The method of Macaulay is a method to determine force and deflection properties of structures. The method makes it possible to describe discontinuous beams with a single equation. The fact that the entire beam can be described in a single equation makes this method well-suited for use in programming. In past Bachelor End Projects students from the TU Delft have made advancements in the application of the method of
Macaulay, making it able do be used for more complicated structures.

SymPy is a Python library that has a Beam module that specialises in calculations of beams. In this
module the method of Macaulay is used for some of these calculations. The goal of this project is to use the advancements made by previous Bachelor End Projects to extend the implementation of acaulay’s method in SymPy.

This leads to the following research question: How can the current implementation of Macaulay’s method be extended in Python to be able to calculate and analyze more complicated beams and structures, based on the advancement made by previous Bachelor End Projects at the TU Delft?

The advancements made by previous Bachelor End Projects can be divided up into different subjects.
These subjects can be implemented one by one. During the course of the project there has been focus on implementing two of these subjects. The first subject is rotation and sliding hinges. The second subject is calculations of influence line diagrams. Both these subjects are completely implemented into the SymPy code.

In the implementation of rotation and sliding hinges, the mechanics calculation done by the SymPy code are changed. These hinges are now directly added to the load equation of the beam using singularity functions. The main advantage of this is that calculations on beams with hinges can be done on the beam as a whole, instead of having to cut the beam up into different parts. The fact that the beam can be calculated as a whole also makes this method able to be scaled to calculate beams with multiple hinges.

There was already an existing implementation to calculate influence line diagrams, but this implementation could be improved. In the new implementation the moving load is added to the load equation using a singularity function. The ability to apply the boundary conditions that come with hinges is also added in the new implementation. This makes the new
implementation able to calculate correct influence lines for beams with and without hinges.

There are more advancements made by previous Bachelor End Projects than implemented during this project. The advancements on some other subjects, for example normal forces or spring connections, can still be implemented into the current Beam module. For other advancements, those regarding 2D structures, it will be better if they are implemented in a new module. This new module could specialize in 2D structures, while the current module stays focused on calculations on single beams...

The increasing prevalence of micromobility vehicles in urban environments has raised concerns about safety in shared cycling spaces. This study examines the overtaking behavior of e-scooter and e-bike riders to inform traffic management strategies and infrastructure development. A controlled experiment was conducted using strategically placed cameras to track vehicle trajectories and inertial measurement units (IMUs) to capture roll data. Extensive data processing ensured accuracy and synchronization of trajectory and IMU information. Key findings reveal that e-bikes overtaking e-scooters initiate maneuvers from greater distances but maintain smaller lateral distances compared to e-bikes overtaking e-bikes.
Lateral position differences showed a stronger correlation with speed difference than longitudinal position differences. The highest roll rates and angles occurred during the overtaking phase. Pre-overtaking, higher roll rates and angles were observed when e-bikes overtook other e-bikes, indicating greater control adjustments. No significant gender differences were found in overtaking behavior. However, in non-interactive scenarios, male e-scooter riders traveled at higher speeds than females, while no gender differences were observed among e-bike riders. These results provide insights into the complex interactions between different types of micromobility vehicles during overtaking maneuvers. The findings underscore the need for targeted safety interventions and infrastructure improvements to mitigate risks associated with shared cycling spaces, ensuring safer coexistence of micromobility users and conventional cyclists in urban environments.

The cycling industry is influenced by the approval of the tire pressure control system in competitive cycling. This system allows real-time adjustments to the tire-road interaction during races. The total rolling losses is the resistance resulting from tire-road interaction, incorporating resistance due to tire deformation and the dissipation of vibrational energy within the rider-bicycle system. This research investigates the influence of tire parameters on the total rolling losses during road cycling through three key measurements: ink print test, drum test, and rolling losses measurement. The ink print test captures the contact area between the tire and road surface under specified loads, revealing significant impacts of tire type, width, inflation pressure and vertical load on the contact patch shape. In addition, this study shows that an increase in contact patch measures is related to an increase in the rolling resistance coefficient (𝐶𝑟𝑟). The drum test extracts 𝐶𝑟𝑟 values related to pure rolling resistance by measuring the power needed to maintain constant velocity of a rotating drum when in contact with a loaded tire. Results indicate a significant influence of tire type, width, inflation pressure, vertical load and velocity on 𝐶𝑟𝑟 estimates. Combining 𝐶𝑟𝑟 obtain with drum testing with 𝐶𝑟𝑟 determined with total rolling losses measurements, provides insights into the contribution of vibrational losses to the total rolling losses. The study employs a novel bike trailer measurement technique to estimate total rolling losses, measuring the cyclist’s power while cycling at constant speed with elimination of aerodynamic drag. Despite some limitations, the bike trailer method successfully identifies optimal tire parameters
for minimizing rolling losses on different road surfaces at varying speeds.

The favorite way of transport for commuters is still by cars, which are designed too heavy and too wide for the average amount of passengers. Accidents without other traffic users make up a large proportion of crashes for free-tilting bicycles. Tricycles have a chance of rollover while cornering fast.Therefore, new human-powered commuter vehicles are needed that have optimized handling performance and are safer. This alternative can be the narrow tilting tricycle, with the combined advantages of bicycles and tricycles. Faster cornering can be performed than with a tricycle, and better balance and more traction can be obtained than with a bicycle. No method exists to evaluate the handling performance of a narrow tilting tricycle that gives a combined conclusion about the handling performance for multiple velocities and aspects of handling.This study evaluated the optimized handling performance for commuting for a prototype tilting tricycle. The tricycle is designed by Andrew Dressel and built by DEMO at TU Delft. The tilt mechanism incorporates tie rods that connect A-arms to the bell crank at adjustable connection points. This coordinates the tilt behaviour which changes with different connections from the tie rods to the bell crank. I created a novel handling evaluation method for commuter vehicles in a quantitative within-subjects study. I selected a moderate-speed slalom manoeuvre and a low-speed line-following manoeuvre as test manoeuvres. I have measured the maximum yaw factor, the mean absolute steer angle, and the time delay between the roll rate and steer as handling metrics using two Shimmer3 IMUs. The first metric is evaluated for the slalom manoeuvre and the second and third metrics are evaluated for the low-speed line-following manoeuvre. I scaled the metrics and combined the results into a single score. The selected metrics are able to discriminate between the performance of conventional bicycles and prototypes of tilting tricycles. For highly similar designs, it is important to add trials until statistical significance can be reached.
The analysis of the data showed the optimal handling performance of the Dressel tilting tricycle for tie rod angles halfway between free-tilting and self-stable when stationary. For commuter vehicles in city traffic, the tie rods can be fixed at 50%. Increased low-speed balance is proven for increased tie rod angles, without finding reduced performance on the moderate-speed slalom. It is not recommended to increase the tie rod angle to 75%. Uncontrollable performance has been observed in this configuration.A tie rod angle of 100% can provide complete rigidity while standing still. The tilt limit has been hit with increased tie rod angles and this limit is increased with a Matlab optimization. For the optimal configuration with tie rods connected halfway in, the bell crank should be designed 380 mm wide and connected 235 mm high from the ground.
The tilt mechanism with the optimal design parameters can make the vehicle safer because of the improved balance, without reducing the handling performance. A fixed design can make the vehicle cheaper and easier to build compared to the adaptable tilting tricycle. 

The main purpose of this report is to investigate flaws within Cornelis Tromp 25T lemniscate crane upper arm joint. This is done in order to figure out why the joint structure is experiencing significant crack propagation and what potentially could have led to a structural joint failure and death of an operator within a crane of the same model.

Assessment is performed by simulating stress distribution within the problematic joint structure and assessing high-cycle fatigue damage accumulation around its welds. Loading conditions affecting crane upper arm are established through multi-body dynamic simulations, which are meant to replicate operation of a lemniscate crane. Multi-body dynamic model is verified for its accuracy using available crane operation measurement data. Loads are acquired within the time domain and include temporal effects of luffing, slewing and hoisting operations as well as pontoon motion.

Fatigue analysis is performed to evaluate damage accumulation within the tubular joint structure of the crane upper arm. A detailed shell finite element model is established to acquire time-dependent stress responses. During stress evaluation stage - a particularly large stress concentration has been observed at the joint brace saddle position. To assess which method best simulate damage accumulation in the joint structure - three specific fatigue assessment approaches are tested: nominal stress approach, hot-spot stress approach and multi-axial fatigue approach. Nominal and hot-spot stress approaches are evaluated and compared to determine how inclusion of stress concentration effects into fatigue assessment influence damage accumulation results. Result comparison has shown a large disparity in results with hot-spot stress approach, indicating that the method capable of determining locations of dangerous stress accumulation, in relation to what has been observed in the real structure.

Evaluation is performed to determine whether multi-axial fatigue assessment is needed to improve calculation results of fatigue damage accumulation.
Based on stress direction properties within the analysed structure - most favorable multi-axial fatigue assessment approach (capable of analysing proportional stress responses) is used. Multi-axial fatigue assessment method results are then compared with results of conventional hot-spot stress approach to evaluate the differences in damage accumulation rate. Analysis results have shown that both methods are capable of determining locations of critical points with present disparity within magnitude of damage accumulation. This indicates that hot-spot stress fatigue approach, which uses Von Mises stress, is more conservative out of two methods. Fatigue analysis has also presented that original joint structure is inherently flawed, as its stress concentration locations are not easily accessible without crane disassembly and its structural capacity has been underestimated during design stage.

Finally methods for extending operational life of crane upper arm structure are evaluated. Three methods for reducing stress within the structure are assessed: increase of structural capacity, stress redistribution and load reduction. Increase of structural capacity is performed by adjusting thickness of relevant joint elements, with optimal thickness being established using a sensitivity analysis algorithm, which simultaneously acquires combined thickness setup for multiple joint elements - making the joint capable of surviving predetermined fatigue life. Stress redistribution approach is implemented by producing an alternative upper arm joint design, which could be exchanged with the problematic original joint during crane refurbishment. Load reduction approach is performed to investigate whether it would be possible to increase fatigue life of the original joint structure without affecting work efficiency, by only adjusting crane motion profile within multi-body dynamic simulation environment. All three methods are quantified and compared through fatigue damage factor results acquired using multi-axial fatigue assessment method. Result comparison has shown that joint redesign is the most preferred approach due to its ability to efficiently improve fatigue life of the structure without significant structural weight increase, while exposing any potential points for crack initiation to locations easily accessible for inspection and repair.

Training with bodyweight support (BWS) systems can improve the likelihood of regaining normal locomotor abilities for neurologically impaired patients. It is known that people alter their gait parameters when walking with BWS. However, it is unclear whether 2D (vertical and lateral support) and 3D (only vertical support) BWS systems affect these gait parameters differently. In this study, participants walked overground in both a 2D and a 3D BWS system to investigate the effects of this lateral support. To compare the contribution of the vestibular system between the different BWS systems, participants received galvanic vestibular stimulation (GVS). Motion capture and force plates were used to find the coupling between the GVS stimulus and the mediolateral ground reaction forces and to calculate the gait parameters. Differences in gait parameters were observed between the 2D and the 3D system. Compared to unsupported gait, participants increased their step width variability by ~10% in the 3D system. Contrarily, participants decreased step width variability by more than 15% in the 2D system. Mean step width decreased slightly in only the 3D system. The margin of stability did not change significantly in any condition. The coupling between the GVS signal and mediolateral ground reaction forces decreased in the 2D and 3D systems compared to unsupported gait, but no significant differences were observed between different BWS conditions. These results suggest that 2D and 3D BWS systems influence gait parameters differently and that they influence the contribution of the vestibular system to balance, but no significant differences between the systems can be observed in this aspect.

Rehabilitation robots have been shown to be effective in post-stroke gait rehabilitation. However, these devices are usually expensive and suffer from high inertia which decreases transparency. The Minimally Actuated Tendon-based exercise Environment (MATE) is a tendon-based rehabilitation device, designed to be cost-effective and minimize inertia effects. The MATE must apply minimal forces to the wearer if the gait cycle is healthy to prevent deviation into an unhealthy gait. Previously a mathematical optimization was performed on the design of the MATE. This thesis aims to make a physical realization of the MATE to investigate the minimal forces during a healthy gait cycle with two experiments. The first experiment attached the tendons to a machine to investigate forces on a non-altering gait. HTC VIVE motion trackers were used to measure the position of the tendon attachments over time. To measure the tension, in each cable inline tension sensors were added. Comparing the measured forces to velocity-based thresholds indicates that the forces applied by the MATE are too high and would cause deviation. The second experiment involved a human walking with and without the MATE. Evaluating the gait cycle trajectory when walking with and without the MATE indicates that the MATE alters a healthy gait cycle, lowering the step height and causing drift. The forces acting on this gait also exceed the thresholds. The MATE in its current design alters a healthy gait. Redesigning the MATE with the suggestions from this thesis will likely show further improvements.

Existing wind load simulators such as wind tunnels and fans have multiple disadvantages, especially when used in a scaled-down environment. This paper proposes to simulate wind loads by using an admittance-controlled industrial robot arm rigidly attached to a research object. Admittance control should make it possible to simulate wind loads and a specific amount of inertia that is higher than the inertia of the original research object. The goal is to verify whether an admittance-controlled industrial robot arm is suitable for wind load and inertia simulations and what the limitations of this simulation method are. The scope of this research is limited to three Degrees of Freedom. First, the admittance controller is tested on a computer simulation model before execution on a Hardware-in-the-loop setup. It is found that an admittance-controlled robot arm is well capable of simulating both wind loads and a specific amount of inertia. However, there are some limitations. The motion controller of the industrial robot should be able to change the end-effector position within a frequency of 50 Hz. Frequencies above 333 Hz result in the most accurate simulations. The upper range of inertia that can be simulated is restricted by the maximum joint torques the robot can apply. The lower range is restricted by the inertia of the real object, the applied wind loads, and the sampling frequency of the admittance control loop.

The establishment of areas for safe automated driving in mixed-traffic settings is one major barrier in the development and adoption of Autonomous Vehicles (AVs). This work investigates safety in the interactions between AVs, human-driven vehicles, and vulnerable road users such as cyclists and pedestrians in a simulated urban environment in the Dutch city of Rotterdam. Proposing new junction and pedestrian models, virtual AVs with an occlusion aware driving system are deployed to deliver cargo autonomously. Assessing the impact of various measures, including V2V, V2I, V2X communications, infrastructure modifications, and driving behavior, we show that traffic safety and network efficiency can be achieved in a living lab setting for the considered case. Our findings further suggest that V2X gets implemented, new buildings are not placed close to intersections, and the speed limit of non-arterial roads is lowered.

The DelFly Nimble is a type of tailless flapping-wing micro air vehicles (FWMAVs) that has received an increasing amount of attention. FWMAVs show efficient and agile flight possibilities at small scale. The aerodynamics and dynamics of these flapping vehicles are challenging and not fully understood. In this work, a strategy to implement a 3D dynamic model and a trajectory control algorithm is proposed for the DelFly Nimble by the use of a quasi-steady state framework. The design of a suitable tracking control algorithm is the essence of this task. A globally defined smooth nonlinear geometric framework of the flapping-wing vehicle’s rigid body dynamics is introduced as a basis for the analysis. This grants an unambiguous coordinate-free dynamic model in which problem of singularities are avoided. The Nimble has four inputs used to control the six translational and rotational degrees of freedom. A nonlinear tracking controller is chosen on the special Euclidean group 푆퐸(3) for the underactuated aerial vehicle, where position and yaw trajectory tracking are achieved. The full system is classified into the coupled attitude and position subsystems. Using the Lyapunov Stability theorem, the nonlinear controller is shown to achieve almost global asymptotic tracking of the attitude error dynamics of the Nimble and almost global asymptotic tracking of the position error dynamics of the center of mass of the Nimble, enabling sufficient tracking of aggressive maneuvers. Finally, the dynamic model and the controller are examined with numeric simulations. From the results can be concluded that the nonlinear control design allows for aggressive aerobatic maneuvers while maintaining stability of the closed-loop system, provided that the control inputs and damping forces remain moderate.