ABSTRACT. In this research, the preliminary activities towards an experimental campaign with the purpose of investigating the contact physics on asteroid-related scenarios are presented. The outcomes will be used to calibrate contact parameters in an multi-body code.Most asteroids are now thought to be gravitational aggregates, and their granular nature suggests that their dynamics can be effectively simulated using N-body codes, such as GRAINS, whose contact dynamics is based on Project::Chrono. However, to date contact parameters in N-body codes are usually tuned to reproduce large-scale scenarios. The motivation behind the experimental campaign under development is that the accurate modelling of the interactions at particle scale is key to enhance the realism of the simulations necessary to support future asteroid exploration missions. The high-level goal of the experiment is to observe the collision between two asteroid simulant cobbles in micro-gravity and vacuum conditions. Then, a digital twin of the experiment will be calibrated to reproduce their 6-dof trajectory to the best accuracy possible. This work describes the requirements and constraint identified for each component of the experimental set up, focusing on the benchmark model of the digital twin and on the strategy designed to estimate the cobbles' states and contact parameters. The estimation results from preliminary numerical simulations show good performances in most of the scenarios tested, providing important guidelines for the next phases of the experiment development. 

ABSTRACT. The frequencies of long period seismic excitations fall within the range of the fundamental natural frequencies of tall structures. This results in their large resonance responses . The resonance motions affect the modular vertical transportation (VT) systems operating in the structures. A typical traction-driven VT system comprises a set of long slender continua (LSC) employed as a means of suspension of discrete masses, representing a passenger conveyance (car) and counterweight, that can be treated as rigid bodies (RB). Another set of LSC, referred to as compensating cables, is suspended from the beneath of the car to the beneath of the counterweight and is used to reduce, or eliminate the effect of the suspension rope mass transfer. To constrain the loop of the compensating cables a compensator pulley assembly is used. The lengths of the LSC elements vary when the VT system moves vertically within the host structure. Therefore, the natural frequencies of the system vary during the travel. Complex resonance interactions arise when the frequency of the seismic excitation is tuned to one (or more) natural frequencies of the system. In this paper an analytical model to predict the dynamic responses of the multibody VT system under seismic conditions is presented. The model is then used to develop a numerical simulation model to predict the dynamic performance of the system under long-period earthquake excitations. The results demonstrate the interactions of RB responses with the LSC resonance conditions when the frequency of the excitation is tuned to the natural frequencies of the LSC system. These in turn inform the development of resonance mitigating strategies to reduce the effects of the resonance conditions.

ABSTRACT. Occupant Safety must be an integral part of the overall technical and management processes associated with the design, development, and operation of Advanced Air Mobility (AAM) systems. Nowadays, the crashworthiness design for aerospace applications under 14 §§ CFR Part *.561 and Part *.562 only addresses the dynamic response of the seat and restraint system during emergency landing conditions. To provide real-world safety, an integrated safety design approach is required. The elements that constitute the integrated safety concept are Pre‐crash sensing technologies, Parachute Ballistic Recovery Systems, and a combination of Landing Gear‐Airframe crashworthy structures, high-energy absorbing seats, and advanced restraints. Through the integrated safety development process, concept development starts by defining the emergency landing conditions, and the architecture and capacity of the aircraft's energy-absorbing subsystems and structures. A numerical model of a representative AAM vehicle was created using the efficient multibody simulation methodology (Siemens Madymo). After analyzing the results from the original design, optimization was conducted using HEEDS to properly define the structure characteristics that allow the occupant to survive an emergency landing condition. This paper explores the implementation of multibody analysis to size aircraft's energy-absorbing subsystems and structures without the need for high computational resources.

1. Federal Register: June 11, 2007 (Volume 72, Number111), Proposed Rules, Page 32021-32023

2. Olivares G., Airframe “Crashworthiness – Certificationby Analysis”, NIAR Technical Report FAA003, 2019

3. Olivares G., Caralt F., and A. Vina, “Integrated OccupantSafety for Urban Air Transport Emergency LandingApplications” 8th Biennial Autonomous VTOLTechnical Meeting & 6th Annual Electric VTOLSymposium. Mesa, USA. Jan 28th, 2019.

ABSTRACT. Realistic and efficient models of remote mainteance scenarios in fusion power tokamaks are important for simulation and control design. This is especially true when heavy, slender structures like the approximately 80 tonne, 12 meter long Breeding Blankets need to be remotely handled.  Distortion, deflection and vibration could potentialy occur in the blanket structure during the remote handling process. This flexible behavior needs to be avoided to prevent catastrophic system failure. One aspect that should be addressed during modelling is the inclusion of damping effects. In the sub-structuring literature, Component Mode Synthesis (CMS) methods like the Craig-Bampton transformation have been enhanced with damped (complex) modes to reduce errors during model reduction in dynamic systems with arbitrary, non-proportional, damping. With the goal of investigating effective modelling approaches for fusion remote mainteance scenarios, this work presents some findings when applying Damping Enhanced CMS to flexible multibody problems modelled using the Finite Element Floating Frame of Reference Formulation. 

ABSTRACT. The present study delves into modeling both planar and spatial flexible-link mechanisms and synthesizing planar flexible-link mechanisms, employing ANCF cable elements. Flexible-link mechanisms refer to linkage mechanisms that achieve motion through the elastic deformation of one or more flexible links. Quasi-static analysis of the mechanism is performed using the finite element method (FEM). Large static deflections of flexible links exhibit a nonlinear problem, solved using the Newton-Raphson method. A critical aspect of achieving convergence in this highly nonlinear system lies in the initial guess of the deformed configuration. Furthermore, the research emphasizes the synthesis of path generation in flexible-link mechanisms. This involves optimizing the error function to obtain a mechanism that accurately follows prescribed precision points along the desired path. Planar mechanisms with flexible rockers are synthesized for circular, symmetric, and straight-line path generation. Circular and straight-line examples are compared to results from the literature, demonstrating the improvements and efficacy possible through ANCF.

ABSTRACT. The determination of critical parameters or control signals of a multibody system (MBS) is a common problem arising in the~analysis and~synthesis of dynamic systems. The indirect methods of optimal control constitute a powerful toolbox to address these complex non-linear problems. The adjoint method is one such approach, which has been employed in various applications, such as parameter identification or sensitivity analysis of systems with flexible components. This contribution presents how the adjoint method can be utilized to control complex electromechanical multibody system with closed-loop kinematic chain. The test model investigated in this paper is a spatial MBS composed of an inverted pendulum and a~five-bar linkage. Its motion is modeled with a set of Hamilton's equations of motion in redundant coordinates. Although the underlying dynamic problem is highly non-linear, we reported a satisfactory convergence of the optimization procedure.

ABSTRACT. Sensitivity analysis is an extremely useful tool in optimization problems or optimal design, but its calculation is usually complex and requires a high computational effort. Among the techniques available to compute the sensitivity analysis of a set of equations, analytical sensitivities have proven to be among the most computationally efficient and accurate. This work explores the sensitivity analysis of a natural coordinate FFR formulation with constraints enforced by means of an Augmented Lagrangian Index-3 formulation with velocity and acceleration projections (FFR-ALI3-P). The sensitivities have been validated against numerical differentiation in several benchmark problems, including a vehicle model that accounts for the elastic deformation of the chassis.

ABSTRACT. The kinematic and dynamic optimization of complex multibody systems opens the possibility of enhancingthe design of novel and existing vehicles. In this work, the sensitivity analysis and optimization ofgeneral multibody systems is described under kinematics and dynamics conditions and applied to the optimization of a tilting three wheeler. The approach proposed is general and valid for any multibody system, because the general kinematics and dynamics sensitivity equations are the starting point. The implementation of the equations and the numerical experiments have been built in the MBSLIM multibody library coded mostly in Fortran 2008.

ABSTRACT. Acquisition of precise parameters is of key importance for accurate numerical simulation for multibody systems. However, it is generally difficult to obtain all parameters required for the simulation by only direct measurements.  The authors have presented a parameter identification technique based on the adjoint method. It incorporates the proper orthogonal decomposition (POD) into a cost function, in order to consider model uncertainties. More specifically, the proposed method uses data samples decomposed into the proper orthogonal decomposition modes (POMs) for the cost function. According to works by the authors, the cost function given by relatively higher POMs leads precise estimated values, even though such higher POMs have quite lower contribution ratios. This study investigates the relation between the POMs and the accuracy of the parameter identification. In order to derive the equations of motion, we employ the floating frame of reference formulation for the description the elastically supported beam. Then, the time series data for the beam displacements are divided into the components of the POMs. Each components of POMs is analyzed by the Fourier analysis. After that, we compare the frequency components for the component of POMs with the analytical values of natural frequencies and discuss the contribution to the accuracy of the parameter identification. 

ABSTRACT. To overcome the difficulties of remote operation, smart operation of the marine robot using cyber physical operating system (CPOS) is introduced. A digital twin model is developed for CPOS system. The underwater robot model has 49bodies, 62joints and 30 degrees of freedom. The driving simulation of the underwater robot is carried out under 0.5m/s. The vertical motion and longitudinal motion on different road condition are analyzed, respectively. The dynamic behavior of the underwater robot vehicle on different driving conditions is analyzed.

ABSTRACT. Semi-analytical simulation methods have the potential to significantly enhance the development of bicycles,as they enable the reproduction of operating loads within the system with high accuracy. To overcome theneed for a numerical model of the human, tires, and track, measured loads at the connection points betweenthe bicycle system and the environment are applied to the bicycle as a load excitation within a multi-bodysimulation. The replacement of constraints with excitation loads leads to the simulation of an unconstrainedsystem. To prevent the occurrence of unwanted, motion-dependent loads, that could potentially compromisethe accuracy of the load calculations, it is essential to prevent a model drift by stabilizing the simulation.Hence, this paper presents the stabilization of an unconstrained bicycle system with the use of differentcontrol concepts. Furthermore, a numerical method is presented to distribute the control loads over thebicycle system, to increase the accuracy of the calculated component loads and enhance the comparabilityfor elastic multi-body simulations. It is demonstrated that the stabilization of unconstrained multi-bodysystems with control loads leads to highly accurate system loads. Furthermore, it is found that for bicycles,a PI-control to minimize the angular velocity of the system is most suitable to calculate accurate results,without the need for data of the system trajectory.

ABSTRACT. The constraint approach is developed to describe the contact between wheel and rail using a set of kinematic constraint equations, ensuring that both surfaces are in contact without penetration or separation. Offline contact detection is carried out and the resulting data is stored in a pre-processing stage. In the dynamic simulation, the contact location can be determined by interpolating the stored data, which greatly reduces the computation load. Over the years, several works have been published to develop the constraint approach for the calculation of wheel-rail interactions. However, this approach is not well popularized because only new wheel-rail profiles are applied, making it difficult to represent the real-life wheel-rail condition. The goal of this paper is to enhance the developed constraint approach, knife-edge contact (KEC) approach, for the estimation of the wheel-rail contact with worn profiles.

ABSTRACT. Multibody dynamics (MBD) represent an essential and consolidated tool for the comprehensive kinematic and dynamic analysis of general mechanical systems, involving both rigid and flexible bodies interactions. However, the reliability and effectiveness of standard multibody dynamic simulation software can diminish in presence of strongly coupled phenomena spanning multiple physical domains, such as in the context of electro-mechanical systems. In these cases, where events of various physical natures are closely interconnected, the simulation software’s applicability may become less reliable. A possible approach to address this issue could involve considering one main macro-domains at time, simulating different phenomena through their own dedicated software. However, in certain applications, the interdependence among various domains exhibits strong correlations, thus a decoupled solution is considered impractical and co-simulation is re-quired. To address this limitation, this paper focuses on the integration of multibody dynamics (MBD) with equivalent circuit modeling (ECM) in order to effectively solve strong coupled mechanical and electrical systems. In particular this work proposes a novel C++/Python framework, called ChElectronicsLib, based on a two-way coupling between the multiphysics dynamics Project Chrono (PC) with the general purpose circuit simulator engine NGSpice (NGS) to solve complex interaction problems between mechanical and electronic domains. This framework aims to address complex interaction challenges between mechanical and electronic domains. Finally, in order to validate the proposed co-simulation library, the results of an experimental test, that takes under analysis a miniature DC motor coupled with a simple mechanical system, are compared with the numerical results obtained through the presented multi-physics model. As reported by the results, ChElectronicsLib allows to solve through a general purpose MBD-ECM coupling framework, strongly interconnected mechatronic and electro-mechanical phenomena. ChElectronicsLib tries to bridge the gap between mechanical and electronic domains, allowing for more accurate and comprehensive simulation of systems where these interactions play a crucial role.

ABSTRACT. Today, virtually any classical time integration method from system dynamics has its Lie group counterpart including implicit and (half-)explicit methods, methods for constrained and for unconstrained systems, variational integrators, one-step and multistep methods, Newmark type methods etc. There is not much known about the numerical stability of these methods in the application to stiff systems. More precisely, one would be interested in criteria and step size bounds that guarantee that the distance between two numerical solutions for different initial values remains bounded on infinite time intervals. In linear spaces, such error bounds are known, e.g., from the theory of B-stability for systems that satisfy a one-sided Lipschitz condition. In the present paper, we follow a different path and focus on the application of Lie group integrators to test problems from rigid body dynamics.

ABSTRACT. Several different methods and formulations have been proposed for the simulation of multibody systems.In this work, the focus is placed on examining the effectiveness of representative formulations by employing well-established benchmark models and evaluation methods.Four formulations were compared using different integration formulas, including an evaluation of the impact of their parameters on the efficiency of the method and the accuracy of the results.

ABSTRACT. The uncertainty of mechanical systems can occur from a lack of information, such as uncertain system parameters, random inputs, random initial conditions, and random forces. To consider these uncertainties, statistical approaches are commonly adopted. Recently, the polynomial chaos method has gained attention because of its fast convergence property and ability to describe uncertainty with functional representation. The polynomial chaos method can provide a stochastic representation of the response of multibody dynamics systems in both time and frequency domains. However, the polynomial chaos method loses its accuracy in the time domain with long-time evaluation. Especially in the multibody dynamics formulation, the polynomial chaos fails rapidly due to the high non-linearity of the system. In this work, we apply the time dependent polynomial chaos in the multibody dynamics problem to investigate the statistical uncertainty of the response after a long-time integration with only a few terms on a low order basis.

ABSTRACT. The teaching of multibody dynamics at Aarhus University for the past 10+ years has been based on the cartesian formulation as presented in [1]. The advantages of this choice in aiding student learning are many: conceptual intuitive, systematic general approach, a natural extension of undergraduate dynamics executed by the application of virtual work, linear algebra, and numerical methods. Simple implementation in coding exercises offers effective means for verification with hand calculations and visualization of results to aid student learning.

While still keeping the cartesian method in our undergraduate elective mechanisms in machine design coursework, we were looking for further insights to the dynamics and the elegant mathematical language for doing so. Spatial Operator Algebra (SOA) offers just that [2]. Among these insights are easy transformations of quantities using straight forward linear algebra manipulation as well as the effective underlying implementations of numerical algorithms to carry out the manipulation in computer code. Furthermore, as the SOA framework is based on a minimal coordinate representation of the mechanical system, the inherent and exploited traits are rich - such as computational speed, ordinary differential equations nature of the dynamics equation of motion, the order n scaling of the computational burden and the effectiveness of the formulation in control applications.

However, the concepts and theory needed to be fluent in SOA are complex and offer a challenge to students when implementing in a first or second semester graduate program. We have experience with the method and implementation to an example three-bladed horizontal axis wind turbine model [3].

The work presented in this paper describes our entry level graduate course introducing SOA in the context of spatial multibody dynamics as listed in Aarhus University’s course catalogue [4].

The course content is delivered in 14 lectures each consisting of 3.5 hours evenly split between lecturing and in class work on concepts, proofs, and programming assignments.

At the time of the IMSD conference the course will have had its debut including the final exam yet. The presented work will show course execution details, student learning progress, examples, exercises and outcomes by student feedback.

References

1. Haug, E. J.: Computer Aided Kinematics and Dynamics of Mechanical Systems: Basic Methods. Flexible Multibody Dynamics. Pearson, 1989.

1. Jain, A.: Robot and Multibody Dynamics: Analysis and Algorithms. Springer, 2011.

1. Dare, A., Madsen N.E.B, Balling, O.: Efficient Modeling of Wind Turbines Including Flexible Bodies using the Articulated Body Algorithm. ASME IDETC/CIE, St. Louis, MO, USA 2022.
2. Balling, O.: Course Catalog. https://kursuskatalog.au.dk/en/course/125004/Computational-Dynamics. Accessed December 2023.

ABSTRACT. Inertial properties (mass, center of gravity, inertia tensor) are crucial parameters in motion control and simulation of multi-body systems, significantly influencing the accuracy of results. The minimal set of inertial parameters, obtained by combining geometric parameters and inertial properties of counterpart elements, is necessary to represent the multi-body dynamics model without redundancy. A new method for identifying the minimal set of inertial parameters of a multi-body system by expanding and applying the identification method based on free vibration measurements has developed. This method enables high-accuracy identification of the minimal set of inertial parameters in three dimensions, and its validity has been assessed by identifying actual body segments and comparing the results with those obtained from regression equations. The study aims to investigate how the ground reaction force estimation results change when using the identified minimal set of inertial parameters. Accurate estimation of ground reaction forces and moments is crucial for biomechanical analysis and inferring information about various musculoskeletal diseases.

ABSTRACT. Humans are highly dexterous and agile in their interactions with the environment. To develop assistive robots that aid humans in their interactions, the first step is to understand, and model, the human motor control system. Here I present a holistic mathematical model for human motor control, which encompasses multiple levels of control, from high-level decision-making to low-level muscle and skeletal dynamics. This holistic model incorporates various known neural and biomechanical processes, which increases its biofidelity and predictive power. The model also runs faster than real-time, making it a suitable choice for the predictive control of assistive robots. 

ABSTRACT. The authors have developed a five-finger robot hand. Four fingers  (index, mid, medicinal, and little) have two serially connected closed four-bar linkages and Single Planetary Gear System (SPGS). It is a two-degree-of-freedom (2-DOF) mechanical system that drives actively and passively. It constitutes a variable stiffness mechanism (VSM) that achieves sensorless shape-fitting motion (envelope grasping) when grasping an object of unknown shape. This mechanism gains robustness on harsh environmental usages since no electric or electronic devices are embedded in the finger part. However, the mechanism of such an under-actuation system requires stability in its motion, specifically, stable object grasping or pinching. It must be achieved on a mechanical basis, not by control maneuver.

Recently, we developed a new finger mechanism having a Hyperextension joint at the fingertip aiming for passively stabilizing the pinching motion. This study shows the mathematical formulation of the finger mechanism to compute its static motion and force that the fingertip applies to an external object. In addition, it shows that VSM allows control of the force applied by the fingertip to an external object.

ABSTRACT. This work presents a stable locomotion of a 12 DoF biped using motion planning of its Centre of Mass (CoM). The biped is modelled as a 3-D Linear Inverted Pendulum (LIP). The walking pattern is generated using the CoM motion planner and foot pattern generator so that the CoM stays inside the Support Polygon (SP) created by feet during the locomotion. Ultimately, simulation and hardware results of biped locomotion using the proposed methodology are presented.