Geometric modeling and processing

Kinematic modeling of continuum robots is challenging due to the large deflections that these systems usually undergone. In this paper, we derive the kinematics of a continuum robot from the evolution of a three-dimensional curve in space. We obtain the spatial configuration of a continuum robot in terms of exponential coordinates based on Lie group theory. This kinematic framework turns out to handle robotic helical shapes, i.e. spatial configurations with constant curvature and torsion of the arm.

Keywords: Continuum robotics , Differential geometry , Kinematics

Industrial robots are commonly designed to be very fast and stiff in order to achieve extremely precise position control capabilities. Nonetheless, high speeds and power do not allow for a safe physical interaction between robots and humans. With the exception of the latest generation lightweight arms, purposely design for human-robot collaborative tasks, safety devices shall be employed when workers enter the robots workspace, in order to reduce the chances of injuries. In this context, Variable Stiffness Actuators (VSA) potentially represent an effective solution for increasing robot safety. In light of this consideration, the present paper describes the design optimization of a VSA architecture previously proposed by the authors. In this novel embodiment, the VSA can achieve stiffness modulation via the use of a pair of compliant mechanisms with distributed compliance, which act as nonlinear springs with proper torque-deflection characteristic. Such elastic elements are composed of slender beams whose neutral axis is described by a spline curve with non-trivial shape. The beam geometry is determined by leveraging on a CAD/CAE framework allowing for the shape optimization of complex flexures. The design method makes use of the modeling and simulation capabilities of a parametric CAD software seamlessly connected to a FEM tool (i.e. Ansys Workbench). For validation purposes, proof-concept 3D printed prototypes of both non-linear elastic element and overall VSA are finally produced and tested. Experimental results fully confirm that the compliant mechanism behaves as expected.

Background and objective: The purpose of the present paper is to pave the road to the systematic optimization of complex craniofacial surgical intervention and to validate a design methodology for the virtual surgery and the fabrication of cranium vault custom plates. Recent advances in the field of medical imaging, image processing and additive manufacturing (AM) have led to new insights in several medical applications. The engineered combination of medical actions and 3D processing steps, foster the optimization of the intervention in terms of operative time and number of sessions needed. Complex craniofacial surgical intervention, such as for instance severe hypertelorism accompanied by skull holes, traditionally requires a first surgery to correctly “resize” the patient cranium and a second surgical session to implant a customized 3D printed prosthesis. Between the two surgical interventions, medical imaging needs to be carried out to aid the design the skull plate. Instead, this paper proposes a CAD/AM-based one-in-all design methodology allowing the surgeons to perform, in a single surgical intervention, both skull correction and implantation. Methods: A strategy envisaging a virtual/mock surgery on a CAD/AM model of the patient cranium so as to plan the surgery and to design the final shape of the cranium plaque is proposed. The procedure relies on patient imaging, 3D geometry reconstruction of the defective skull, virtual planning and mock surgery to determine the hypothetical anatomic 3D model and, finally, to skull plate design and 3D printing. Results: The methodology has been tested on a complex case study. Results demonstrate the feasibility of the proposed approach and a consistent reduction of time and overall cost of the surgery, not to mention the huge benefits on the patient that is subjected to a single surgical operation. Conclusions: Despite a number of AM-based methodologies have been proposed for designing cranial implants or to correct orbital hypertelorism, to the best of the authors' knowledge, the present work is the first to simultaneously treat osteotomy and titanium cranium plaque.

Keywords: Additive manufacturing , CAD , Cranium surgery , Image processing

Background: Current approaches to quantifying the severity of pectus excavatum require internal measurements based on cross-sectional imaging. The aim of this study is to exploit a novel index evaluated on the external surface of the chest with a three-dimensional (3D) optical scanner. Methods: Fifty-one children (41 male, 10 female) between 2 and 17 years of age were evaluated with a 3D optical scanner. Pectus excavatum severity was calculated by using an ad hoc instant 3D scanner and defining an automatic procedure to generate an optical 3D correction index (CI3D). For the latter, an ideal threshold was derived from a statistical analysis, and five blind surveys were collected from pediatric specialists on chest wall deformities. The CI3D was then correlated with blind clinical assessments of PE severity. Results: The cutoff thresholds were determined to optimally discriminate between six degrees of severity of PE patients by a correlation analysis. The correlation coefficient obtained by matching the CI3D with the average subjective severity shows that the proposed method outperforms traditional approaches. Conclusions: The optical 3D index has a good match with the average subjective assessment in distinguishing patients with mild to severe PE. This innovative approach offers several advantages over existing indices, as it is repeatable and does not require cross-sectional imaging. The index might be particularly suitable for monitoring the efficacy of nonoperative treatment and, in the future, for designing an optimal personalized usage of therapeutic devices.

Reverse Engineering (RE) is a long-term goal of engineering and computer science; it aims at the reconstruction of CAD models from measured data by means of 3D mathematical surfaces and geometrical features representing the geometry of a physical part. In the last two decades, reviews and surveys have occasionally covered this topic, but a systematic dissertation of modeling methods from a mechanical engineering point of view is still missing. The purpose of this paper is to fill this gap; starting from a general description of the overall RE framework (acquisition, segmentation, classification, fitting), both an up-to-date survey and a categorization of available modeling techniques and tools working on 3D data are provided. The main aspects of various strategies are discussed as well, in order to highlight strengths and weaknesses characterizing different approaches. Moreover, an overview of commercial software for RE is presented, considering both dedicated solutions and packages supplied as add-on with ‘traditional' CAD systems. Finally, possible improvements to be addressed by the research in the RE field are discussed, outlining potential future trends that are still to be investigated.

Keywords: 3D modeling , CAD reconstruction , constrained fitting , Reverse engineering , reverse engineering software

The percutaneous interventions in the treatment of structural heart diseases represent nowadays a viable option for patients at high risk for surgery. However, unlike during the traditional open heart surgery, the heart structures to be corrected are not directly visualized by the physician during the interventions. The interpretation of the available medical images is often a demanding task and needs specific skills i.e. clinical experience and complex radiological and echocardiographic analysis. The new trend for cardiovascular diagnosis, surgical planning and intervention is, today, mutually connected with most recent developments in the field of 3D acquisition, interactive modelling and rapid prototyping techniques. This is particularly true when dealing with complex heart diseases since 3D-based techniques can really help in providing an accurate planning of the intervention and to support surgical intervention. To help the research community in confronting with this new trend in medical science, the present work provides an overview on most recent approaches and methodologies for creating physical prototypes of patient-specific cardiac structures, with particular reference to most critical phases such as: 3D image acquisition, interactive image segmentation and restoration, interactive 3D model reconstruction, physical prototyping through additive manufacturing. To this purpose, first, recent techniques for image enhancement to highlight anatomical structures of interest are presented together with the current state of the art of interactive image segmentation. Finally, most suitable techniques for prototyping the retrieved 3D model are investigated so as to derive a number of criteria for manufacturing prototypes useful for planning the medical intervention.

Keywords: 3D modelling , Cardiovascular diseases , Heart , Medical imagery , Rapid prototyping , Surgical planning

Template-Based reverse engineering approaches represent a relatively poorly explored strategy in the field of CAD reconstruction from polygonal models. Inspired by recent works suggesting the possibility/opportunity of exploiting a parametric description (i.e. CAD template) of the object to be reconstructed in order to retrieve a meaningful digital representation, a novel reverse engineering approach for the reconstruction of CAD models starting from 3D mesh data is proposed. The reconstruction process is performed relying on a CAD template, whose feature tree and geometric constraints are defined according to the a priori information on the physical object. The CAD template is fitted upon the mesh data, optimizing its dimensional parameters and positioning/orientation by means of a particle swarm optimization algorithm. As a result, a parametric CAD model that perfectly fulfils the imposed geometric relations is produced and a feature tree, defining an associative modelling history, is available to the reverse engineer. The proposed implementation exploits a cooperation between a CAD software package (Siemens NX) and a numerical software environment (MATLAB). Five reconstruction tests, covering both synthetic and real-scanned mesh data, are presented and discussed in the manuscript; the results are finally compared with models generated by state of the art reverse engineering software and key aspects to be addressed in future work are hinted at.

Keywords: 3D mesh , CAD reconstruction , CAD template , Constrained fitting , Particle Swarm Optimization , Reverse engineering

Pectus Excavatum, one of the most frequent chest wall deformities, is characterized by a depression of the sternum and costal cartilages. Patients with mild deformities are generally treated conservatively by using the so called Vacuum Bell (VB) i.e. a suction cup to be placed on the patient's sternal region. Three different sizes, as well as a model fitted for young women, of VB are available on the market. Unfortunately, the variability of the surface to be treated, the possible asymmetry of the caved-in area and the prolonged use, can make the device uncomfortable and, in some cases, ineffective for the patient. In order to cope with these issues, the present paper proposes a computer-aided method for customized vacuum bell design to be used by non-expert user, e.g. by medical staff. In particular, the present work entails the development of a system comprising: 1) a dedicated software capable of acquiring the 3D chest geometry - by using a low-cost range sensor, i.e. Kinect v2 - and of processing the point cloud so to generate NURBS surfaces of the chest; 2) a procedural CAD modeling of a personalized VB implemented within Siemens NX 11 CAD environment. Using the devised method, the medical staff is required only to use the 3D scanning system for acquiring the patient chest and to sketch, in a CAD-based interface, the boundary of the area to be treated. Once these tasks are performed, the system automatically builds the personalized VB model, ready to be manufactured.

Keywords: design customization , Procedural CAD modeling , reverse engineering , vacuum bell

With the aim of retrieving 3D surfaces starting from single shaded images, i.e. for solving the widely known shape from shading problem, an important class of methods is based on minimisation techniques where the expected surface to be retrieved is supposed to be coincident with the one that minimise a properly developed functional, consisting of several contributions. Despite several different contributes that can be explored to define a functional, the so called 'smoothness constraint' is a cornerstone since it is the most relevant contribute to guide the convergence of the minimisation process towards a more accurate solution. Unfortunately, in case input shaded image is characterised by areas where actual brightness changes rapidly, such a constraint introduces an undesired over-smoothing effect for the retrieved surface. The present work proposes an original strategy for avoiding such a typical over-smoothing effect, with regard to the image regions in which this is particularly undesired such as, for instance, zones where surface details are to be preserved in the reconstruction. The proposed strategy is tested against a set of case studies and compared with other traditional SFS-based methods to prove its effectiveness.

Keywords: 3D model , Minimisation , SFS , shape from shading , Smoothing , Smoothness constraint , variational approach

Underwater exploration, in the last years, has evolved toward a wide adoption of increasingly smaller ROVs (Remotely Operated Vehicle). As a consequence, the need to equip these underwater vehicles with robotic arms is currently rising as well. According to this demand, the paper presents three innovative solutions achieved in the UVMS (Underwater Vehicle-Manipulator System) field. Firstly, the paper proposes a modular architecture for a lightweight underwater robotic arm, which can be mounted on small-sized ROVs. The modular concept of the arm enables several different configurations, each one characterized by the related DOFs, deployed according to the type of application to be performed. Secondly, the arm has been equipped with an adaptive gripper that, taking advantage of the additive manufacturing techniques, is able to easily grip differently shaped objects. Lastly, the underwater arm is controlled through a Master–Slave approach, designed for commercial off-the-shelf electronics, that on the one hand, entailed a significant reduction of the bill of materials, but, on the other hand, required a greater effort in the software development. Experimental tests have been carried out to measure and evaluate the gripping and manipulation capability of the robotic arm and the performance of the proposed control system.

Keywords: Flexible gripper , Master-slave control , Modular robotic arm , Underwater manipulation , Underwater vehicle-manipulator systems (UVMS)

Within the T-VedO project, financed by Tuscany Region, the Reverse Engineering and Virtual Prototyping Lab team of the Department of Industrial Engineering of Florence (Italy) developed a number of methods for the semiautomatic generation of digital 2.5D models starting from paintings. Once such models are prototyped, they can be used to enhance visually impaired people tactile experience of artworks. Such methods, combined into a systematic procedure, allow to solve most of the typical problems arising when dealing with artistic representation of a painted scene. The present paper presents both an overview of the proposed procedure, including most recent updates, and the results obtained for a selected number of artworks of the Florentine Renaissance.

Keywords: 2.5D models , 3D Reconstruction , CAD

Wrist injuries are one of the most common fractures, specifically around 25% of fractures among the pediatric population and up to 18% in the elderly age group are distal radius fractures. To date, the standard treatment entails the use of a tailor-made plaster of Paris cast. Although it is a simple and reliable treatment, it presents several disadvantages: its weight generally causes discomfort, it cannot be taken off without breaking it, it can cause skin rashes and prevents ventilation of the treated area. To overcome the limitations of the above mentioned treatment, 3D printed orthopaedic casts based on reverse engineering (RE) and additive manufacturing (AM) techniques have been proposed in literature. Despite these solutions prove to be a valid alternative to the standard treatment, the clinical use of AM-based devices is not trivial due to the need of expert CAD modelers to design the 3D model of the orthosis starting from the patient's anatomy 3D acquisition. In this work, the authors identify a systematic procedure to create an orthosis model, compliant with medical guidelines, using common CAD tools. The systematic procedure, even still manually performed, envisages a set of tasks, grouped into five main blocks, that will be easy to be automatized in the future, thus eliminating the necessity of designing expertise to model the orthosis. The proposed procedure allows to design a device composed of two halves, to ease the application, locked through a zip tie-based mechanism. A preliminary ventilation pattern is proposed and tested with a FEM analysis to ensure structural resistance. The procedure has been tested on six case studies: all the orthoses models were correctly generated without major complications and positive user feedbacks were generally obtained throughout the tests.

Keywords: Cad , Cast modeling , Orthosis modelling , Personalized medicine , Reverse engineering

The surgical process adopted to repair cranial defects using an implant, typically called Cranioplasty, has seen an abrupt increase in recent years due to the introduction of Reverse Engineering (RE) and Additive Manufacturing (AM) techniques. By adopting these techniques, CT/MRI data can be used to reconstruct, in a pre-operative stage, the 3D anatomy of the defective skull in order to design a patient-specific digital model of the prosthesis. The so-designed cranial plate can be then fabricated via AM, in a suitable metal alloy, and implanted. This allows for a perfect fit of the implant during the actual surgery, reducing the risks for the patient and increasing the efficacy of the treatment. This paper reviews existing approaches for the virtual reconstruction of defective skulls, and a basic classification, proposing four different classes of strategies (Mirroring, Surface Interpolation, Template-Based and Slice-based techniques) is provided. The findings of the study suggest that the reconstruction of skull defects is still an open problem, due to the complexities imposed by surface that needs to be retrieved (i.e. the human anatomy). All the presented approaches share weaknesses and limits, which are discussed in the article. Finally, possible directions to improve the existing techniques are briefly presented.

Keywords: Biomedical engineering , Cranioplasty , Reverse engineering , Skull reconstruction

This paper presents a knowledge based engineering environment methodology to support the designer in the correct setting of geometrical and dimensional tolerances in assemblies of mechanical components. The procedure is based on the definition of the functional requirements needed to allow the proper working of the assembly; in the further, a software tool is used to do a statistical analysis of the assembly relations, providing an estimation of the components waste due to poor compliance to the tolerances. A case study given by the design of a marine power transmission is presented: the methodology leads to the change of some tolerances to improve the design by reducing the number of waste components. The strength of the methodology is represented by the fact it can help unskilled designers in the correct setting of tolerances in drawings.

Keywords: CAD , CAT , design , GD&T , power transmission

Advances in additive manufacturing technologies facilitate the fabrication of cellular materials that have tailored functional characteristics. The application of solid freeform fabrication techniques is especially exploited in designing scaffolds for tissue engineering. In this review, firstly, a classification of cellular materials from a geometric point of view is proposed; then, the main approaches on geometric modeling of cellular materials are discussed. Finally, an investigation on porous scaffolds fabricated by additive manufacturing technologies is pointed out. Perspectives in geometric modeling of scaffolds for tissue engineering are also proposed.

Sintering shrinkage of prior cold compacted iron rings with different geometry (height to wall thickness ratio) and green density in the 6.5–7.3 g/cm3 range was investigated. It displays a minimum at an intermediate green density. Axial, tangential and radial shrinkages are different, due to the gradients of green density along the axial and the radial directions. Therefore, the effect of height on shrinkage and its anisotropy is the result of their effect on the stress distribution in the green parts during cold compaction, and the resulting green density and deformation experienced by the powder. Anisotropy decreases on increasing shrinkage.

Keywords: geometry , green density , Shrinkage anisotropy

A densification equation derived from deformation occurring in the powder mix during cold compaction was applied to investigate densification of a commercial water atomized AISI 316 stainless steel powder with different particle size distribution, mixed with 1% organic binder, in the production of rings with different H/(Dext-Dint). Knowing the constitutive model of the powder mixes, the mean compaction pressure was determined and correlated to the deformation of the powder column. From these correlations it is possible to derive a densification equation having a physical meaning, also individuating the parameters describing the densification behavior, and in turn the compressibility, of the different powders investigated.

Keywords: Densification equation , Particle size , Powder compaction

In previous work the anisotropic dimensional change on sintering has been investigated in depth. An anisotropy parameter has been identified, depending both on geometry and on sintering conditions, and it has been used to define a model for the anisotropic behaviour. A design procedure accounting for anisotropic dimensional changes has been proposed. This work summarizes the main results obtained within the Design for Sintering Club Project, aimed at validating and enlarging the aforementioned design procedure by the application on real industrial parts. Project partners provided axi-symmetric parts, which were measured both in the green state and after sintering in standard industrial conditions. The real dimensional changes were compared to the dimensional changes predicted by means of the design procedure based on the anisotropy model. The results, also compared to the attainable dimensional tolerances, allowed validating the design procedure, and showing directions to further improvement.

Keywords: Anisotropy , Design for sintering , Dimensional change

This work aims at determining the constitutive model of four commercial water atomised low alloyed steel powders during cold compaction. Single-action experiments were performed, obtaining cylindrical specimens with different H/D ratios. The distribution of axial and radial stresses was investigated, and the relationships describing both the radial stress transmission coefficient and the flow stress as functions of the relative density were determined. The radial stress transmission coefficient also confirmed the hypothesised value of Poisson's coefficient. The friction coefficient between the powder column and the die wall was determined, also highlighting the influence of the H/D ratio. Measuring the axial and radial strains due to spring-back, the axial and radial elastic moduli were determined, as functions of the relative density. The results obtained for the four materials were compared, also highlighting both differences and similarities.

Keywords: Cold compaction , constitutive model , low alloyed steel powders

The use of composite structures is increasing constantly in the last years, pushed by advantages of reduced weight and high strength. Moreover, the recent scenario points out a great attention on thermoplastic matrix composites due to their intrinsic recyclability as well for their possibility to re-use and re-manufacturing. However, the adoption of these materials can be further appreciated considering the secondary material workability as far as by demonstrating the possibility to re-manufacture the thermoplastic composite. The proposed work presents an experimental analysis carried out to investigate the downstream workability of a thermoplastic composite by one of the most versatile and flexible process. Glass fiber reinforced Polyamide 6 is the investigated material and the Single Point Incremental Forming is the implemented manufacturing approach. Since the composite matrix is characterized by a glass transition temperature higher than 50 °C, an external heating source has been necessary to perform the process in “hot” conditions. The process feasibility was fully demonstrated as well as the same was optimized in order to derive proper guidelines that can drive the process designer in the method star-up.

Keywords: Downstream process , Short glass-fibers , SPIF , Thermoplastic composite