Despite growing interest in multi-colour FDM printing, current methods remain limited by hardware complexity, material waste, and the inability to produce smooth gradients. This research investigates a novel method for multi-colour printing using a single nozzle combined with dual-colour and triple-colour filament, with controlled rotation, to influence perceived colour blending and transitions.

A standard Ender 3 printer was modified to include a rotational B-axis, with hardware enhancements such as a slip ring and belt-driven stepper motor to reduce torsion and nozzle deviation. Custom G-code was generated via Grasshopper, linking image-based colour data to nozzle rotation angles, allowing for systematic testing of smooth gradient and snappy colour switch performance. Extensive testing was conducted on 2D and 3D samples to evaluate the effects of parameters such as rotation angle, step size, speed, and print direction on colour reliability and gradient quality.

The results demonstrate that nozzle rotation can produce smooth gradients and snappy colour switches without purging, with reliable reproduction of the base colours and limited success with intermediate colour filaments. Mechanical factors such as nozzle deviation and filament torsion still affect reliability, but calibration and passive settings can reduce these effects significantly. These findings position rotational nozzle systems as a promising third category in multi-colour FDM printing, combining expressive colour control with relatively simple hardware adaptations and low waste.
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This dissertation develops an optimization framework for multi-axis additive manufacturing, with a particular focus on wire arc additive manufacturing (WAAM). It introduces the novel space-time topology optimization approach that integrates structural design and fabrication sequence planning by defining material distribution across both spatial and temporal dimensions.
In this framework, a pseudo-density field defines the structural layout, while a pseudo-time field encode the fabrication sequence, offering detailed insights into the layer-by-layer manufacturing process. Two key advancements are developed in order to improve the manufacturability: First, a thermal regularization method is proposed to ensure a smooth and continuous pseudo-time field without local minima. Second, a layer geometry control scheme is implemented to improve the consistency of the layer dimensions.
The framework is further adopted to address challenges associated with residual stress and thermal-induced distortion in WAAM, employing the inherent strain method as a simplified process simulation model. In addition, the anisotropic nature of material properties in WAAM is considered, enabling the rational alignment of material deposition orientation to enhance performance.
Numerical results demonstrate the feasibility and effectiveness of the proposed optimization framework, inspiring the exploration of the innovative potential offered by multi-axis additive manufacturing.

Negative linear compressibility (NLC) describes the relative increase or decrease in a material's linear dimension when subjected to an increase or decrease in external pressure, or a decrease or increase in internal pressure, respectively. This is a rare material property found in only a few naturally existing materials. These materials are not only limited by their availability but also by the range, strength, and stability of NLC behavior. This limitation can be addressed through the design of NLC metamaterials, which are engineered materials composed of repeating architectures or material layouts on the microscopic scale, known as base or unit cells. These cells define the macroscopic properties of the material. In this case, negative linear compressibility.

While there are different methods for designing NLC metamaterials, none of them involve the use of topology optimization (TO), which serves as a powerful tool for designing optimized metamaterial structures. Materials can be designed for different parameters such as base material and pressure applied, while also considering different constraints that may be application-specific.

This study aims to create isotropic NLC metamaterials by designing NLC metamaterial unit cells using a systematic design methodology. We achieve this goal using a density-based TO approach, incorporating different constraints and selecting appropriate parameters to obtain different metamaterial unit cells that exhibit NLC behavior in both two and three dimensions.

The resulting 2D designs exhibited an NLC value of -2.370 %/bar and -3.367 %/bar. While the 3D designs exhibited an NLC value of -2.212 %/bar and -3.534 %/bar. The obtained NLC value and the efficacy of the design method are validated through numerical analysis and experimental testing, with the experimental design showing a maximum deviation of 26.099% from the NLC value obtained through TO. Finally, comparative and parameter studies helped better elucidate the advantages, limitations, and areas for improvement of the methodology used to obtain these designs.

Wire arc additive manufacturing (WAAM) is attributed to higher material deposition rates and medium to large build volumes. Integration of multi-axis (more than three) material deposition kinematics in WAAM can bring a paradigm shift in the metal additive manufacturing industry. The material build-up mechanism employing directed energy deposition results in localized melting and solidification of feeding wire making the fabricated structure inherently prone to deposition defects such as dimensional distortion, residual stresses, solidification cracking, and porosity. Optimization of welding process parameters can improve cracking and porosity behavior. However, the problem of distortion is inevitable, and current mitigation strategies rely on post-processing or symmetric material deposition; while the former decreases the effectiveness of WAAM and increases costs, the latter could only be implemented for specific parts. Tackling this problem with the help of computational design tools is a recent approach, and Fabrication Sequence Optimization dictating material deposition is numerically predicted to limit the extent of the distortion effectively compared to conventional planar horizontal deposition; however, this still lacks experimental validation. This research presents a series of fabrication experiments using Al5356 Aluminum-magnesium alloy wire in a 6-axis robotic WAAM setup in two parts: (1) Process parameters identification for optimal bead characteristics for Al5356 wire, (2) Fabrication of single-bead multi-layered thin-walled shell structures using planar and optimized material deposition. A digital image correlation-based non-contact in-situ distortion measurement setup is constructed to analyze strain development during fabrication process and 3D scanning of fabricated structures is performed to estimate dimensional deviation. The experimental findings revealed an improvement in geometrical formation and a qualitative indication of distortion minimization with an optimized fabrication sequence.

Performance-driven generative design has been commonly used in engineering applications. In addition to performance metrics, aesthetics play an important role in the acceptance of generatively designed forms. When generating these shapes using generative programs, it is not clear in advance what the outcome will be, and thereby what they will look like. However, the appearance of these shapes can currently almost always be described as quite novel and organic. This affects the acceptance of these shapes and the number of iterations or post-processing needed to end up with a shape that is aesthetically acceptable.

This graduation project aims at exploring, identifying and validating aspects of 3D generated designs that contribute to a more aesthetic appearance in order to increase aesthetic acceptance and move towards intentional aesthetics in 3D generative design.

A review of existing literature was done on the history of aesthetics, aesthetics in product design and aesthetics in generative design. This resulted in useful insights in aesthetic principles. These existing principles were then reviewed in relation to 3D generative designed forms. Through that analysis, hypotheses were synthesised on how the aesthetic appeal of these shapes could be increased.

A first user study was conducted to test these hypotheses and to gain valuable insights into what aspects of a 3D form are important for aesthetic appreciation. For this study, many 3D generated designs were created across different product groups. The products were placed in a virtual environment in order for the participants to view them in true 3D through a virtual reality headset. Via an open discussion with the participants during the viewing of the different designs, valuable insights were gathered on aspects that positively or negatively contributes to the aesthetic appreciation of these forms.

These insights resulted in guidelines to increase aesthetic appreciation for 3D generated designs. A second, quantitative user study was then set up to validate the desired effect of the new guidelines. Twenty new designs were created and selected to be put in pairs containing designs that did and did not display features from the new guidelines. Through an online survey, these pairs were judged by 90 respondents on the desired effects, resulting in an extensive data set. Data analysis was conducted, and Pearson correlations showed a positive effect between the effects from the guidelines and the aesthetic appreciation of the generated forms.

These guidelines can therefore be used as actionable recommendations for designers, engineers and architects seeking to optimize both the structural and aesthetic qualities of generatively designed product.

Additive Manufacturing (AM) plays a crucial role in the revolution towards Industry 4.0, by enabling the direct translation of digital 3D models into physical objects while reducing process steps and minimizing human intervention. While conventional AM machines are generally limited to three-axis movement, multi-axis AM equipment extends the manufacturing flexibility by enabling the fabrication of freeform layers, thus creating new opportunities to improve part quality, though at the cost of increased complexity in process planning. Wire Arc Additive Manufacturing (WAAM) is a multi-axis technique for producing large metal components, with potential applications in maritime, aerospace and civil infrastructure. However, this potential is hindered by factors such as deformation during fabrication, which compromises part precision and can lead to process failure. Recently, a computational approach has been developed to reduce distortion by optimizing the fabrication sequence. While promising, the optimized sequence is characterized by large variations in layer thickness, rendering them non-manufacturable. This research proposes numerical methods to evaluate and restrict layer thickness in fabrication sequence optimization, ensuring uniform thickness within each layer and a consistent average thickness across the entire sequence. A 3D computational framework has been developed, integrating latest advancements in sequence optimization. To address the intensive computation in 3D, this framework features a parallel implementation using the PETSc library. This framework enables the numerical assessment of the method’s performance and provides a foundation for future experimental validation.

Background: Despite over a century’s worth of technical improvements, the longterm survivability associated with orthopedic implants continues to fall short. In contrast to earlier designs, implant failure is no longer caused by structural failure of the implant itself. Rather, it results from the implant’s long-term detrimental effects on the surrounding bone tissue. Over time, changes in mechanical loading conditions induce a reduction in bone density, increasing the risk of fracture, and destabilizing the bone-implant interface. The mechanisms which drive peri-prosthetic bone loss are complicated and inter-related. Add to this the unique morphological variations among patients, and an optimal one-size-fits-all solution seems unlikely.....

The use of multi-axis additive manufacturing has enabled the possiblity to fabricate parts using curved layer deposition. Compared to the traditional deposition using planar layers of a fixed thickness, multiaxis additive manufacturing significantly increases the number of possible fabrication sequences. With the introduction of a time component for topology optimization in recent work, fabrication-processdependent physics can now be incorporated in the optimization process. The fabrication sequence resulting from such complex optimizations can lead to layers with large variations in thickness. For manufacturability reasons, considering multi-axis additive manufacturing, this variation should be controlled. In this thesis, we present a method to control the variation in thickness of the projected layers to improve the manufacturability. We use the continuous pseudo-time field and its gradients to track the development of the layer boundaries. To demonstrate the effectiveness of the method, we apply the thickness control method on a fabrication sequence optimization for minimizing thermal distortion. The results show that the proposed method is able to reduce the variation of thicknesses compared to the original sequence optimization without thickness control resulting in improved manufacuturability.

In the realm of traditional additive manufacturing, design and fabrication sequence planning have historically followed separate tracks. However, recent strides in the field, particularly in the utilization of robotic arms with multiple degrees of freedom, have brought forth a revolutionary approach known as Space-Time Topology Optimization (STTO). This groundbreaking algorithm breaks down the barriers between design and fabrication by simultaneously optimizing the structure and fabrication sequence. It achieves this feat by employing density and time fields as design variables, allowing for a holistic and integrated approach to the manufacturing process.
However, within the framework of STTO, multiple iterations of finite element computations become necessary. This results in a substantial computational burden throughout the overall process.
My contribution within STTO lies in its adoption of a multi-resolution strategy. This strategy enables the use of different resolutions for the design fields, enhancing computational efficiency. Coarsening, a critical component of this strategy, is implemented through a sophisticated weighted average scheme. This coarsening process facilitates the construction of stiffness matrices with significantly reduced finite element calculations, resulting in substantial time savings during the optimization process.
The impact of coarsening in STTO has been rigorously studied across various levels, yielding remarkable results and advantages. In 2D scenarios, this approach has achieved an impressive 5-fold reduction in computation time, while in the more complex 3D domain, it has led to an astounding 30-fold decrease. Moreover, it's worth noting that compliance, a crucial performance metric, maintains its integrity even with coarsening, with compliance drop remaining below 5% for levels deemed acceptable. This study illuminates the profound implications of coarsening within the STTO framework, emphasizing the significant strides made in computational efficiency while ensuring structural integrity and performance.

We explain the design and analysis of a novel voxel design with the goal of reducing assembly time and complexity of the robot-material system. Recent advances in robot-material systems, on the other hand, have focused on mechanical properties, design, and production methods. Making it possible to create cellular structures in harsh and remote environments. These systems, which are built up of voxels and small mobile robots that live on top of the structure and move the cellular structures, nevertheless lack a connecting mechanism that reduces total system complexity and assembly time to a level that is desirable to people.

The design of these voxels prioritizes ease of assembly through simple actuation and is investigated by proposing a method to connect voxels via an end effector without removing mechanical qualities while maintaining the system’s modularity principle. Modularity is a design idea that divides a structure into smaller sections called voxels that can be built and assembled separately to build the required structure. Simultaneously, the end effector’s design aims to connect a voxel with the fewest degrees of freedom possible, while also holding a voxel throughout transit and placing the voxel in the desired spot.

A new connection mechanism for cuboctahedral cellular structures was devised, which would enable the building of required large-scale structures faster and easier. Several prototypes and experiments were used in the design of this connection mechanism. The final prototype was built by fused deposition modeling and demonstrated by attaching the end effector to a Universal Robot 5 (UR5) and completing a series of movements to simulate the autonomous assembly of a bridge. The concept evaluation resulted in an end effector that can connect all sides of the voxel with only two movements, without requiring the robot to go around the voxel. This idea lays the groundwork for enhancing the way robots form cellular structures and creating a mechanism to make them more appealing to humans when exploring remote settings. The study finishes with future research opportunities and prospective applications of such a connection mechanism in robot-material systems.

The principles of repair and maintenance, reuse, and repurposing of products in a circular economy aim at further minimizing the environmental impact during the use of products before being processed for recycling. However, studies on lattice structures in various fields focus on mechanical characteristics, design, and manufacturing methods. Lattice structures are known for being lightweight, shock resistant, etc., but repair and maintenance of these lattice structures are rarely investigated. In this study, the repairability of lattice structures is explored to extend product lifespan by enabling multiple Repair & Reuse loops before the recycling loop in a circular economy. The principle of modularity was tested on lattice structures and its impact on the ease of repair, and manufacturing of large-scale lattice structures was analyzed. Modularity is a design principle of subdividing the structure into smaller parts called modules which can be independently created and assembled to form the desired structure. A hierarchical modular approach was introduced for cuboctahedral lattice structures that proposes assembling desired large-scale structures by using modules that are themselves assembled as a result of interconnecting sub-modules. The design of these unique sub-modules, intraconnection to form modules, and interconnections within these modules involved various prototypes and simulated iterations. The final prototype was fabricated using fused deposition modeling and tested under a quasi-static compression test to validate that there is no/negligible negative impact of modularity on the lattice structure’s mechanical strength. The hierarchical modular approach and its benefits for ease of repair and manufacturing were demonstrated over a fabricated and assembled scaled-down model of an arch-type pedestrian bridge. The product journey of structures built using this approach is illustrated with a focus on ease of manufacturing and the repair & reuse loops. The study concludes with possibilities for future explorations in regards to this study and potential applications of such hierarchical modular lattice structures.

During this project the possibilities of enriching the functionality of an Ankle Foot Orthosis (AFO) by implementing mechanical metamaterials are researched. The project is executed for Buchrnhornen, a company based in Eindhoven which has over 70 years of experience in manufacturing orthopaedic shoes and orthosis in a traditional way. Mechanical metamaterials are artificial structures with mechanical properties defined by their structure rather than their composition. They consist of rationally designed unit cells with unique mechanical properties. The project focusses on replacing the hinges and stops used in a traditional AFO to block plantar or dorsal flexion by a mechanical metamaterial structure which could achieve the same mechanical functioning. A digital program in Grasshopper (Rhino plug-in) is developed which generates a design space based on an input scan of the patients lower leg. The design space is split up in different parts based on the mechanical requirements of the specific areas in the AFO. For each design space, a suitable topology infill which meets the mechanical requirement of the area is developed and generated. Through an input which can be defined per generated model, mechanical requirements can be customized per patient. The output of the digital program is a ready to 3D print .stl file. An extensive research on 3D print methods and materials is done in order to find the most suitable method to fabricate the generated model. The best option was found in a Composite Fibre Co-extrusion (CFC) printer which is able to implement carbon fibre in a model. The addition of carbon fibre ensures much stronger prints which are able to resist the high forces which are applied on the AFO. The project is finished with a conceptual model generated through the developed digital program as well as an extensive evaluation and advice on the researched print methods and topologies. To conclude the research, a list of generic findings and recommendations for further development within Buchrnhornen is provided.

Repair and maintenance of products require few resources in a circular economy, minimising the environmental impact of manufacturing and use of products. Although lightweight lattice structures have been widely investigated in various fields owing to their advantages in terms of their mechanical characteristics and the development of additive manufacturing, research on lattice structures has focused mainly on process and design methods for structural development, and not on the repair of lattice structures. In the present study, the repairability of lattice structures was studied to extend the lifetimes of lattice-structured products; this would enable the reuse of products and induce people to directly get involved in creating a circular economy. To determine the factors to be considered for repairing lattice structures, standard specimens fabricated in the form of single undivided and adhesively bonded joint samples were fabricated by fused deposition modeling and compared under four quasi-static tests: compression, tensile, shear, and three-point bending. The octet-truss unit cell was used in the specimen with a strut diameter of 1–2.5 mm at 0.5 mm intervals and a length of 10 mm. The difference in mechanical response between the two groups was significant in the tensile and three-point bending tests, while the compressive and shear tests showed similar results. Therefore, determination of the direction of the stress imposed on the products is essential for the proper repair of the underlying lattice structures, prolonging the life cycle of the product and thus leading to a positive effect on the circular economy.

Interwoven is a textile grown from plant roots, showing the intelligence of plants. It is originally from the attempt of training plant roots to form a manmade pattern since 2015 by visual artist Diana Scherer based in Amsterdam. Due to fragility, it still remains an artistic work. However, Interwoven has a great potential for sustainable product design if further development is made through altering the material structure.

Collaborating with Materials Experience Lab of Industrial Design Engineering in TU Delft, Diana Scherer wants to bring an artistic material closer to people’s daily life. The author, by following the Material Driven Design method (Karana et al., 2015)*, develop the material by altering material structure through hacking the growing process, incorporating generative design techniques and the results from the user studies, with a particular emphasis on people’s experience on interpretive level. Digital Fabrication techniques are used to design the structural pattern for achieving functionally graded material properties (e.g. spatially graded stiffness), and shape optimisation.

Based on Diana Scherer’s experience and early experiments, a few techniques are synthesized and developed in the tinkering with Interwoven. Some potential structures for digital biofabrication are: [1] root growth can be manipulated to mirror digitally generated patterns, which would provide intended technical and experiential characteristics in Interwoven; [2] roots grown in agar gel change properties to stiffer and stronger by hand feeling (further mechanical tests are needed); [3] roots can sew through descrete obstacles in their growing direction and these obstacles can be designed with digital fabrication techniques.

Combining the insights and experiential studies, a material concept has been created: showing roots glue-ability to porous materials and growing traces to blend nature and man-made world. The material experience vision is to exhibit the glue-ability of Interwoven through a daily object co-created by roots and digital manufactured structures and bring forward the collision and collaboration between natural growth and man-made world. The final product concept is to imitate one of the most mass-produced daily products - IKEA ALSEDA, questioning the current way of manufacturing and material use. The co-creation structure increased durability of Interwoven.

The learning curve of novice surgeons takes about 25 surgeries to be proficient at the knee replacement procedure. So it is not just enough if we design efficient and more ergonomic surgical tools, it is also important to provide a learning platform for them to get better before they operate on a real patient. Although many training simulators are available to train different surgical procedures, most of them are digital trainers that simulate the surgical process in a virtual world. There are physical training simulators available in the market for surgeries like laparoscopy and arthroscopy, but not for arthroplasty. FOXPAT is a reusable training simulator for knee arthroplasty surgery. Unlike the existing digital simulators, FOXPAT is a physical simulation of a patient knee with integrated sensors. The training tool lets novice surgeons use actual instruments that are used in the operating theatre. Besides providing a realistic experience of the surgical procedure, the sensors track the usage of tools provide feedback to the surgeons on their outcome.
Arthroplasty being an invasive surgical procedure, any training model will be destroyed in every training session. This makes it difficult for any manufacturer to provide a reusable design that the novice surgeons can train multiples of times. Foxpat can promise such a long term reusability. Novice surgeons can practice the whole surgical procedure of knee replacement before they try on an actual patient. This includes letting surgeons performing actual cutting, drilling and milling procedures. By just replacing a set of low-cost polyurethane bones after every practice session, Foxpat will be ready for a next practice session. As the product is used for training the novice surgeons, these sessions take place either in a conference hall or in a hospital. A training support team or a local technician in the hospital helps to set up the device.
During this project, two iterations of working prototypes were developed and tested before reaching the final design. This design is now ready to be manufactured in small quantities of 50 pieces per year and requires another iteration for large-scale production.

We present a novel DC motor driven soft robotic fish and optimization based on experimental, numerical and theoretical investigation into oscillating propulsion for primarily speed and secondarily efficiency. Our system outperforms the previously fastest soft robotic fish Zhong et al. 2017 by a significant margin of 27%, with speeds up to 0.85m/s. A simple wire-driven active body and soft compliant body were used to mimic highly efficient thunniform swimming. The efficient DC motor to drive the system decreases internal losses compared to other soft robotic oscillating propulsion systems which are driven by one or multiple servo motors. The DC motor driven design allows for swimming at higher frequencies. The current design has been tested up to 5.5 Hz but can potentially reach much higher frequencies.

The versatility of the hands is revealed in its movements, but often not noticed before trauma occurs. Joint range of motion is used as a measure to follow the progress of diseases. A digital workflow for 3D data in medical appliances is envisioned for years.
The aim of this research is to develop a method that reliably and reproducability determine the range of motion of the digits. In current practice, the angles are measured using a goniometer. This method is very imprecise. Three methods to determine the location of joints in 3D hand scans can be distinguished: using heuristics, computer vision, and deep learning. Of those, deep learning is the most flexible, modern and accurate method and is therefore applied. The end result is a matrix containing the range of motion per joint and is applied to anatomically correctly manipulate a 3D model. For ease of manipulation, a physical manipulator is proposed. The results of this novel method show lower interrater differences than measurements with a goniometer.

Microstructural materials with spatially-varying properties, such as trabecular bone tissue, are widely seen in nature. These functionally graded structures possess smoothly changing microscale topologies that enable performance far superior to that of their base material. While the optimization of periodic microstructures has been studied in depth, less attention has been paid to the assembly of optimized microstructures with spatially varying properties. Existing works address this problem by ensuring geometric connectivity between adjacent microstructural unit cells. In this report, we argue that geometric connectivity is insufficient to ensure the continuation of physical properties, and propose the concept of mechanical compatibility. Mechanical compatibility directly examines the effective mechanical properties of the individual cell together with its neighbour. Our approach simultaneously optimizes the mechanical properties of individual microstructures as well as those of neighbouring pairs, so that material connectivity and smoothly varying physical properties are ensured. We demonstrate the application of our method in the design of functionally graded material for implant design, and in the design of both coupled and decoupled multiscale structures.

This report is the result of an IPD (Integrated Product Design) master thesis at the faculty of industrial design engineering at the TU Delft. The company, for which the project was executed, is mainly focused on manufacturing flight-deck seating for the airline industry (pilot seats for airliners). Their biggest and main client is Boeing, for which they provide all airliner flight-deck seats.

A graduation report ‘Back injuries among KLM pilots’ (Vaart, 2009), showed that the graduation company’s flight-deck seat pan and backrest contour does not provide a good sitting posture. They both initiate a slouched seating posture, which can lead to severe back problems (Al-Eisa, et al., 2006). Due to the lack of ergonomically designed flight-deck seats, pilots seemed to be more absent compared to other airline employees. In fact, KLM pilots report much more absenteeism (5,8%) due to back problems than the average KLM employee (4,4%) (Vaart, 2009).

The first goal of the master thesis was to highlight multiple ways of improving the flight-deck seats in order to reduce discomfort among airline pilots. This was achieved by analysing the seat, analysing the flight-deck, interviewing pilots and by co-operating in an extensive user research on Boeing 737 aircraft. It appeared that most airline pilots are obligated to use tablets, for filling in checklists and doing calculations. However, they do not have an assigned place for the tablet on board the flight-deck. Additionally, data from the user research showed that pilots perceive most discomfort in the upper back and often adapt into a slumped seating posture due to reaching for the flight-deck controls, using the tablet or during reading activity. Furthermore, the pilots seemed to have a large area of visual attention, which causes them to move their heads from side to side. These findings lead to the final search area, formulated into the following design goal:

“Designing a tablet holder to reduce discomfort among airline pilots”

The tablet holder design can reduce discomfort among airline pilots while enhancing their work environment and supporting growth towards future technology advances in the flight-deck. The product can be beneficial for the aircraft manufacturer and the airline. It enables the aircraft manufacturer to work towards making airplanes easier to control. Additionally, a platform to incorporate flight-control systems into the tablet could act as the instigator for a distributed, air/ground, socio-technical system. Both aspects that adhere to the growing demand of pilots and which supports the change towards single-pilot operated aircraft. Additionally, the tablet allows the aircraft manufacturer to get rid of a fixed EFB and allows the airline to work towards a digitalized documentation system, which can be accessed through the tablet.

The use of tangential vector fields and thus the need for designing them has steadily been increasing over the years. In this master thesis, a method is proposed and implemented that defines localized tangential vector fields on a mesh surface, which allows for the designing of vector fields on the triangulated surfaces of these meshes. Similarly, as with 2D radial basis functions for function values, it is possible to accurately approximate, compress and design vector fields using the localized tangential vector fields with an applied radial basis function scalar. The proposed system constructs multiple localized tangential vector fields on the surface and creates a basis from them that covers the entire surface. Other works have already suggested methods for the designing of tangential vector fields but most did not allow for both soft and hard constraints to be used when designing fields in real-time. One approach was able to design fields in real-time but had the bottleneck that it required a lot of precomputation time as it was using spectral processing techniques and a spectral transform to work in the spectral representation. Using the proposed localized tangential vector fields basis in this work also allows for the real-time modeling of tangential vector fields without to much precomputation time. However, it should be noted to fully optimize the proposed system several improvements on the current techniques used in this work have to be made to compete with the spectral representation. The proposed system is the first to our knowledge that uses localized tangential vector fields on meshes for the designing of tangential vector fields.