The development of computationally efficient and validated single-track vehicle-rider models has traditionally required handcrafted one-off models. Here we introduce BRiM, a software package that facilitates building these models in a modular fashion while retaining access to the mathematical elements for handcrafted modeling when desired. We demonstrate the flexibility of the software by constructing the Carvallo-Whipple bicycle model with different numerical parameters representing different bicycles, modifying it with a front fork suspension travel model, and extending it with moving rider arms driven by joint torques at the elbows. Using these models we solve a lane-change optimal control problem for six different model variations which solve in mere seconds on a modern personal computer. Our tool enables flexible and rapid modeling of single-track vehicle-rider models that give precise results at high computational efficiency.@en

We previously presented a narrow-track tilting tricycle with a variable stability mechanism integrated between the swing arms that support a pair of rear wheels, in the so-called “delta” configuration, and with recumbent seating. We now examine adopting that variable stability mechanism to work on a tricycle with a split-parallelogram linkage between a pair of front wheels, in the so-called “tadpole” configuration, and with upright seating. It was fairly straightforward to allow for tilting by replacing the front wheel and fork with a split parallelogram comprising two paired A-arms and kingpins, controlling the motion of the two halves with a bell crank and two tie rods, and then varying the handling of the vehicle by moving the connection point of the tie rods on the bell crank, just as we did with the swing arms of the previous vehicle. We have also separated the two tasks of positioning the tie rod ends on the bell crank and enforcing symmetry of the tie rods. The former does not require much force and can be easily implemented with Bowden cables, but the latter does require large forces and is better implemented with a local rigid-bar linkage. Implementing decent Ackermann steering geometry, allowing for both large tilt and steer angles, and decoupling tilting from steering, however, proved to be quite a challenge, at least while we attempted to implement it with bar linkages. Fortunately, we discovered a 2006 paper by Prof Drstvenšek et al. describing a Bowden cable and cam system that looked promising. Finally, the resulting vehicle handles very nicely. When in “full bicycle” mode, it handles quite similar to the original bicycle that we had converted into the tricycle. When in “rigid tricycle” mode, it keeps the rider upright when stationary or when riding at a walking pace. In between these two extremes, it handles even better than the original bicycle in a slalom course and when slowly following a straight line.@en

The paper presents measurements of the lateral force and self-aligning torque from cargo and city bicycle tyres. Based on the experimental data, we have determined the parameters for the Magic Formula model, for lateral force and self-aligning torque. We performed tests with VeTyT, an indoor test rig specific for bicycle tyres, under different vertical loads (ranging from 343 N to 526 N), camber angles (−5, 0, 5) deg and inflation pressure (from 300 kPa to 500 kPa). For each condition, we evaluated the cornering stiffness and found that it generally decreases with the increase in inflation pressure for the tour/city bicycle tyres. However, the cargo tyre tested showed an opposite trend, with an increase in the cornering stiffness as the inflation pressure increased from 300 kPa to 400 kPa.

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This project was designed to understand the causes and mechanisms of bicycle disc brake noise and use that information to formulate and evaluate possible mitigation techniques. Brake noise was generated by a real bicycle running on a treadmill and recorded by microphone and laser vibrometer. Six independent variables, brake force, rotor thickness, front fork stiffness, weather conditions, spoke tension, and friction coefficient, were varied according to a one-quarter fractional factorial design. A finite element model of the rotor, pads, and calliper was also formulated and analysed. The results of these two methods, particularly the disc mode shapes and frequencies, suggest that doublet mode splitting and reconverging plays a role in noise generation and that changing the rotor mass or breaking its symmetry could interfere with such noise generation. Finally, of these mitigations, breaking disc symmetry proved the most fruitful, with noise magnitude reductions from 72% to 99%, depending on frequency.

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The ollie is the base aerial human–board maneuver, foundational to most modern skateboarding tricks. We formulate and solve an optimal control problem of a two-dimensional simplified human model and a rigid body skateboard with the objective of maximizing the height of the ollie. Our solution simultaneously discovers realistic human-applied force trajectories and optimal board geometry. We accomplish this with a direct collocation formulation using a null seed initial guess by carefully modeling the discontinuous aspects of board–ground impact and foot–board friction. This leads to efficient and robust solutions that are 10 times more computationally efficient than prior work on similar problems. The solutions show that ollie height can increase 3% by decreasing the wheelbase and that a smaller board with a back-foot-dominated force strategy can give 12% higher ollies. Our model can be used to inform jump strategy and the effects of changes to the essential board geometry.

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We evaluated the impact of Model Predictive Control (MPC) robotic-assisted versus unassisted training on motor learning of a complex bicycle steering task. Ten participants were divided into two groups, alternating between MPC-assisted and unassisted training to ride a steer-by-wire bicycle on a treadmill to collect virtual stars. At Baseline, Mid-Training, and Post-Training, motor skills were assessed by the average and standard deviation (SD) of distance to stars, while performance was measured by the mean absolute and SD of the steering rate. We found significant improvements in task skill and steering performance, with notable benefits observed in the performance of the group initially trained unassisted. Our findings suggest that starting the training unassisted could stimulate an internal focus (concentrating on one's own body movements) and intrinsic skill perception. This foundation may then form a basis for later integration of MPC assistance to refine further the gained motor skills. Such a sequential training approach may benefit motor skill acquisition of complex dynamics tasks. Further research is necessary to validate and apply these findings to enhance training methods.

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Microscopic simulation is an established tool in traffic engineering and research, where aggregated traffic performance measures are inferred from the simulation of individual agents. Additionally, measures describing the safety and efficiency of road user interactions gain importance for recent developments such as automated vehicles and urban cycling. However, current simulation frameworks model interactions including cyclists only with limited realism. To address this issue, we propose to bring bicycle dynamics to traffic simulation. We demonstrate that a novel reformulation of the social force framework can create input signals for a controlled inverted pendulum bicycle model and thereby enable a fully two-dimensional open space simulation of cyclist interactions. The inverted pendulum model introduces the need to stabilize the bicycle as a constraint to the reactive behavior of simulated cyclists. Furthermore, it enables the simulation of countersteering and weaving for stabilization. Our cyclist social forces have anisotropic force fields with respect to relative interaction position and orientation to describe the varying interaction constellations in open space. With these models, we simulate five single- and multi-cyclist test cases and show that the generated trajectories notably differ from results obtained from a 2D bicycle model without lean angle simulation. Measurements of the maximum lateral path deviation and post-encroachment time show that these differences are relevant for typical applications. Our work demonstrates the potential of introducing physics-based realistic bicycle dynamics to the microscopic simulation of individual road user interactions and the fundamental capability of our reformulated cyclist social forces to do so. Going further, we plan to calibrate and validate our model based on naturalistic cycling data to support the initial results of this work.@en

The use of bicycles as a cheap and healthy way to travel the “last mile” is spreading widely in the cities. This new way of dealing with short trips, known as “micro-mobility”, is also fostered by the new awareness of the global impact of ICE vehicles and rising fuel costs. In recent years, also cargo bikes are knowing a large use, both for families with children and for delivery purposes. They are featured by a long frame that can carry loads usually placed in between the rider and the front wheel. This requires fairly skilled riders to deal with driving dynamics, different from the common bicycle we are used to (Miller, M., 2023). They can easily reach a speed of 25 km/h (according to the regulations in most EU countries) being usually pedal-assisted. Tyre characteristics may strongly affect bicycle dynamics (Bulsink, V., 2015). This applies even more for cargo bikes as they are featured by remarkable load variation (load/unload configuration), relatively high speed and torque applied to the tyres, both during acceleration and braking phases. In this context, it is important to have a good understanding of tyre characteristics. With the aim of designing safer and more performant bicycles, numerical models are required. Furthermore, existing mechanical models of bicycles mostly ignore tyre dynamics and need to be updated with realistic tyre models (Dell’Orto, G., 2022). Measurements were performed with VeTyT, an indoor test-rig specific for bicycle tyres, designed at the Department of Mechanical engineering of Politecnico di Milano (Figure 1) (Dell’Orto, G., 2022). It is the only test-rig for bicycle tyres complying to the standard ISO 9001-2015. We can measure lateral force and self-aligning torque, as tyre parameters vary. The tyre 20”x2,15 was mounted on a standard aluminum rim and tested on flat track. The specific dimensions of the cargo bicycle wheel forced us to update the test-rig, designing a new steel fork to ensure sufficient stiffness and new steel plates to carry the wheel on flat track (Figure 2). Inflation pressure was set to 400 kPa, as recommended by the manufacturer. Tests were performed applying a vertical load of 411 N and 526 N, according to the technical limits of the test-rig. The camber was set to 0 degree, as first stage of the study. The lateral force and self-aligning torque as function of the slip angle are shown in Figure 3 and Figure 4, respectively. It is clear the difference in outcomes adjusting the vertical load. As the vertical load increases, both the lateral force and the self-aligning torque increase in magnitude as well. As expected, the tyre can generate higher forces with higher vertical load. It is worth noticing that the peak value of lateral force will be reached for very large slip angles (> |6| degrees, as maximum value tested in this study). Tyres for cargo bicycles are designed to carry large loads, therefore we expect to reach saturation conditions for higher vertical forces or, conversely, large slip angles. The cornering stiffnesses are reported in Table 1: for vertical load 526 N it is 23% higher than that found at 411 N.@en

Bicycles are more difficult to control at low speeds due to the vehicle’s unstable low-speed dynamics. This issue might be exacerbated by factors such as aging, disturbances, and multi-tasking. To address this issue, we developed a prototype ‘balance assist system’ with Royal Dutch Gazelle and Bosch eBike Systems at Delft University of Technology, which includes an electric motor capable of providing additional steering torque. We implemented a speed-adaptive feedback controller to generate the additional steering torque to that of the rider. We conducted a study with 18 older and 14 younger cyclists to first examine the effect of aging, disturbances, and multi-tasking on cycling at lower forward speeds, and evaluate the effectiveness of the system in improving the stability of the rider-bicycle system while facing these challenges. The study consisted of two scenarios: a single-task scenario where participants rode the bicycle on a marked narrow straight-line track, and a multi-task scenario where participants performed a shoulder check task and followed visual cues while tracking the straight-line. We introduced handlebar disturbances using the steer motor in half of the trials in both scenarios. All trials were repeated with and without the balance assist system. We calculated the bicycle mean magnitude of roll and steering rate—as indicators of bicycle balance control and required steering actions, respectively—and the rider’s mean magnitude of lean rate with respect to the ground to investigate the effect of the balance assist system on rider’s lateral motion. Our results showed that aging, disturbances, and multi-tasking increased the roll rate, and the balance assist system was able to significantly reduce it. The effect size of the balance assist system in reducing the roll rate across all conditions was found to be larger in older cyclists, indicating a more substantial impact compared to younger cyclists. Disturbances and multi-tasking increased the steering rate, which was successfully reduced by the balance assist system. Aging did not significantly affect the steering rate. The rider’s lean rate was not significantly affected by age, disturbances, or the balance assist, indicating that the upper body plays a minor role when riders have good steering control authority. Overall, our findings suggest that lateral motion and required steering action can be affected by age, multi-tasking, and handlebar disturbances which can endanger cyclists’ safety, and the balance assist system has the potential to improve cycling safety and reduce the incidence of single-actor crashes. Further investigation on riders’ contribution to control actions is required.@en

The potential advantages of tilting trikes have been tantalizing for years: they can lean like a bike so that they do not have to be low, wide, or slow in turns; and they can keep the rider upright like a trike when stopped or going slow. Implementing this functionality, however, has been somewhat problematic. Many tilting trikes have been built in which the extra wheel only offers some redundant traction, in the case of inconsistent friction with the road surface. Some have been built with a so-called ''tilt-lock', in which the third wheel can also act as a kickstand to hold the trike rigid when stopped. A few tilting trikes have been built with sophisticated sensors, actuators, and control algorithms to assume the proper tilt angle in every situation, and the motorcycle press breathlessly announces the latest patent filings in this area from major motorcycle manufacturers. @en

With aging, the sensory, motor, and central nervous system deficiencies lead to inadequate bicycle postural control in older cyclists. Similarly, variety in riding skills leads to different bicycle postural control strategies. Cycling seems to be an automated task but keeping the bicycle stable at low speed, pedaling, and steering requires continuous physical and cognitive effort, and in long term may lead to fatigue induced by steering and stabilizing the e-bike at low forward speeds especially in older cyclists. E-bikes enables riders to cycle for langer duration and distance by reducing the physical fatigue. There is an increasing societal interest in electric bicycles where in 2021, 26. 73 billion US dollars worldwide have been invested on e-bikes and by 2027 this global market size will increase to 53.53 billion US dollars (Statista). However, with increased numbers of e-bikes, bicycle accidents due to inadequate steering and balance control by older cyclists have increased, which suggests needs for extra safety measures to maintain balance on a bicycle for challenging situation such as facing undesired disturbances or low forward speeds. We developed a prototype steering assist which aims to increase safety and improve the user experience, by reducing the steering effort and enhancing the bicycle postural control (rider-bike balance control). We investigated the potential effectiveness ofthe steering assist technology in real life challenging situations. Our present study should be considered exploratory research to find the potential effectiveness of the steering assist technology in improving the user experience and safety compared to a non-assistive e-bike. The improved bicycle postural control is validated by smaller range, variability, and rate of steering and roll trajectories when the rider is subjected to an unwanted disturbance. Improved bicycle postural control is expected based on the reduced need for compensatory behavior in the presence of assistive technology. Decreased steering effort is expected due to reduced demand for acute steering control in the anticipatory control strategy.@en

Wobble, also known as speed wobble or shimmy, and the hazard it can cause to cyclists, is a well-known behavior of some bicycles. lt is a relatively high-frequency oscillation, 4-10 Hz. of the front fork and wheel assembly about the steering axis, and it can result in loss of control if left unaddressed. The importance of tyre mechanical properties, specifically conering stiffness, to the wobble motion of bicycles has been shown. Some tyres can make a bicycle more likely to wobble, while others can make the same bicycle less likely to wobble. There are only a few facilities in the world, however, capable of measuring these properties of bicycle tyres, and facilities for testing motorcycle and automobile tyres are not designed to work with bicycle wheels and/or are prohibitively expensive to use. We introduce and characterize an inexpensive, table-top device for measuring the necessary mechanical properties of bicycle tyres.@en