Multibody System Dynamics最新文献

Abstract

Analyzing the walking motion of the bipedal robots that have upper-body parts as well as lower-body legs and exhibit a human-like gait is a challenging task. One of the main objectives of this paper is to present a new and systematic method for designing a desired movement trajectory for a bipedal robot such that it has the greatest conformity with the system dynamics and makes the gait of a bipedal robot similar to the configuration of a human being walking on a sloping surface. To this end, first, the kinematics and the dynamics of a bipedal robot walking down a ramp of shallow slope are investigated. Using the recursive Gibbs–Appell (G-A) methodology and Newton’s kinematic impact law, the governing dynamic equations of this bipedal robot in the two single-support and double-support phases are derived so that we can alter the system’s degrees of freedom without having to perform manual computations. Based on the dynamic equations obtained in the process, an eigenvalue problem is achieved, which can be solved to determine the suitable initial conditions needed for the passive gait of the bipedal robot. Then, having the initial and final conditions (before an impact with the inclined surface), a new method called “passive gait-based trajectory design (PGBTD)” is employed to determine the desired walking trajectory of the robot for one step. Considering the nonlinearity of the examined system, an optimal control method based on the state-dependent Riccati equation (SDRE) is employed to track the desired trajectory obtained. The performed simulations show that by just using a small amount of control energy at the beginning of each step, the steady and continuous gait of the bipedal robot on sloping surfaces can be controlled.

Computational models are conventionally created with input data, script files, programming interfaces, or graphical user interfaces. This paper explores the potential of expanding model generation, with a focus on multibody system dynamics. In particular, we investigate the ability of Large Language Model (LLM), to generate models from natural language. Our experimental findings indicate that LLM, some of them having been trained on our multibody code Exudyn, surpass the mere replication of existing code examples. The results demonstrate that LLM have a basic understanding of kinematics and dynamics, and that they can transfer this knowledge into a programming interface. Although our tests reveal that complex cases regularly result in programming or modeling errors, we found that LLM can successfully generate correct multibody simulation models from natural-language descriptions for simpler cases, often on the first attempt (zero-shot).

After a basic introduction into the functionality of LLM, our Python code, and the test setups, we provide a summarized evaluation for a series of examples with increasing complexity. We start with a single mass oscillator, both in SciPy as well as in Exudyn, and include varied inputs and statistical analysis to highlight the robustness of our approach. Thereafter, systems with mass points, constraints, and rigid bodies are evaluated. In particular, we show that in-context learning can levitate basic knowledge of a multibody code into a zero-shot correct output.

In biomechanics, computing muscle forces and joint efforts with mathematical optimisation copes with the muscle-redundancy problem, i.e. an infinity of possible muscle forces for a unique configuration. Achievements have been made to develop cost functions that reflect physiologically more correct muscle strategies and to validate them with experiments. It has also been proposed to use experimental input such as electromyography (EMG) in the model to guide the optimisation computation. In line with that, the present study proposes an EMG-based approach to compute back-muscle forces and the resulting intervertebral efforts in a horizontal static configuration of the trunk. This approach is based on EMG signals of three back muscles, lumbar and thoracic paravertebral muscles and the quadratus lumborum (QL), recorded on 19 healthy male subjects. Results of this approach were compared with those from optimisation computations involving four cost functions, classically used in the literature for the trunk and the spine. Our approach showed that muscle forces and intervertebral efforts were in line with these computed by mathematical optimisation, but muscle forces obtained with our approach were more representative of the measured EMG signals compared to muscle forces computed by optimisation. Indeed, three of the four cost functions completely missed to recruit the QL, while the latter was clearly activated during the experiment. This result highlights that EMG and experimental input should be more considered when using a musculoskeletal model and optimisation tools. Since the EMG-based approach used in this study was based on a pure deterministic distribution of a global equivalent force, future work will focus on involving EMG input in the optimisation process to guide its solution in a more physiological manner.

This paper discusses modelling of a multibody system consisting of airship, gondola, and a slung payload. Lighter-than-air vehicles undergo inertial forces that are often neglected in heavier-than-air vehicles. These inertial forces are modelled using added mass and added inertia. The dynamics of the multibody system were first modelled using the Udwadia–Kalaba method. Three constraints were derived and enforced. The resulting equation of motion was used to identify the added mass, added inertia, and inertia of the airship through system identification procedure. The proposed system identification method utilizes semidefinite programming with equality and inequality constraints to find any unknown parameters in the mass matrix of the multibody system. Three experiments were carried out to perform the system identification and validate the dynamic model. The identified mass matrix was used to reconstruct the trajectories of the experiments. Using the experimentally obtained mass matrix demonstrated (35%) lower error when compared with simulated trajectories using approximated mass matrices.

Symbolic generation of multibody systems equations of motion appeared in the 1980s. In addition to their computational advantage over their numerical counterparts, symbolic models can be very easily and straightforwardly interfaced with a wide range of software environments and hardware devices. These two features place this approach in a pole position to participate and intervene in the design of digital twins for systems such as vehicles, manipulators, walking robots or haptic devices.

In this context, the first goal of this paper is to highlight the interest of symbolically generated multibody models – at the root of the ROBOTRAN program – in the form of a standalone set of equations calculating the dynamic model of multibody systems, for use as a computational component within a Digital-Twin-type process. The next goal is to embed realistic and complex multibody models within processes or devices whose functioning requires a synchronized real-time computation – or analysis – of their motion.

An implementation (i) on specific hardware and (ii) on two extremely opposite but revealing applications (namely a railway vehicle and a digital piano) are presented to highlight the usefulness of symbolic models for the development of current and future multibody-based digital twins.

The talocrural and the talocalcaneal articulations collectively form the ankle joint complex of the human foot and are the focus of investigation of this work. The talocrural articulation enables plantarflexion and dorsiflexion, while the talocalcaneal articulation allows inversion and eversion of the foot. A comprehensive analysis of the literature suggests that the ankle joint complex is modeled in different manners considering approaches with varying complexity levels, which more or less accurately mimic its intrinsic anatomical features. Several studies assume that the foot articulates with the leg via the talocrural articulation only, which is modeled as a revolute joint. Other studies consider the movements allowed by both articulations and model the ankle joint complex as spherical, revolute, or classical universal joints. Most existing approaches do not consider sufficiently accurate anatomical modeling of this joint complex. Thus, this work presents a new skeletal model for the ankle joint complex of the human foot that considers the actual anatomy and movements of the talocrural and the talocalcaneal articulations. The proposed approach uses a modified universal joint, which incorporates a massless link to mimic the actual function of the talus bone. The developed formulation is compared with a model available in the literature, which uses a classical universal joint. The outcomes show that modeling the ankle joint complex as a modified universal joint allows a more realistic representation of the anatomy of the human foot. The main differences between the two joint models are observed in the mediolateral direction.

Bearings are mechanical components designed to restrict the relative rotary motion between moving parts and transmit loads with low friction. Their performance directly impacts the durability, efficiency and reliability of various machinery. Therefore, bearing failures can lead to economic costs, repair/stoppage times, accidents and regulatory compliance issues. In the context of Industry 4.0, the development of detailed and reliable computational models for simulating bearings’ dynamics plays a crucial role in establishing digital twins and implementing advanced predictive maintenance strategies.

This work focuses on modelling radial-loaded deep groove ball bearings under the multibody systems dynamics framework and the components of the bearing (inner and outer rings, rolling elements, and cage) are treated as separate bodies. A smooth contact approach is utilised to characterise the contact/impact phenomena, providing flexibility and efficiency in monitoring the whole contact event. In this sense, suitable normal and friction contact force models are used to describe those interactions between the contacting bodies. The main contribution of this work relies on the modelling strategies to represent the cage/rolling element interaction.

Having that in mind, several multibody models of radial-loaded deep groove ball bearings are developed considering different modelling assumptions, resulting in dynamic analyses with various levels of complexity. The underlying simplifications are described, and their main advantages and shortcomings are discussed. The simulation results demonstrated the significant impact of accurately selecting the modelling parameters. The promising results of this study pave the way for future investigations, extending to other geometries of rolling contact bearings and working conditions.