Multibody Model Research Articles

Dynamic modelling and energy-efficiency optimization in a 3-DOF parallel robot

AbstractEnergy efficiency is a challenging and relevant research field in modern manufacturing industries, where robotic systems play an essential role in the automation of several industrial operations. In this paper, we present an approach for the energy-efficiency optimization of a 3-DOF parallel robot. The proposed strategy leverages the task placement, the execution time, and the length of the robot lower arms to minimize the energy consumption for the execution of a predefined high-speed pick-and-place operation. To evaluate the actuators energy consumption, the kinematic, dynamic and electro-mechanic mathematical models, as well as an equivalent multibody model, of the parallel robot are implemented. The results of extensive numerical simulations show that the proposed strategy provides notable improvements in the energy efficiency of the parallel robot, with respect to alternative approaches. Starting from a pick-and-place task with optimal task placement with a consumption of 38.2 J (with a cycle time of 0.4 s), the energy expenditure can be reduced to 3.75 J (with a cycle time of 1.86 s), with a reduction percentage of 90.2%, by additionally optimizing the execution time, and the length of the robot lower arms. These results lead to a reduction from 5733 J/min (for 150 cycles/min) to 121 J/min (for 32 cycles/min), allowing to choose the best trade-off between robot productivity and consumed energy.

Steering ability rapid evaluation of the slide drilling system based on multi-body dynamics model

Efficiently and accurately predicting the steering ability of the bottom hole assembly (BHA) in slide drilling is a crucial yet challenging task. While the industry standard three-point geometry method is computationally efficient, it cannot capture the intricate mechanics involved in the drilling process. Conversely, utilizing the whole drill string dynamics model for simulating slide drilling provides a more comprehensive representation but involves time-consuming evaluations, making it difficult to balance precision and efficiency. This study addresses this challenge by proposing a rapid evaluation method that ensures both speed and accuracy by developing a multi-body dynamics rapid model of the slide drilling system. Based on the whole drill string model, this method incorporates two key techniques to achieve its primary objective. Firstly, it utilizes the equivalent torque model of the bit, which includes the fixed joint and the virtual rotational velocity, to replace the original revolute joint between the positive displacement motor (PDM) and the bit. Secondly, a segmentation model is established to decouple the simulation of the BHA drilling process from the drill string equilibrium process, thereby significantly reducing the slide drilling system’s degree of freedom (DOF). The proposed method offers a new approach to improving the efficiency of evaluating the steering ability of the slide drilling system while ensuring a high level of accuracy.

Quantification and visualization of vibration power flow in train-track-bridge coupled system under thermal effects

This paper presents an approach to investigate the effect of temperature on the transmission and distribution of vibration energy for train-track-bridge coupled systems. The vibration of the coupled system can be simulated by integrating the multi-body dynamics model of the train with the finite element models of the track and bridge. The transmission and distribution of vibration energy can be evaluated using a structural intensity method. This approach was implemented to investigate the vibration characteristics of a coupled system under extreme temperature conditions. The system consisted of a CRH2 high-speed train, a CRTS I double-block ballastless track, and an arch bridge. The results show that extreme temperature not only impacts the characteristics of vibration energy transmission in the coupled system but also affects vibration energy distribution. This research provides new insights into vibration control and optimization design for bridges in regions with significant temperature variations.

Cable-Driven Mechanism Models for Sensitive and Actuated Minimally Invasive Robotic Instruments

Cable-driven mechanism models are, usually, included in actuated systems; however, recently, their use for sensitive systems has been explored. In this paper, two cable-driven multi-body mechanism models are compared, underlining advantages and constraints in using sensitive cable-driven mechanisms for minimally invasive robotic instruments. The proposed approach could be useful in bypassing sterilization problems for surgical robotic instruments because our system allows for the separation of the robotic sterilizable part from the sensitive-actuated part of the surgical instrument. The real implementation of the proposed mechanism models, presented partially in other works, are validated in this paper, performing a simulation using a multi-body environment. Results confirm the feasibility of the proposed sensitive-actuated approach, defining new bases for the next challenges of the future.

Service Performance Optimization and Experimental Study of a New W-W Type Non-circular Planetary Gear Train

To address the vibration problem in traditional W-W-type non-circular planetary gear trains during operation, this study proposes two new combinations of W-W-type non-circular planetary gear trains. The study focuses on analysing the transmission error and improving service performance. By utilizing the conjugate theory and the coordinate transformation theory, an accurate mathematical model for non-circular gears is derived. The transmission error models for the two combination forms of the non-circular planetary gear train are established using the incremental meshing line method. The analysis also examines the influence of eccentricity on the transmission error. Kinematic analysis of the multi-body dynamics model confirms that the new W-W type non-circular planetary gear train, formed by combining non-circular gears and cylindrical gears, exhibits superior transmission performance. Furthermore, a test analysis is conducted on the roller pumping unit test platform and the indicator diagrams of the pumping unit under various working conditions are obtained. The study concludes that the optimal matching mode for the sucker rod counterweight and motor frequency of the reversing device of the pumping unit is 20 kN and 20 Hz, and the dynamic balance of the pumping unit load can be achieved by adjusting the motor frequency.

Numerical study on train-induced vibrations: A comparison of timber and concrete buildings

This paper deals with the prediction of train-induced building vibrations by using a numerical framework. The framework is based on a sub-structure approach, where a sequence of different models are used. The free-field ground vibrations and the track receptance are calculated using 2.5D technique where the railway track is represented by finite elements that couple to a dynamic stiffness of the underlying soil, which in turn is obtained from the Green’s function of a horizontally layered half-space using a layer transfer matrix approach. A planar multi-body model of the train, coupled to the track receptance, is used for calculating the train–track interaction forces as the train runs over an uneven rail. Finally, the building response to the incident wavefield is calculated using a 3D finite element model, accounting for the soil dynamic stiffness.The framework is used to evaluate the vibrations in two buildings with identical layout, one lightweight wooden building and one heavyweight concrete building, due to a passenger train passing by at two different speeds. It was found that the difference in response between the two buildings were small. Compared to the incident wavefield, an amplification of the response inside the building was found in frequency bands around the fundamental natural frequencies of the slabs; however for higher frequencies and in terms of the 1 s running RMS velocity the building response was reduced. Further, it was found that accounting for soil-structure-interaction, as opposed to simply enforcing the free-field displacements at the building foundations, significantly reduced the building response in terms of 1 s RMS velocity.

The influence of asymmetric rail cant on rail corrugation in a small-radius curve section

A suitably designed rail cant can improve the wheel-rail alignment, effectively reduce the wheel-rail contact pressure and reduce the wheel-rail wear. However, the rail base cant has rarely been specifically designed for suppressing rail corrugation. Furthermore, no studies have yet been conducted on using different inner and outer rail cants in small-radius curve sections from the perspective of suppressing rail corrugations and wear. In this study, the growth rate index of rail corrugation is obtained by combining an impact hammer origin admittance test and a coupled vehicle-track multi-body dynamic model simulations. The wear depth of rail surface is obtained by combining a three-dimensional transient wheel-rail rolling contact model and Archard wear theory. From the overall perspective of preventing rail corrugation and slowing down rail wear, based on the multi-objective optimization using a particle swarm optimization algorithm, the optimal configuration of inner and outer rail cants in a small-radius curve section were determined as 1/22 and 1/40, respectively, which provided effective suppression of rail corrugation initiation and further development of rail wear.

Understanding the role of head size and neck length in micromotion generation at the taper junction in total hip arthroplasty

Modular hip implants allow intra-operative adjustments for patient-specific customization and targeted replacement of damaged elements without full implant extraction. However, challenges arise from relative micromotions between components, potentially leading to implant failure due to cytotoxic metal debris. In this study magnitude and directions of micromotions at the taper junction were estimated, aiming to understand the effect of variations in head size and neck length. Starting from a reference configuration adhering to the 12/14 taper standard, six additional implant configurations were generated by varying the head size and/or neck length. A musculoskeletal multibody model of a prothesized lower limb was developed to estimate hip contact force and location during a normal walking task. Following the implant assembly, the multibody-derived loads were imposed as boundary conditions in a finite element analysis to compute the taper junction micromotions as the relative slip between the contacting surfaces. Results highlighted the L-size head as the most critical configuration, indicating a 2.81 μm relative slip at the mid-stance phase. The proposed approach enables the investigation of geometric variations in implants under accurate load conditions, providing valuable insights for designing less risky prostheses and informing clinical decision-making processes.

Evaluation of trunk muscle coactivation predictions in multi-body models

Musculoskeletal simulations with muscle optimization aim to minimize muscle effort, hence are considered unable to predict the activation of antagonistic muscles. However, activation of antagonistic muscles might be necessary to satisfy the dynamic equilibrium. This study aims to elucidate under which conditions coactivation can be predicted, to evaluate factors modulating it, and to compare the antagonistic activations predicted by the lumbar spine model with literature data.Simple 2D and 3D models, comprising of 2 or 3 rigid bodies, with simple or multi-joint muscles, were created to study conditions under which muscle coactivity is predicted. An existing musculoskeletal model of the lumbar spine developed in AnyBody was used to investigate the effects of modeling intra-abdominal pressure (IAP), linear/cubic and load/activity-based muscle recruitment criterion on predicted coactivation during forward flexion and lateral bending. The predicted antagonist activations were compared to reported EMG data.Muscle coactivity was predicted with simplified models when multi-joint muscles were present or the model was three-dimensional. During forward flexion and lateral bending, the coactivation ratio predicted by the model showed good agreement with experimental values. Predicted coactivation was negligibly influenced by IAP but substantially reduced with a force-based recruitment criterion.The conditions needed in multi-body models to predict coactivity are: three-dimensionality or multi-joint muscles, unless perfect antagonists. The antagonist activations are required to balance 3D moments but do not reflect other physiological phenomena, which might explain the discrepancies between model predictions and experimental data. Nevertheless, the findings confirm the ability of the multi-body trunk models to predict muscle coactivity and suggest their overall validity.

An electric kickscooter multibody model: equations of motion and linear stability analysis

AbstractIn this work, a detailed multibody model of an electric kickscooter is presented. The model includes toroidal wheels as well as rear and front suspensions. The equations of motion are derived and linearized along the steady forward motion of the vehicle. Using an efficient linearization approach, suitable for complex multibody systems with holonomic and nonholonomic constraints, allows for obtaining the reduced linearized equations of motion as a function of the geometric, dynamic, wheels’, and suspensions’ parameters. The proposed electric kickscooter multibody model is validated with the stability results of a previously presented electric kickscooter benchmark. Since the resulting eigenvalues are parameterized regarding the design parameters, a detailed linear stability analysis of the system is performed. In particular, the influence on the stability of the toroidal geometry of the wheels, the elliptic cross-section of the toroidal wheels, the rider model, the steering axis inclination angle, the inertia tensor of the front frame, and the rear and front suspensions is analyzed. The model presented, together with the linearized equations of motion obtained in this work, enables a systematic analysis of the stability of these vehicles, which helps design new electric kickscooters with improved vehicle safety conditions and oriented to a wider range of potential users.

Study on dynamic performance of high-speed railway vehicle using roller rig and numerical simulation

The development of high-speed trains has increased the demand for dynamic vehicle tests on roller rigs. This study presents a nonlinear multi-body dynamic model of a vehicle system running on a roller rig and an actual track. Dynamic tests for a high-speed vehicle were performed using a full-scale roller rig to validate the numerical model. The hunting stability characteristics of the vehicle were investigated by performing a comparative analysis of the roller rig tests and numerical simulations of the vehicle on roller rigs and tracks. The results indicate that the critical hunting speed of the vehicle on a roller rig is lower than that on a track, particularly under significantly high or low equivalent conicity and yaw damper failure conditions. The characteristics of the hunting stability, riding performance, and lateral acceleration of the bogie frame were comparable in both rig tests and line operations, exhibiting consistent trends under the normal operation of the suspension system with the wheel/rail matches existing within the ideal range of equivalent conicity. However, the lateral acceleration or lateral Sperling index of the carbody could better detect the carbody hunting under low equivalent conicities, particularly when the lateral acceleration of the bogie was not sufficiently effective.

Multi-body dynamical modeling and prediction of flexible origami/kirigami structures by affine transformation

A generalized multi-body dynamical modeling method of Origami/Kirigami structures considering the elastic–flexible coupling of surfaces and nonlinear creases is proposed. For different structures with complex spatial configuration and constraints, an Affine Transformation (AT) technique based on Absolute Nodal Coordinate Formulation (ANCF) is proposed to make the modeling more convenient and efficient. The surfaces are discretized by triangle reduced elements, and the constitutive relations of creases are described by nonlinear state-dependent torque constraints. The proof of the topological invariance of configurations is also given. The simulation of the folding capacity and dynamic behaviors on two Origami structures, Origami solar array mechanism, and enclosed Yoshimura Origami, are given, which verifies the effectiveness of the modeling method. Additionally, the quantitative dynamic behaviors contributes to the design principle of a Kirigami structure for multi-stability. Comparisons between theoretical results from modeling and experiments demonstrate the effectiveness of the modeling method and crease design. The AT-ANCF lays a theoretical foundation for dynamic prediction and design for large deformation Origami/ Kirigami structures, which has significant potential applications in dynamic properties design in the fields of aerospace, robotic etc.

Multibody dynamic study and optimization for a flexible support shaft system in unmanned underwater vehicle

This paper presented a multibody dynamic model for the shaft system in an unmanned underwater vehicle (UUV), the model considers the flexible coupling, ball bearing and flexible support. The stiffness characteristics of flexible coupling are calculated by using the finite-element analysis. The effects of load condition, bearing location and support stiffness on shaft vibrations are investigated. Then, an optimization for the bearing locations and support stiffness is conducted. This study provides some guidance for the design and vibration optimization of the shaft system in UUVs.

Evaluation of Ground Pressure, Bearing Capacity, and Sinkage in Rigid-Flexible Tracked Vehicles on Characterized Terrain in Laboratory Conditions.

Trafficability gives tracked vehicles adaptability, stability, and propulsion for various purposes, including deep-sea research in rough terrain. Terrain characteristics affect tracked vehicle mobility. This paper investigates the soil mechanical interaction dynamics between rubber-tracked vehicles and sedimental soils through controlled laboratory-simulated experiments. Focusing on Bentonite and Diatom sedimental soils, which possess distinct shear properties from typical land soils, the study employs innovative user-written subroutines to characterize mechanical models linked to the RecurDyn simulation environment. The experiment is centered around a dual-tracked crawler, which in itself represents a fully independent vehicle. A new three-dimensional multi-body dynamic simulation model of the tracked vehicle is developed, integrating the moist terrain's mechanical model. Simulations assess the vehicle's trafficability and performance, revealing optimal slip ratios for maximum traction force. Additionally, a mathematical model evaluates the vehicle's tractive trafficability based on slip ratio and primary design parameters. The study offers valuable insights and a practical simulation modeling approach for assessing trafficability, predicting locomotion, optimizing design, and controlling the motion of tracked vehicles across diverse moist terrain conditions. The focus is on the critical factors influencing the mobility of tracked vehicles, precisely the sinkage speed and its relationship with pressure. The study introduces a rubber-tracked vehicle, pressure, and moisture sensors to monitor pressure sinkage and moisture, evaluating cohesive soils (Bentonite/Diatom) in combination with sand and gravel mixtures. Findings reveal that higher moisture content in Bentonite correlates with increased track slippage and sinkage, contrasting with Diatom's notable compaction and sinkage characteristics. This research enhances precision in terrain assessment, improves tracked vehicle design, and advances terrain mechanics comprehension for off-road exploration, offering valuable insights for vehicle design practices and exploration endeavors.

Inertial Parameter Identification for Closed-Loop Mechanisms: Adaptation of Linear Regression for Coordinate Partitioning

Abstract This study investigates the use of linear-regression-based identification in rigid multibody system applications. A multibody system model, originally described with differential-algebraic equations (DAE), is transformed into a set of ordinary differential equations using coordinate partitioning. This allows the identification framework (where the system is described with ordinary differential equations) to be applied to rigid multibody systems described with nonminimal coordinates. The methodology is demonstrated via numerical and experimental validation on a slider–crank mechanism. The results show that the presented methodology is capable of accurately identifying the system's inertial parameters even with a short motion trajectory used for training. The presented linear-regression-based identification approach opens new opportunities to develop more accurate multibody models. The resulting updated multibody models can be considered especially useful for state-estimation and the control of multibody systems.

A frequency-domain simulation method for the evolution of rail corrugation in curves

Rail corrugation remains a major problem in many railways and metros, leading to high noise and vibration levels as well as potential damage to the track and vehicle. A frequency domain simulation method is proposed for the evolution of the rail surface roughness, which can simulate the formation and development of rail corrugation in curves. A coupled vehicle-track dynamic model is established in the frequency domain to calculate the dynamic vertical and lateral wheel-rail contact forces and the associated vibration. The wheel-rail contact state is determined by using a multi-body dynamics model. The frictional-work wear model is used to calculate the roughness change caused by wheel-rail dynamic interaction. The method is verified by comparing the results with those of on-site testing on a 300 m radius curve of a metro line. It is shown that the main causes of rail corrugation are associated with the peaks in the vertical wheel-rail forces in the frequency domain, generated by the interaction between the wheel and rail. At short wavelengths the corrugation is associated with the wave reflections in the rail between adjacent axles. The phase relationship between the vertical wheel-rail force and the initial roughness has a strong influence on the roughness growth trend, leading to preferential growth in certain wavelength bands. The wheel-rail contact state and friction parameters affect the rate of development of the corrugation. Finally, a corrugation index is proposed to allow quick evaluation of the wavelength and growth rate of corrugation.

Train–Bridge Coupled Vibration of a Long-Span Steel Truss Suspension Bridge Under Complex Driving Conditions

To investigate the vibration characteristics of long-span suspension bridges under the impact of high-speed trains, a method for conducting a time–frequency domain analysis of the dynamic response of a coupled system is presented in this study. First, the finite element model of a suspension bridge is established to conduct modal analysis, and simulation results are compared with measured data to validate the correctness of the bridge model. Subsequently, a multi-body dynamics model of a high-speed train is developed. Then, two approaches, the dummy method and flexible-track method, are employed to create the train–bridge coupled system. Finally, the flexible-track method is used to perform time–frequency domain analysis of the system under complex operational conditions. The research revealed that large-span suspension bridges exhibit lower natural frequencies. The vertical bending vibrations of the main beam have the potential to significantly impact train operations. Under the combined impact of cable tension and wheel–rail forces, the vibration patterns of large-span suspension bridges become notably intricate. The number of trains and their loading configurations both exert influence over the dominant frequencies and amplitudes in the PSD of bridges. In the complex traffic of large-span suspension bridges, the rational arrangement of travel lanes can reduce the possibility of resonance in the bridge–train system.

Coupled occupant-suspension-seat system analysis and vehicle-specific design optimization

A suspension seat is generally designed to achieve attenuation of low frequency whole-body vibration for a broad range of vehicles. Owing to the strong dependence of its vibration isolation performance on the nature of vibration excitation, an optimal performance could be realized via optimal tuning of suspension for specific classes of vehicles. In this study, a coupled occupant suspension seat model is developed and analyzed to identify optimal design parameters for different classes of vehicles. The multibody dynamic model of the air suspension seat is formulated considering kineto-dynamics of the suspension system and the elastic motion-limiters. The component models, namely, air spring with auxiliary air volume, hydraulic damper, and cushion, are identified from the laboratory-measured static and dynamic characteristics. A two-degree-of-freedom occupant model, is integrated to the suspension seat model to account for contribution due to occupant biodynamics. Model validity is examined using the laboratory-measured responses with a rigid load and a human occupant of similar body weight, and analyzed for different body weights and excitation spectra. The results suggest strong dependency of the suspension resonance frequency on nonlinear behavior of the air spring and the seated body mass. The model is subsequently employed to identify optimal coordinates of the air spring to achieve nearly constant natural frequency for a broad range of body masses. Furthermore, the model is used to identify optimal linkage and suspension design parameters with an objective to minimize the SEAT (Seat Effective Amplitude Transmissibility) for different spectral classes of earth moving machines defined in the ISO-7096 standard, while limiting the suspension travel. It is shown that the optimal coordinates of air spring could yield nearly constant natural frequency for different body weights, while damper could help limit the suspension travel, in addition to notable reductions in SEAT, ranging from 9% to 31% for different spectral classes of vehicles.

Anti-lock braking system control design using a non-linear multi-body dynamic model for a two wheeled vehicle

This paper investigates the design of an Antilock Braking System for a Two Wheeled Vehicle using a non-linear multi-body dynamic model developed by an approach widely used in robotics. The Antilock Braking System is controlled using Matlab/Simulink by applying the Bang-Bang, Proportional-Integral-Derivative and Fuzzy Logic controllers in order to set the longitudinal slip to a desired value. The developed model is used to study the braking performances of a Two Wheeled Vehicle in a straight-line maneuver under different road conditions: dry, wet and a transition between both. The simulation results indicate that the non-linear dynamic model can effectively simulate the behavior of the Two Wheeled Vehicle under emergency braking conditions and with the different types of controllers. The braking performance of the Two Wheeled Vehicle with Antilock Braking System was improved by decreasing the stopping distance, avoiding wheel lockup and therefore contributes to ensure the vehicle control and stability and to reduce the risk of falling. Also, it can be seen through comparative analysis that the Fuzzy logic is one of the most efficient controllers that improve the braking safety.

Variability of intervertebral joint stiffness between specimens and spine levels.

Introduction: Musculoskeletal multibody models of the spine can be used to investigate the biomechanical behaviour of the spine. In this context, a correct characterisation of the passive mechanical properties of the intervertebral joint is crucial. The intervertebral joint stiffness, in particular, is typically derived from the literature, and the differences between individuals and spine levels are often disregarded. Methods: This study tested if an optimisation method of personalising the intervertebral joint stiffnesses was able to capture expected stiffness variation between specimens and between spine levels and if the variation between spine levels could be accurately captured using a generic scaling ratio. Multibody models of six T12 to sacrum spine specimens were created from computed tomography data. For each specimen, two models were created: one with uniform stiffnesses across spine levels, and one accounting for level dependency. Three loading conditions were simulated. The initial stiffness values were optimised to minimize the kinematic error. Results: There was a range of optimised stiffnesses across the specimens and the models with level dependent stiffnesses were less accurate than the models without. Using an optimised stiffness substantially reduced prediction errors. Discussion: The optimisation captured the expected variation between specimens, and the prediction errors demonstrated the importance of accounting for level dependency. The inaccuracy of the predicted kinematics for the level-dependent models indicated that a generic scaling ratio is not a suitable method to account for the level dependency. The variation in the optimised stiffnesses for the different loading conditions indicates personalised stiffnesses should also be considered load-specific.