, the boundaries to which are curves parallel to the true profile. The single profile tolerance may be used to control position, orientation, and form of the profile. In this paper, the Tolerance-Map (Patent No. 6963824) is a hypothetical volume of points that captures all the positions for the true profile, and those curves parallel to it, which can reside in the tolerance-zone. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. T-Maps have been generated for other classes of geometric tolerances in which the variations of the feature are represented with a plane, line or circle, and these have been incorporated into testbed software for aiding designers when assigning tolerances for assemblies. In this paper the T-Map for line-profiles is created and, for the first time in this model, features may be either symmetrical or nonsymmetrical simple planar curves, typically closed. To economize on length of the paper, and yet to introduce a method whereby T-Maps may be used to optimize the allocation of tolerances for line-profiles, the scope of the paper has been limited to square, rectangular, and triangular shapes. An example of tolerance accumulation is presented to illustrate this method.

A new mathematical model for representing the geometric variations of a planar surface is extended to include probabilistic representations for a 1D dimension of interest, which can be determined from multidimensional variations of the planar surface on a part. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map ® (T-Map ® ) (Patent No. 6963824), a hypothetical volume of points that models the 3D variations in location and orientation of a feature, which can arise from tolerances on size, position, orientation, and form. The 3D variations of a planar surface are decomposed into manufacturing bias, i.e., toward certain regions of a Tolerance-Map, and into geometric bias that can be computed from the geometry of T-Maps. The geometric bias arises from the shape of the feature, the tolerance-zone, and the control used on the mating envelope. Influence of manufacturing bias on the frequency distribution of 1D dimension of interest is demonstrated with two examples: the multidimensional truncated Gaussian distribution and the uniform distribution. In this paper, form and orientation variations are incorporated as subsets in order to model the coupling between size and form variations, as permitted by the ASME Standard when the amounts of these variations differ. Two distributions for flatness, i.e., the uniform distribution and the Gaussian distribution that has been truncated symmetrically to six standard deviations, are used as examples to illustrate the influence of form on the dimension of interest. The influence of orientation (parallelism and perpendicularity) refinement on the frequency distribution for the dimension of interest is demonstrated. Although rectangular faces are utilized in this paper to illustrate the method, the same techniques may be applied to any convex plane-segment that serves as a target face.

Fixture layout robust design of multistation manufacturing systems aims for an optimal design that enables the dimensional variation of a product insensitive to the variations of process variables in the manufacturing process. The robust design involves a high dimension and complex global optimization problem. Recent advances in stream of variation modeling techniques enable effective formulation of the optimization problem at the system level. However, there is a challenge of computation complexity in terms of searching optimal design parameters in a high dimension, nonconvex, and discontinuous design space. This makes many available algorithms ineffective or even invalid. In this paper, an alternative sequential space filling strategy is proposed, which adopts sampling approaches to search optimal designs. To improve computation efficiency, the search space is sequentially reduced to generate a series of subspaces, and a method is designed to ensure a complete coverage of these subspaces in the original feasible space. In order to validate the proposed method, a floor pan assembly from an automotive body assembly process is modeled, and then the fixture robust design is conducted with the developed methods. To show the effectiveness of the proposed method, genetic algorithm and sequential quadratic programming are also applied in the case study for comparison.

This paper considers the problem of inferring the geometry of an object from values of the signed distance sampled on a uniform grid. The problem is motivated by the desire to effectively and efficiently model objects obtained by 3D imaging technology such as magnetic resonance, computed tomography, and positron emission tomography. Techniques recently developed for automated segmentation convert intensity to signed distance, and the voxel structure imposes the uniform sampling grid. The specification of the signed distance function (SDF) throughout the ambient space would provide an implicit and function-based representation (f-rep) model that uniquely specifies the object, and we refer to this particular f-rep as the signed distance function representation (SDF-rep). However, a set of uniformly sampled signed distance values may uniquely determine neither the distance function nor the shape of the object. Here, we employ essential properties of the signed distance to construct the upper and lower bounds on the allowed variation in signed distance, which combine to produce interval-valued extensions of the signed distance function. We employ an interval extension of the signed distance function as an interval SDF-rep that defines the range of object geometries that are consistent with the sampled SDF data. The particular interval extensions considered include a tight global extension and more computationally efficient local extensions that provide useful criteria for root exclusion/isolation. To illustrate a useful application of the interval bounds, we present a reliable approach to top-down octree membership classification for uniform samplings of signed distance functions.

A new mathematical model for representing the geometric variations of tabs/slots is extended to include probabilistic representations of 1D clearance. The 1D clearance can be determined from multidimensional variations of the medial-plane for a slot or a tab, and from variations of both medial-planes in a tab-slot assembly. The model is compatible with the ASME/ANSI/ISO Standards for geometric tolerances. Central to the new model is a Tolerance-Map (Patent No. 6963824) (T-Map), a hypothetical volume of points that models the range of 3D variations in location and orientation for a segment of a plane (the medial-plane), which can arise from tolerances on size, position, orientation, and form. Here it is extended to model the increases in yield that occur when the optional maximum material condition (MMC) is specified and when tolerances are assigned statistically rather than on a worst-case basis. The frequency distribution of 1D clearance is decomposed into manufacturing bias, i.e., toward certain regions of a Tolerance-Map, and into a geometric bias that can be computed from the geometry of multidimensional T-Maps. Although the probabilistic representation in this paper is built from geometric bias, and it is presumed that manufacturing bias is uniform, the method is robust enough to include manufacturing bias in the future. Geometric bias alone shows a greater likelihood of small clearances than large clearances between an assembled tab and slot. A comparison is made between the effects of specifying the optional MMC and not specifying it with the tolerance that determines the allowable variations in position of a tab, a slot, or of both in a tab-slot assembly. Statistical tolerance assignment for the tab-slot assembly is computed based on initial worst-case tolerances and for (a) constant size of tab and slot at maximum material condition, and (b) constant virtual-condition size.

Nonuniform rational B-splines (NURBs) have unique properties that make them attractive for engineering metamodeling applications. NURBs are known to accurately model many different continuous curve and surface topologies in one- and two-variate spaces. However, engineering metamodels of the design space often require hypervariate representations of multidimensional outputs. In essence, design space metamodels are hyperdimensional constructs with a dimensionality determined by their input and output variables. To use NURBs as the basis for a metamodel in a hyperdimensional space, traditional geometric fitting techniques must be adapted to hypervariate and hyperdimensional spaces composed of both continuous and discontinuous variable types. In this paper, we describe the necessary adaptations for the development of a NURBs-based metamodel called a hyperdimensional performance model or HyPerModel. HyPerModels are capable of accurately and reliably modeling nonlinear hyperdimensional objects defined by both continuous and discontinuous variables of a wide variety of topologies, such as those that define typical engineering design spaces. We demonstrate this ability by successfully generating accurate HyPerModels of ten trial functions laying the foundation for future work with N -dimensional NURBs in design space applications.

In this paper, a fast algorithm for the simulation of deformable objects composed of multiple components made of different materials is introduced. By using the boundary element method and considering individual components and their interfaces separately, a relationship between the unknown and known displacements is established. Based on this expression, a component-based condensation method can be applied. This reduces the size of the matrix to be inverted to depend only on the number of unknown displacements of the components with changing boundary condition. To speed up the construction of the required matrices, a maximal matrix method is proposed. By categorizing the changes in boundary conditions, three fast update strategies on matrix inverse are introduced. Based on the maximal matrix method and the matrix inverse update strategy, we define eight easily formed characteristic matrices, which enhance the computation speed further. The efficiency of the proposed method is demonstrated by a set of experimental results.